INTELLIGENCE, MIND, AND REASONING Structure and Development
ADVANCES IN PSYCHOLOGY
106 Editors:
G. E. STELMACH
P. A. VROON
INTELLIGENCE, MIND, AND REASONING Structure and Development
Edited by Andreas DEMETRIOU and
Anastasia EFKLIDES Department of Psychology Faculty of Philosophy Aristotelian University of Thessaloniki Thessaloniki, Greece
1994
NORTH-HOLLAND AMSTERDAM LONDON * NEW YORK TOKYO
NORTH-HOLLAND ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O.Box 211, lo00 AE Amsterdam, The Netherlands
ISBN: 0 444 89714 3 0 1994 Elsevier Science B.V.
All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science B.V., Copyright & Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owner, Elsevier Science B.V., unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper. Printed in The Netherlands
V
Preface
Most of the contributions to this volume are revised versions of papers presented at two symposia, organised by the editors, at the 4th Conference of the European Association for Research on Learning and Instruction in Turku, Finland, in 1991. Four of the contributors were specifically invited to submit a paper for this volume, so that the various approaches to intelligence, mind and reasoning are better presented. The contributions in the first part deal with intelligence and mind. The contributions in the second part deal with mind and reasoning. Robert Sternberg in the concluding chapter offers an overview and discussion of all the papers and, through an analogy, makes it clear that if we are to understand intelligence we need a multi-tradition approach that takes into account and perhaps transcends all individual approaches. This is a need also recognised by most of the contributors and the editors themselves, who feel that there are various levels of description of that evading entity called intelligence. The editors would like to express their warmest thanks to Smaragda Kazi from the Department of Psychology of the Aristotelian University of Thessaloniki and the Art of Text Publishing Company, Thessaloniki, Greece for the secretarial assistance and diligence in producing the text. Andreas Demetriou Anastasia Efklides
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vii
Contents
Preface ........................................................................................................
Page v
List of contributors ............................................................................................ Intelligence, mind and reasoning: Three levels of description Andreas Demetriou and Anastasia Efldides ....................................................
vii 1
Part I. Intelligence and mind
1. A person-situation interaction theory of intelligence in outline Richard E. Snow............................................................................................. 11 2. Taking stock of what there is: The case of cognitive abilities Johan Olav Undheim ..................................................................................... 29 3. Hierarchical models of intelligence and educational achievement Jan-Eric Gustafsson ..................................................................................... ..45 4. Structure, development, and dynamics of mind: A meta-Piagetian theory Andreas Demetxiou and Anastasia Efldides.............................................. 75 5. The older child’s theory of mind William V.Fabricius and Paula J Sch wanenflugel............................... ..111 Part 11. Mind and reasoning
1. Reasoning, metareasoning and the promotion of rationality David Moshman ........................................................................................... 135 2. The structure and development of propositional reasoning ability: Cognitive and metacognitive aspects Anastasia EMides, Andreas Demetriou, and Yiota Metallidou ...........151 3. Reasoning models and intellectual development Leslie Smith,................................................................................................ ..173 4. A representational communication approach to the development of inductive and deductive logic Peter E. Langford and Robert Hunting .................................................... 191
viii
Concluding chapter Gulliver Ravel's travels: An excursion to the theoretical islands of intelligence Robert$ Stemberg............................................................................................
213
Name index ....................................................................................................... 233 Subject index .....................................................................................................
237
ix
Contributors
Demetriou Andreas, Department of Psychology, Faculty of Philosophy, University of Thessaloniki, Thessaloniki 54006, Greece Efklides Anastasia, Department of Psychology, Faculty of Philosophy, University of Thessaloniki, Thessaloniki 54006, Greece Fabricius William V., Department of Psychology, Arizona State University, Tempe AZ 85283-1104, USA Gustafsson Jan-Eric, Department of Education and Educational Research, University of Goteborg Box 1010, S-43126 Molndal, Sweden Hunting Robert, School of Education, La Trobe University, Bundoora, Victoria, Australia 3083 Langford Peter E., School of Education ,La Trobe University, Bundoora, Victoria, Australia 3083 Metallidou Yiota, Department of Psychology, Faculty of Philosophy, University of Thessaloniki, Thessaloniki 54006, Greece Moshman David, Department of Educational Psychology, University of Nebraska, Lincoln, NE 68588-0641, USA Schwanenflugel Paula J., Department of Educational Psychology, Aderhold Hall, University of Georgia, Athens, Georgia 30602, USA Smith Leslie, Department of Educational Research, Lancaster University, LA1 4TY, UK Snow Richard E., School of Education, Stanford University, Stanford, California 94305-3096, USA Sternberg Robert J., Department of Psychology, Yale University, Box 11A Yale Station, New Haven, CT 06520-7447, USA Undheim Johan Olav, Department of Psychology, AVH, University of Trondheim, N-7055 Dragvoll, Norway
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Intelligence, Mind, and Reasoning: Structure and Developmen' A. Demetriou and A. Efklides (Editors) Q 1994 Elsevier Science B.V. All rights reserved.
1
Intelligence, Mind, and Reasoning: Three Levels of Description Andreas Demetriou and Anastasia Efklides Department of Psychology, Aristotelian University of Thessaloniki, Greece The psychometric, the cognitive, and the developmental approach to the study of human intelligence and cognition have been powerful and prolific in the last fifty years. All three approaches have enhanced greatly our understanding of human mind and they have contributed significantly to our attempts to strengthen and enhance intelligence and the mind. The psychometric approach has been successful in illuminating the structure of intelligence. That is, it has shed light on the hierarchical organisation of intelligenceand pinpointed the boundaries between the abilities involved in each hierarchical level. Thus, modern psychology must be indebted to the psychometric study of intelligence because it provided the ground for the understanding of intra- and inter-individual differences in intelligence and for the development of important practical applications. Intelligence testing and programs designed to boost intelligence are the most notable applications that resulted from this tradition. The cognitive approach focused on the functional and the procedural aspects of intellect. As a result, it highlighted how different functions such as perception, attention, memory and thought work, how they are used by the person in different environments, what their limitations are, and how these limitations might be overcome. Thus, cognitive psychology has illuminated the "black box" to a considerable extent and it paved the way for the genesis of a new field, namely cognitive science. This field has led to a reunion of psychology with mother philosophy via logic and epistemology and it opened the way for fruitful interactions with other sciences concerned with human knowing and information processing, such as computer science, neuroscience, linguistics, etc. The fruits of this union may still be hard to foresee. However, many people believe that the real engineering of knowing will not be possible before we harvest these fruits. The developmental approach to the mind has been primarily concerned with the general forms that mind takes along the years and with the dynamic processes and mechanisms underlying the transformation of the one form into the other. This approach has been very successful in revealing that minds of different age live into largely different worlds and in showing their advantages and
2 A. Demetriou and A. Efilides
disadvantages. This knowledge has, implicitly or explicitly, been very influential in societal activities directed to children in general, such as education, child rearing, and the toy and film industry addressed to children. Despite their admirable strengths and successes all three approaches suffer from serious and incapacitating weaknesses. In the psychometric field, the roads that go from structure to process, from the one level of cognitive organisation to the other, or from the group to the individual are not always open and direct, if they exist at all. Even more, intelligence often appears mindless and unchanging in this field. As a result, one does not know how to deal with processes in order to influence structure and vice-versa. Likewise, using performance on psychometric tests to predict intellectual performance in real life situations, where minds interact with each other as well as with themselves, often proves an almost impossible task. The problems that one would face in the cognitive field are equally serious. That is, the cognitive models of how different functions, such as attention, memory, and reasoning, are applied on their input and how they work are frequently useless in one's attempt to understand how and why these functions are differentially used by different "structures of the intellect", such as spatial or mathematical thought. Moreover, these models may give a satisfactory account of the various functions at maturity but they have not much to tell about their development. As a result, knowledge in this field cannot easily be used for predicting and/or influencing cognitive performance in different fields of knowledge or at different phases of development. Being the science of the "epistemic subject", as Piaget has called it, that is the science of the mechanisms common to all individuals of the same age, the developmental approach faces similar problems. Specifically, the models of cognitive development developed in this century, Piaget's in particular, failed to do justice to different cognitive functions and to individual differences in development. These models have also been very weak in dealing with processes of conceptual change which lead one from naivit6 to expertise in different conceptual domains. Thus, the traditional models of cognitive development proved to be a very weak basis for understanding how different cognitive functions and abilities interact with each other and with different knowledge domains during development and how they change as they interact. These models also do not help much in one's attempts to design intervention programs suited to the needs of different individuals. One of the reasons that might have been responsible for this undesirable state of affairs is the fact that, because of historical and epistemological reasons, the three approaches have remained separate of each other. As a result, ideas growing in the one tradition were not able to fertilise the other traditions. Although things are now changing, the three fields do not really interact with each other. The aim
Intelligence, Mind, and Reasoning 3
of this book is to bring the three fields closer to each other, open channels that would make their communication possible, and, to the extent this is feasible, facilitate their integration. Specifically,the book as a whole will attempt to provide answers to questions such as the following. What is common to intelligence, mind, and reasoning? What properties are specific to each of them? What is the role of each of them in the organisation and development of the others? In the sake of this aim, the book involves ten chapters. These are organised in two parts. The first part focuses on the structure and development of intelligence and mind and has reasoning at the background. The second part focuses on the structure and development of reasoning and mind and has intelligence at the background. First part: Intelligence and Mind In the first chapter Snow puts forward his own theory of intelligence. This theory is intented as a general framework that might be used to integrate the theory of aptitute, for which Snow is well known, with the general theory of intelligence and theories of cognition. The aim is to advance a theory that would be able to predict and explain learning from instruction. Snow‘s framework seems complete in the dimensions that one would need to invoke in order to understand intelligent performance and learning in complex and multiply determined situations. In so far as structure is concerned, Snow argues that intelligence is multifaceted, multileved, hierarchical, and nonmodular. In so far as development is concerned, he argues that development differentiates and specialises with experience, it is both pervasive and situated, and personal. In so far as function is concerned, intelligence is relational, selective, constructive, and adaptive. Interestingly enough, and perfectly in line with the aim of the book, Snow shows that although differential in origin, his model of intelligence is compatible with Gibson’s theory of perception. Snow shows how this model can be used to predict aptitude-treatment interactions in the classroom. In the second chapter Undheim elaborates on the relations between the psychometric tradition and other approaches that were developed in the context of the cognitive tradition, such as the information-processingapproach and the knowledge approach to cognitive functioning. The thrust of Undheim’s argument is that the basic methodology of the psychometric approach is sound and that the other approaches are actually dependent on the psychometric approach. This dependence will tend to increase in the future due to the development of new analytic methods such as linear structural equations and new measurement theories such as models of multi-level analysis which have revitalised the psychometric approach in recent years. The third chapter by Gustafsson is a fine demonstration of the assumptions
4 A. Demetnou and A. Efklides
and claims advanced by the two previous chapters summarised above. Specifically, Gustafsson first elaborates on the classical and more recent hierarchical models of intelligence. He then goes on to show how these models can be exhaustively tested by means of modem structural modelling. Gustafsson makes a convincing case that these methods seem able to resolve the old debate regarding the unistructural or multistructural nature of intelligence. He then draws upon the data of two large studies conducted in his laboratory and demonstrates that performance on any task is determined at one and the same time by a hierarchy of abilities that range from the very general (the old G) to broad but specialized abilities, such as spatial or mathematical ability, to very specific abilities related to particular sub-domains of skills and knowledge. The next chapter presents our theory of the structure and development of human mind. This theory is inspired by the assumption that human mind can only be understood if the strong points of the psychometric, the cognitive, and the developmental tradition are allowed to interact and get integrated into a comprehensive system. Thus, the chapter first clarifies how the theory relates to each of these traditions. It then presents the propositions of our theory about the architecture of human mind and intelligence. The main argument is that the human mind is organized on three levels. At the most elementary level there is the processing system which defines the potentials of mind at different ages to construct the structures involved at the other levels. At the next level there is a set of specialized structural systems that enable the person to represent and process different domains of the environment. At the most advanced level there is a hypercognitive system which refers to the person's theory of mind that governs self-understanding and self-management.This enables the individual to use his knowledge and skills in intelligent, rational, or wise ways according to his needs and goals and according the rules and the needs of one's society and culture. The chapter also summarises the major developmental landmarks of the various structures of mind and presents our basic assumptions about the dynamics of development. The main argument is that developmental causality is synergic. That is, it is due to intra- and inter-structural interactions both within and between levels. The last chapter in the first part of the book focuses on one of the levels of cognitive organization invoked by our theory. Specifically,the chapter by William Fabricius and Paula S. Schwanenflugel summarises their studies on the development of a theory of mind that enables the person to differentiate between distinct mental functions such as attention, memory, inference, and comprehension on the basis of the particular mental activities involved in each of them. According to Fabricius and Schwanenflugel, it is not before the age of ten years that a constructive theory of mind begins to be established, although these functions start to be differentiated earlier on the basis of more external characteristics.
Intelligence, Mind, and Reasoning 5
These findings are in close agreement with both, the findings and assumptions of our theory presented in the previous chapters and with the ideas advanced in the chapters following about the role of a constructive theory of mind in the development of reasoning. That is, they indicate that logical reasoning as a means of processing formal relations begins only when the person becomes minimally aware of the structure and functioning of his own mind. Thus, logical reasoning becomes necessary as a means for diagnosing the validity of the relations between the minds products. Second part: Mind and Reasoning The chapters in the second part of the book are concerned with the emergence of mind and reasoning and their interaction. David Moshman offered the first chapter in this part of the book. Moshman argues convincingly that reasoning might at one and the same time be formally correct and irrational if it were not directed by metareasoning. He argues that metareasoning involves three distinct but interrelated aspects which are all critical to human rationality and intelligence. Namely, procedural metareasoning, which involves monitoring and directing of one’s own reasoning, conceptual metareasoning, which involves declarative knowledge about reasoning, and constructive metareasoning, which involves the developmental reconstruction of one’s reasoning and metareasoning. According to Moshman, constructive metareasoning is the dynamic process that creates conceptual metareasoning and new inference schemas. Thus this is the process of learning and development. The next chapter presents our work on the structure and development of what we call the verbal-propositional SSS. This is one of the five SSSs described by the theory (see the chapter by Demetriou and Efklides). According to the theoly, the defining property of this system is the filtering of semantic relations so as to focus processing on the formal relations connecting the mental entities processed. The results and models about this SSS presented in this chapter support and extend Moshman’s views. Specifically, the chapter summarizes a study that investigated the development of propositional reasoning and related metareasoning from 12 to 20 years of age. The study investigated the effect of content, logical relation, logical connective, and validity on the structure and development of reasoning. The subjects were also asked to make a number of subjective (metacognitive) evaluations of their own experiences and performance. The results clearly showed that semantic factors related to the empirical truth of the propositions and logical factors are important in the organization of propositional reasoning. In so far as development is concerned, propositional thought gradually shifts from meaning to form and from form to analytic consideration of alternative inferences. Cognitive
functioning generates experiences which are recognizable by the developing
6 A . Demetriou and A. Efifides
subject’s mind. Thus, metacognitive estimations prove to be reliable indicators of underlying cognitive processes. However, metacognitive experiences are only grossly analyzable before reasoning itself is well developed. This occurs in college years when the reasoner becomes a virtual logician; that is, a theorist of reasoning. What formal models are better able to capture the structure and development of reasoning? The two last chapters in the book are concerned with this question. The chapter by Leslie Smith embarks directly on the problem of modelling human reasoning. The aim he set to himself is to examine if and to what extent each of two currently popular accounts of human reasoning is indeed sufficient to explain the emergence and consolidation of reasoning‘s two defining properties, namely, coherence and necessity. Specifically, Smith first elaborates on Johnson-Laird’s mental models approach to reasoning. According to this approach, reasoning is not logical. That is, the basic claim is that inferences are based on the construction and manipulation of mental models. This process is based on meaning rather than on formal rules. The second model is based on entailment logic which embodies the dual criteria of relevance and necessity. That is, “a set of premises (A) entails (->) a conclusion (B) just in case the relation A -> B, where A is relevant to B, is, if true, necessarily true.” According to Smith, the first model is too weak as an account of human reasoning because it explains logical reasoning although it is itself devoid of logic. The second model is too strong because it assumes logical relations where they cannot exist. Thus, the mental models approach devaluates logic in favor of meaning and the logic of entailment devaluates meaning in favor of some logical principles. However, Smith does not propose the rejection of the two models. He argues, on the contrary, that they are complementary. The mental models approach seems able to capture the psychological component of human reasoning and the entailment model its logical component. Thus, the two of them together seem able to account for epistemic growth that leads from meaning and experiencebased mental models to functioning on the basis of normative criteria of coherence and necessity. This assumption is fully in line with the results presented by Efklides, Demetriou, and Metallidou in the previous chapter. In the following chapter, Peter Langford and Robert Hunting summarize their research on the nature and development of reasoning and present their model. This model is close to the models presented in the previous chapters in some respects but it differs in others. Like the other models, Langford and Hunting’s model assumes that reasoning and ensuing logical competence is a process of individual and social construction. In order to be possible, this process requires the presence of an underlying general reasoning ability. The developmental end of this process is coherence and necessity. They believe, unlike the other authors, that predicate logic is a better candidate to model this achievement than entailment or propositional logic. Moreover, they warn us not to identify personal feelings
Intelligence, Mind, and Reasoning 7
of coherence and necessity with coherence and necessity based on truth tables. This is so because individuals may have these feelings for personal reasons that do not coincide to those of the logician. Finally, Langford and Hunting elaborate on the differences between deductive and inductive reasoning more than the other authors. Conclusions: The Dynamic Intelligence-Mind-Reasoning Loop To conclude, we hope that all contributors to this volume agree that intelligence is tool and product of adaptation. Mind is tool and product of the functioning of intelligence. Development is the force that makes mind to gradually emanate from the functioning of intelligence and then orchestrate its functioning. In this process reasoning is a means that enables intelligence to make logical and rational decisions about the person-environment relations. Reasoning is also a means that enables mind to grasp its own and the other minds’ organization and functioning. In turn, the power of reasoning as a means for intelligent action increases the more it comes under the direction of mind. Therefore, the theory for any of the three aspects of human knowing to which we devoted this book must also be a theory for the others. This theory must also involve a strong developmental component because the interplay between intelligence, mind, and reasoning and their fusion in schemes of wisdom and rationality take place along ontogenetic development. We would even argue that this interplay and fusion also takes place along phylogenetic development. That is, the theories about intelligence, mind, and reasoning of one generation become part of the intelligence, the mind, and the reasoning of the next generations. Does the work presented in this volume approach this aim? We have asked Bob Sternberg to answer this question. He gives his answer in the concluding chapter of the book. In fact he goes far beyond the present book to answer the question as he deals with most variations of psychometric, cognitive, and cognitive developmental theory. Although unconventional and highly idiosyncratic in style, his answer is clear and straightforward. None of the theories alone will ever be able to generate the answer if it would restrain itself on its own isolated epistemologicalisland. We hope that the ideas presented here may lay the ground for constructing bridges among the islands, if not for uniting them into a common grand state, so that Sternberg has a more easy way to go around in search of his lost intelligence! Come back Bob, you may be more lucky this time!
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PART I
Intelligence and Mind
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Intelligence, Mind, and Reasoning: Structure and Development A. Demetriou and A. Efklides (Editors) 0 1994 Elsevier Science B.V. All rights reserved.
11
A Person-Situation Interaction Theory of Intelligence in Outline* Richard E. Snow Stanford University, Stanford, USA
BACKGROUND My long range goal is a theory of aptitude for learning. My concept of aptitude includes cognitive, conative, and affective characteristics of an individual's psychology that are propaedeutic, i.e., needed as preparation or readiness for learning in particular situations. But I am interested mainly in the structure, development, and function of individual differences in learning in the sorts of instructional situations found in schools. Thus, my theory of aptitude must ultimately be "larger" than a theory of intelligence, because it must cover more than cognitive abilities. At the same time, it can be "smaller" than a theory of intelligence, because it deals only with individual differences in learning from instruction; it need not cover all that is meant by "intelligence". It takes intelligence as a first focus, however, because of two centrally important facts; general ability differences strongly predict individual differences in learning from instruction and they also interact frequently with variations in instructional treatment in this prediction. These kinds of interactions are called aptitude-treatment interactions, or AT1 for short. The fact that AT1 are ubiquitous in education emphasizes the need for a person-situation interaction theory of intelligence. Since there is substantial literature in support of the above introduction, space is not used for further background summary here. Interested readers should see, e.g. Cronbach and Snow (1977), Snow (1989a, 1991, in press), and Snow and Lohman (1984).
A THEORETICAL FRAMEWORK Since I am in substantial agreement with several other chapters in this book regarding the basic framework for intelligencetheory, I also do not need to belabor the review of that literature. Here I merely set out in outline form some basic propositions for my theoretical framework, each with just a few supporting references. * Author's address: Richard E. Snow, School of Education, Stanford University, Stanford, California 94305-3096, USA.
12 R.E.Snow
Propositions about structure
Intelligence is multifaceted. Intelligence has many faces, a characteristicthat is usually described as “multifaceted. I have preferred the term “aspects” rather than “facets” so as not to lose sight of the adaptive whole while focussing on subdivisions (seeSnow, 1986). But “facets” is the more popular term, due probably to Guilford (1967) and Guttman (1969). At any rate, there is no denying that intelligence is manifested in performance situations that differ in content (verbal, figural, numerical, etc.), operation (speed vs. power, recall vs. recognition, convergent vs. divergent thinking, etc.) product (units, classes, relations, transformations, etc.) and many other facets (Humphreys, 1962).The specialized structural systems of the Demetriou-Efklides theory (this volume) are also facets in this sense. InfelZigenceis multileveled. There are clearly multiple levels on which intellectual processes operate. Many theorists posit metacognitive as well as cognitive functions; in the Demetriou-Efklides terminology these are hypercognitive functions. Sternberg’s (1985) analysis of intelligence specifies metacomponent as well as component processes in performance. Whatever the terminology, the meta or hyper level seems clearly distinct from the primary or component process level. Many theorists also refer to “executive” processes, and some seem to lapse into the homunculus problem. As Dennett (1981) warns us, this assumption can be accepted provisionally, as long as it is recognized as an intellectual loan that must in due time be paid back; in other words, we must at some point explain executive processes without resort to other executive processes. Intelligence is hierarchical. The organization of intellectual abilities is best represented as a hierarchical structure. The long history of factor analytic research evidence has been reviewed and reanalyzed by Carroll (1993) to yield a comprehensive and integrated hierarchical model; first-order abilities are incorporated into the second-order ability constructs of fluid reasoning (GO, crystallized language (Gc), visual perception (Gv), auditory perception (Ga), memory (Gm), speed (Gs), and idea retrieval (Gi), under a third-order general intelligence (G). A similar list comes from Horn’s (1989) work. Furthermore, Gustafsson (1984,1988,1989, this volume) demonstrated that Gf can be equated with G and also with Thurstone’s (1938) first-order induction (I) factor, that residualizing Gc and Gv for G reproduces Vernon‘s (1950) hierarchial model, and finally that both higher-order and lower-order abilities are needed to understand individual differences in learning from instruction; different ability levels can relate differently to performance, within or between instructional treatments, and each level is needed to clarify the influence of the other. Intelligence is nut modular. The hierarchical model stands in opposition to the view that intelligence is at base modular (Fodor, 1983; Gardner, 1983). Although at the first- and second-order levels of hierarchy, different special
Person-situa tion interaction theory 13
abilities can be distinguished, each is understood as a partial, not a whole; i.e., each involves G variance as well as special ability variance. Different situations do seem to call for and produce specialized abilities and domain achievements, but these are better conceived of as acquired contextual modules, in the sense intended by Bereiter (1990), rather than as hard-wired distinctions in the brain. That is, they are the products of differentiated and specialized learning and development in particular person-situation interactions. This can be spelled out further by considering the developmental side of the evidence. Propositions about development
Intelligence differentiates withexperience. Abilities develop and differentiate through learning, including that derived from educational experience (Snow, 1982).Thus, individual differences in ability patterns reflect different patterns of prior learning. Anastasi (1970) summarized the earlier evidence and various theoretical explanations. Not only do adults with less education show less ability differentiation than do adults with more education, but different levels of ability development and different patterns of ability differentiationresult from different types of educational programs. Comparisons of different socioeconomic and cultural groups similarly suggest more ability differentiation with more differentiated learning experience. Greater differentiation is also seen among higher G students than among lower G students, and among experimental subjects trained in some of the constituent ability tasks as contrasted with untrained subjects. Higher ability students appear to benefit more from such training (Bangert-Drowns, 1991). Intelligence specializes with experience. Not only does learning promote the development and differentiationof abilities, but specialized learning experience yields specialized patterns of abilities. Balke-Aurell(1982)provided an empirical example, obtained within the Swedish program of longitudinal research on ability development initiated by Harnqvist (1968). Using ability constructs designed to represent the current theory of ability hierarchy (Gustafsson,19841, Balke-Aurell found that the higher the individual's educational level, the more positive the change in G, but also that students pursuing educational programs with a predominately verbal emphasis showed more change toward the development of verbal Gc ability, whereas those pursuing more technical lines of education showed more change toward the development of Gv ability. Results comparing occupational groups also suggested that work demanding verbal functioning promotes verbal Gc development, whereas work demanding spatial-technical functioning promotes Gv development. The more concentrated, spatial technical experience seemed to produce more specialized change in ability. Intelligence is both pervasive and situated. As a summary of the previous
14 R.E.Snow
points, intelligence can be interpreted as general and pervasive, but also as specialized and situated. There is no contradiction in this. There are variable functional properties of intelligence that constitute aptitude for learning in a wide variety of situations. Such situations are usually characterized as requiring the construction of meaningful performance in complex, incomplete, and relatively unstructured learning conditions. Indeed, Resnick and Glaser (1976) defined intelligence as the ability to learn from incomplete instruction. Such situations seem to call for flexible adaptation and agility in inferential structuring, and the evaluation of same, by the learner. One could say more simply that such situations involve to a significant degree Spearman’s (1927) eduction of relations and correlates, as well as apprehension. However, learning situations vary substantially in this respect, so AT1 occurs frequently; that is, situations differ in their demand for or opportunity to use these functional properties, so relations between G and learning vary across situations. Furthermore, over time, these functional properties become adapted to the specialized mixture of demands and opportunities provided by different types of learning situations; that is, abilities become tuned to each such situation. In Cattell’s (1971) theory, Gf is invested in learning in everyday situations, but especially also in school situations, to produce Gc, and there can be various kinds of specialized knowledge structures within the Gc network. In Ferguson’s (1954,1956) theory, abilities emerge through the coalescence of skill acquisition among specific tasks due to differential transfer functions among the tasks. These transfer relations are reflected in the size of correlations between tasks (Heinonen, 1962). The breadth of transfer of skills among tasks determines the breadth of the emergent ability. Verbal, reasoning, and metacognitive skills transfer broadly, whereas certain perceptual, memory, and spatial skills transfer among a narrow range of tasks, so these transfer functions account for the hierarchy of ability correlations usually obtained in factor analytic research. Further, more general abilities appear to transfer to earlier stages of new skill learning, whereas more specialized abilities transfer to later stages of new skill learning, as Ackerman’s (1989) theory suggests. The result is an expanding array of abilities both specialized and generalized - increasingly tuned to the patterned structures of many particular, familiar situations yet ready for attunement to the structures of new situations. Situations that share aspects of structure in common afford use of the same abilities. Situations that show no common structure afford use of different abilities. But situations that share only the need to overcome novelty still afford use of those abilities that are attuned to that purpose. One might say that Gf ability reflects this attunement or accommodation to novelty, whereas the network of Gc abilities reflects the assimilation of many now familiar learning demands and opportunities (Snow, 19811, but this oversimplifies. It also oversimplifies to distinguish sharply between academic and practical
Person-situationinteraction theoq 15
intelligence (see e.g., Sternberg &Wagner, 1986). These are not separate coequal modules even if they may have some distinct, specialized constituents. Rather, if one takes the expanding array of abilities noted above as representing the growth of everyday intelligence, then academic intelligence is its specialization for performance in the increasingly demanding situations of everyday life called “school”. Again, following Cattell (1971), Gf is invested in everyday learning to produce specialized abilities, but especially in school learning to produce the development of Gc. However, neither the practical vs. academic nor the Gf vs. Gc distinction adequately captures the dynamic, transactional, adaptive process of individualized ability development and application in particular situations. Intelligence ispersonal. As individuals share a common culture in which homogeneous learning situations are imposed, via socialization, schooling, apprenticeship, etc., common patterns of ability will be seen to develop across persons. Yet each individual’s learning history is also unique and personal. Imposed situations cannot be uniform across persons. Individuals perceive situations differently, transform them differently, and choose different situations following their interests and predilections, as their own unique learning history accumulates. Thus, just as each situation calls for a somewhat different mix of ability, each person brings to a situation a somewhat different mix of ability. We can identify types of situations by identifying those that bear family resemblance in terms of the kinds of able performances they afford. We can also identify types of persons who are similar in terms of the kinds of performances they are able to produce. These person types and situation types can be useful for some theoretical and practical purposes, even though they are gross approximations. For many purposes, they may leave out more important information about persons and situations than they capture. Propositions about function
Intelligence isrelational. But to say that intelligence is situated and personal is to claim much more than that it is specialized by types of situations and types of persons. It is to claim that intelligence is fundamentallya relational, relativistic construct; that is, it should be interpreted as existing in the person-situation interaction, not in the head of the person alone or in the structure of the situation alone, but in the “interface”between them. This means that defining the situations in which intelligence operates is part of defining intelligence (Snow & Lohman, 1984). It also means that person-in-situation - the person-situation union -is the unit of analysis, not persons or situations or bits and pieces of persons and situations independently. Intelligence is selective. Persons sample from their environments. They differ in how they do this and how well they do this. There is a tuning process over
16 R.E.Snow
time through which a person becomes accustomed or attuned to the demands and opportunities of performance in particular situations. The person not only becomes able to perform well in such situations by perceiving and selecting the appropriate demands and opportunities, but becomes able to select situations that fit that person’s strengths. To some degree, then, intelligence is situated by the person as well as for the person. InfeZZigenceis consfrucfive.But intelligence is indeed situated for the person. Over the long run, persons and situations have adapted to one another, albeit selectively. In the short run, persons adapt situations to their own strengths by selecting, as above. But they also adapt to situations by building strengths needed to meet the demands and opportunities of situations they cannot avoid. Intelligence is constructive in the sense that it is used to build personal meaning as well as personal success in a situation. Intelligence is adaptive. Through selection and adaptation, but also through invention, intelligence is used to build performances that are not only uniquely and personally meaningfulbut that work -that fit the demands and opportunities of situations. In this aspect, intelligenceis fundamentallya learning function. It is just as Simon (1976, p. 6) supposed; “...that intelligence is the learning program that assembles the performance program”. In short, intelligence is an assembly function at once selective, adaptive, and constructive. It is also assembly control as well as control of assembled performance, but that hypothesis goes beyond the cognitive to include the conative aspect of intelligence, and that is beyond this outline (see Snow, 1989b).
A MODEL OF INTELLIGENT INFORMATION PROCESSING What kind of model of intelligent information processing can be fashioned that will incorporateall of the above, but also describe intraindividual as well as interindividual differences in the dynamics of person-situation interactions in performance, particularly in instructionallearning performances? In other words, what kind of theoretical language can we adopt to describe such processes? My candidate is a generalization of the ThorndikeThomsonresponse sampling model (due originally to Thomson’s, 1919,1939, use of Thorndike’s, 1921, theory; see Humphreys, 1979,1981; also Snow & Lohman, 1984).But I add the concepts of affordances (Gibson, 1979), artifacts (Simon, 19691, performance assembly (Simon, 1976),and action control (Kuhl, 1990). There are also other related origins and constituents too numerous to detail in the brief presentation allowed here (see Snow, 1991,1992, in press). The basic event at the interface of person and situation is a sampling of person by situation and situation by person. This sampling is governed by associative networks of stimulusand response components residing in the inner environment
Person-situationinteraction theory 17
of the person and the outer environment of the situation. Although based on associative networks of components, which might be described in terms of SS, S-R, and R-R connections, the model is by no means limited to an association theory. Rather, the associative networks provide a base from which varieties of mental structures and representations can be assembled as needed in a particular person-situation match. The neutral term component is used to cover associative bonds but also other kinds of hypothesized mental units or connections, including information processing components, plans, images, learning sets, schemata, nodes in semantic networks, productions in production systems, and the like. The model is not restricted to any one cognitive representational construct, and is designed to accommodate nonrepresentational constructs as well. Furthermore, although components are described in the model as bits and pieces of ability, the term applies as well to aspects of conative and affective aptitudes. Each individual's inner environment contains a vast assortment of potential response components. These are probabilistically interconnected in multiple associative networks. Individuals differ in what components, or nodes, are present or absent. Also, the connectionsbetween these nodes vary in strength to reflect the personal learning history of each individual. Many sorts of assemblies of these components can be constructed in different ways for different situations. These assemblies are also decomposable so parts can be used in other assemblies as needed. The products of past learning are components already assembled into units to be triggered anew by situations similar to those previously faced. The products of continuing learning are additional components, new assemblies of both new and old components, and strengthened connections between them. But learning also exercises and thus strengthens the assembly and control functions themselves. In short, the human mental system is designed to be loosely coupled and flexible in assembling and reassembling components into performance programs to meet varying situational needs. Since it reflects personal learning history in this regard, it is also highly idiosyncratic. Now consider the person-situation interface. Each performance situation samples from each person. The demands and opportunities it presents will draw forth whatever relevant response components and assemblies of components each person can muster. But the person also samples the situation, in the sense that stimulus components are perceived and selected. Stimulus components may suggest a demand for particular response components or assemblies. They may also provide an opportunity to use particular response components or assemblies. And the situation may contributecomponents to the performance that the person then need not provide. Of course, each person's learning history will influence this perception-selection process, and the sampling will be designed partly by the demands and opportunities afforded by the Performance situation presented,
18 R.E.Snow
and partly by the possibilities and constraints afforded by the assembly and control history of the performing person. Considering the person‘s learning history suggests some further distinctions between several kinds of situational demands and opportunities. Some involve the retrieval and application of old familiar component assemblies, whereas some involve the construction and application of novel component assemblies. Also, some call forth familiar or novel performance assemblies from the learner, whereas some supplant the need for such performance assemblies -they provide stimulus components as prosthetics that substitute for needed response components. Complex tasks will typically involve some of each kind of component, and will further require the flexible reassembly of interconnections within and between them as various parts of the learning task proceed. But all these situational components are there to be perceived and used as such, at least for persons who are tuned to do so. Thus, situations can be described as consisting of networks of stimulus components that represent either demands for or opportunities to use particular response components or assemblies, but that may also supplant the need for particular response components or assemblies, and that may be either familiar or novel with respect to the person’s learning history. These essential aspects of situations are defined by their connections with aspects of person performance, just as the essential features of person performance were defined earlier by their connections to situations. To simplify the language, and bring out some other implications, note that all these person-situation connections are affordancesin Gibson’s (1966,1979) sense of that term, and also arfifactsin Simon’s (1969) sense of that term. Gibson’s concept of affordances addresses the mutuality of person and situation in the control of perception-action sequences. To paraphrase Gibson (1979, pp. 127-9, pp. 138-91, the affordances of a situation are what it offers the person, what it provides or furnishes, for good or ill. The term implies a complementarity of person and situation, as in an ecological niche. A niche is a place or setting that is appropriate for a person -a combination of situational components into which the person ”fits”. So a situation is an assembly of affordances with respect to some particular person or kind of person. Affordances reflect the invitation, demand, or opportunity structure of a situation for those persons who are tuned or prepared to perceive them. Particular affordances invite particular actions. Gibson‘s concept of affordances is thus at many points close to the old meanings and roots of the concept of aptitude (seeSnow, 1991,1992). However, the concept of aptitude brings in the individual differences aspect directly. A situation provides a suitable niche only for some persons - those prepared to meet and use its affordances effectively. Those not properly tuned or prepared will in some minor or major ways fail to perform effectively in the situation as given.
Person-situationinteraction theory 19
Only rarely will a situation be completely suitable for all persons. Instructional learning situations, in particular, cannot be designed to fit optimally the range of learning histories that enter them. Thus, research on aptitudes, including work on individual differences in intelligence, requires a detailed analysis of the affordance-effectivity matches of different learners and different instructional treatments. This analysis emphasizes the opportunities offered by a particular treatment to be detected and capitalized upon by a particular person to achieve a goal. The analysis also remains at a level that identifies the unique person-situation synergy in local ecological terms, rather than reducing to physical or biological description or abstracting to generalized principles. Since ecological information is personal, it is unique to particular person-situation units. There is therefore no detached or abstracted list of qualities of instructional treatments that will be equally important for all persons, or of persons that will be equally important for all treatments. Aptitude, and thus intelligence, is the unique coalition of affordances and effectivities in particular person-treatment systems. This analysis of intelligence as affordances emphasizes the important ways in which person and situation are tuned to one another - to be in harmony for successful performance. But an equally important question for aptitude theory is the analysis of inaptitudes -the disharmonies in the person-situation interface that result in failure. Some aspects of these disharmonies can be described as failures of tuning to perceive affordances. But other aspects seem better described in Simon's language of artifacts and interface redesign. To paraphrase Simon (1969, pp. 7-13), artifacts are interfaces between inner and outer environments. If these inner and outer environments are appropriate to one another - that is, if they are adapted or designed to fit one another optimally - then the artifact serves its purpose unnoticed. But often, interface design is only approximate. Then the limiting properties of the inner system will appear in the failure to match the demands of the taxing outer environment. For a particular person in a particular environment, the empirical evidence of aptitude arises from the inabilities of the behavioral system to adapt perfectly to its environment. Aptitude differencesbetween persons in particular environments "show through at the interface as inabilities. For a person who is perfectly suited to a treatment or a treatment that is perfectly suited to a person, the goal is reached successfully;the presence of aptitude is inferred from this fact, but it is attributable to both person and environment, that is, to their benign interface. For a person who is not perfectly adapted to a treatment or a treatment that is not perfectly adapted to a person, the goal is not successfully reached; this fact shows that inaptitude of some kind is present. But again, inaptitude is attributable to the interface; either the inner system or the outer system, or both, need redesign to bring them into adaptive harmony. Research aimed at system redesign thus
20 R.E.Snow
needs to find the key inabilities in the interface that constitute the mismatch, and correct them. System redesign proceeds by reshaping the treatment to eliminate demands, thereby circumventing limitations, or by removing limitations directly by retraining the person. From the view of Simon's artifact design, future research on aptitude requires a detailed analysis of the treatment design features that seem mismatched to the person when limiting properties of the person show through in the performance interface. The analysis is geared to detect inaptitudes (weaknesses) so as to remove or circumvent them in treatment redesign. From the view of Gibson's affordance theory, future research on aptitude requires a detailed analysis of the affordance-effectivity matches in different person-treatment unions. The analysis is geared to detect aptitudes (strengths)so as to capitalize upon them in treatment redesign. The two views are complementary because the most successful instructional treatments will be those that both capitalize on strengths and compensate for weaknesses, for each individual to be treated. Thus aptitude is situated. It is reflected in the tuning of particular persons to the particular demands and opportunities of a situation. It thus resides in the union of person in situation, not "in the m i n d alone. It is a two-way sampling of performance components and their assembly between person and situation and is thus also distributed between person and situation; the situation contains some pieces of what the person needs or can use to accomplish a given task. But individuals need to be tuned to perceive and use those pieces, and need also to supply some pieces from their own learning history. Some individuals are prepared to perceive these affordances - to use the pieces provided by the situation; but some are not. Among those who are so tuned, each may supply slightly different pieces, though each piece thus supplied may be equally effective. The result is that some persons succeed in learning in a given situation; they are in harmony with it. Others do not, because they are not tuned to use what the situation affords or to produce what it demands. Persons assemble their performances in response to these perceived affordances from vast banks of potential response components organized into associative networks. As a function of learning history, parts of these may be tightly coupled and triggered as units; others may be loosely coupled and easily disconnected when parts are triggered. Actually, each component might itself be thought of as a network, also either tightly or loosely coupled. Continuing this reduction might eventually reach the neural networks of new connectionism. But that would go beyond the present outline. Persons also control or adapt these component assemblies as affordances change in a dynamic situation. In a heterogeneous group of persons, some components and assemblies will be held in common and some will not. The connections among components will differ in strength. The assembly and control history of
Person-situationinteraction theory 21
these components and assemblies will also differ from person to person, and so therefore will their facility for adaptive assembly and control during performance in a present situation. In this view, valid measures of ability are situations that evoke some semblance of the sample of components and assemblies and their adaptations that are also evoked by some learning or achievement task to which the ability measures are therefore correlated. The test situation and the criterion situation involve affordances that are invariant across these situations; that is, the samples drawn by the two situations overlap substantially. The size of the correlation suggests how large is the overlap. AT1 occurs because the affordance profiles of person-situation interfaces differ. To use an example given elsewhere (Snow, 1989a, in press), a relatively incomplete and unstructured situation samples just the kinds of assemblies that persons described as able, independent, mastery-oriented, flexible and the like, are tuned to produce. Highly structured and complete instruction does not provide that opportunity for such persons. It does, however, provide some of the assemblies that less able, less independent, less mastery-oriented learners cannot provide for themselves, and it does not sample what such learners cannot produce. The three major cognitive aptitude constructs can be distinguished in this assembly and control process. Fluid intelligence (Gf) reflects the more flexible assembly and adaptation of strategies for performance in novel unfamiliar tasks. Crystallized intelligence (Gc) reflects more the retrieval and adaptation of old assemblies for familiar tasks. Visualization (Gv) ability reflects a collection of specialized skills that pop in and out of relevance in a variety of tasks that afford their use; other special abilities can be similarly described. Finally, there is a performance assembly pathway, from activation in and retrieval from the persons's bank of components, to adaptation in the personsituation interface, to action in the task or instructional situation. Performance is assembled and reassembled along this path to meet the characteristic affordance profile of the situation. An analysis of this profile with respect to familiaritynovelty, structure-completeness, and the use of special knowledge and skills provides a picture of its intelligence requirements and opportunities for each person. AN EXAMPLE A study by Swanson (1990) shows how an instructional treatment called "contingent tutoring" might display some aspects of the sampling-assemblyaffordance model introduced above. It also stands as an important example of adaptive shifting between contrasting treatments to optimize instruction for each kind of student.
22 R.E.Snow
The concept of contingent tutoring derives from Wood's (1980) studies of mothers teaching children, which use Bruner's (1978) notion of scaffolding,which comes from Vygotsky's (1978) ideas about proximal development and the internalization of social interaction. It relates in turn to analyses of instruction in apprenticeships. Briefly, contingent tutoring assumes that learning depends on one already understanding something of the nature of what is to be learned, so an important function of teaching is to create links between the goal and context of a novel task and more familiar tasks, allowing the learner to recognize and apply relevant skills and knowledge previously acquired. The tutor also controls those aspects of the task that are initially too difficult for learners, thereby permitting them to concentrateupon and complete those aspects that each is able to perform. By adapting the task demands, keeping them within each learner's zone of proximal development, the tutor not only helps the learner complete the task at hand, but also gradually promotes the additional skill and strategy development that will enable eventual performance of similar tasks independently. Tutor effectiveness depends on this scaffolding being contingent upon the interaction of task affordances and student assembly of performance. Tutorial interventionsare inversely related to the student's level of competence. The more difficulty a student has with a task, the more the tutor must direct the student's sampling-assembly function.The more success the student experiences, the more the tutor can encourage the student to work independently,developing functional though probably idiosyncratic procedures. To make tutoring interventions contingent, the tutor must understand what the student is attempting to achieve, and be able to diagnose degrees and kinds of success and failure. Swanson (1990) compared contingent tutoring with mastery-oriented lecture or high structure (HS) condition and guided discovery low structure (LS) conditions in teaching optics to college undergraduates who varied in academic intelligence (Gas represented by combined SAT score). The HS condition put tutors in full control of the transaction, whereas the LS condition gave students full control; in the contingent condition, tutor control vaned to adapt to individual student needs and progress as described above. There were 2 tutors and 48 students. Pretests indicated minimal prior knowledge. Instruction lasted a week. Post-tests included both knowledge and problem-solving tasks. All sessions were videotaped. Results are shown in Figure 1. Panel a), which gives the aggregated results, shows that LS was good for the most able students, but it was particularly ineffectivewith lower G students, who benefitted most from contingent tutoring. HS produced intermediateresults. In Panel b), the tutor who was best at contingent control produced the highest learning outcomes across the G range with this treatment. For the tutor in Panel c), this strategy proved difficult to use, so HS was more effective for less able students.
Person-situationinteraction theory 23
In effect, this result is a macro-level AT1 used to evaluate a microadaptation of instruction. Tutoring that is contingent on learner performance should provide more scaffolding for less able learners and less scaffolding for more able learners. In the extreme, the tutor ranges between mastery-style direct instruction (HS) and guided discovery (LS); this is the major treatment contrast emphasized by Glaser and Bassok (1989) in their extensive review of research on instructional theory alternatives. The AT1 result is also consistent with much prior research on the HS vs. LS contrast. Furthermore, Swanson’s tutors seemed to be adapting not only to the student’s specific responses but to behavioral correlates of more general aptitude differences. Thus, human tutors may integrate domain general and domain specific learner communications in their adaptations. Further research needs to understand how this is done. The videotape analyses, as yet incomplete, suggest that tutors are using a sampling adaptation process. Meanwhile, Swanson‘s macro- and micro-ATI results underscore the need for a more detailed, transactive process model of mutual intelligence as adaptive person- situation interaction.
CONCLUSION The above example hardly represents adequately the wealth of prior research evidence regarding cognitive abilities and academic tasks and treatments. But it does make the old high vs. low structure hypothesis concrete and it suggests how major contrasts in research on instructional design need to include an AT1 perspective; AT1 can moderate effects to produce different local accounts of optimal instruction in different research programs. Swanson’s study also shows how traditional AT1 research, although focussed on statistical interactions among independent variables, provides a shell within which reciprocal and transactive interpretations of interaction can be considered (Snow, in press). Over the past decade or so, my colleagues and I have sought to bring together the process analytic research on A and T variables, including our own studies, within this AT1 shell. The aim has been to reinterpret the concept of aptitude, including intelligence, as a property of the person-task interface, rather than of person or task alone, and to build a process model of person-situation interaction that would account for all the evidence in hand. The model needs to be general enough to cover conative and affective as well as cognitive aptitude. It also needs to account for intra- as well as inter-individual differences in person adaptation to task conditions. The development of this view can be traced through a series of earlier publications (Snow, 1978,1981,1989a, 1992, in press; Snow & Lohman, 1984; see also Kyllonen, Lohman & Woltz, 1984, and Snow, Kyllonen & Marshalek, 1984). It will proceed beyond this brief chapter in continuing research on the human ability to adapt performance to the fine structure of task and treatment
i km
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izw
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SAT SCORE
Tutors Combined
Tutor B
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,
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Figure 1. Regression slope showing aptitude-treatment interaction results for two tutors, separately and combined,comparing high (HS)and low (LS)structure treatments with contingent tutoring, using SAT score as aptitudeand optics posttest as learning outcome. Data from Swanson (1990).
Person-situationinteraction theory 25
characteristics as they unfold. Thus, intelligence differences in learning appear in the person-task interface as differences in within-person adaptation to the stream of continuing changes in task and treatment demands and opportunities. Learners construct their performances in academic tasks by drawing on their resources and assembling, reassemblingand controlling them to adapt to perceived needs and opportunities in the situation. Individual differences in learning occur because of qualitative and quantitative differences in this adaptation function across person-situation unions. I believe it will be these unions that form the units for intelligence theory and analysis in the future. REFERENCES Ackerman, P. (1989). Individual differences and skill acquisition. In P.L. Ackerman, R.J. Sternberg, & R. Glaser (eds.), Learning and individual differences. New York W.H. Freeman. Anastasi, A. (1970). On the formation of psychological traits. American Psychologist, 25,899-910. Balke-Aurell, G. (1982). Changes in ability as related to educational and occupational experience.Goteborg, Sweden: Acta Universitatis Gothoburgensis. Bangert-Drowns, R.L. (1991). Teaching critical thinking, problem-solving and other higher-order cognition: Evidence from ability test performance. In R.L. Bangert-Drowns (ed.), Problem-solving, critical thinking and instructional design (pp. 66-73). Monograph of the Albany Consortium for Research on Instructional Design and Theory. State University of New York: Albany, NY. Bereiter, C. (1990). Aspects of an educational learning theory. Review of Educational Research, 60,603-624. Bruner, J.S. (1978). The role of dialogue in language acquisition. In A. Sinclair, R.J. Jarvell, & W.J.M. Levelt (eds.),The child’s conception of language (pp. 241256). New York: Springer. Carroll, J.B. (1993). Human cognitive abilities. New York: Cambridge University Press. Cattell, R.B. (1971). Abilities:Their structure, growth, and action. Boston: Houghton Mifflin. Cronbach, L.J. & Snow, R.E. (1977). Aptitudes and instructional methods: A handbook for research on interactions. New York: Irvington. Dennett, D.C. (1981). Brainstorms. Cambridge, MA: MIT Press. Ferguson, G.A. (1954). On learning and human ability. Canadian Journal of psycho lo^, 8,95-112. Ferguson, G.A. (1956). On transfer and the abilities of man. Canadian Journal of Psychology, 10,121-131. Fodor, J.A. (1983). The modularity of mind. Cambridge, MA: The MIT Press.
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Gardner, H. (1983). Frames of mind. New York Basic Books. Gibson, J.J. (1966). The senses considered as perceptual systems. Boston: Houghton Mifflin. Gibson, J.J. (1979). The ecologicalapproach to visual perception. Boston: Houghton Mifflin. Glaser, R. & Bassok, M. (1989). Learning theory and the study of instruction. Annual Review of Psychology, 40,631-666. Guilford, J.P. (1967). The nature of human intelligence. New York: McGrawHill. Gustafsson, J.E. (1984). A unifying model for the structure of intellectual abilities. Intelligence, 8,179-203. Gustafsson, J.E. (1988). Hierarchical models of the structure of cognitive abilities. In R.J. Sternberg (ed.), Advances in the psychology of human intelligence, Vol. 4 (pp. 35 - 71). Hillsdale, NJ: Lawrence Erlbaum Associates. Gustafsson, J.E. (1989). Broad and narrow abilities in research on learning and instruction. In R. Kanfer, P.L. Ackerman, & R. Cudeck (eds.), Abilities, motivation, and methodology (pp. 203-237)’. Hillsdale, NJ: Lawrence Erlbaum Associates. Guttman, L. (1969). Integration of test design and analysis. Proceedings of the 1969 invitational conference on testing problems. Princeton, NJ: Educational Testing Service. Harnqvist, K. (1968). Relative changes in intelligenceform 13 to 18. Scandinavian Journal of Psychology, 9,50-82. Heinonen, V. (1962). A factor analytic study of transfer of training. Scandinavian Journal of Psychology, 3,177-188. Horn, J.L. (1989). Cognitive diversity: A framework of learning. In P.L. Ackerman, R.J. Sternberg, & R. Glaser (eds.), Learning and individual differences: Advances in theory and research. New York Freeman. Humphreys, L.G. (1962). The organization of human abilities. American Psychologist, 475 - 483. Humphreys, L.G. (1979). The construct of general intelligence. Intelligence, 3, 105-120. Humphreys, L.G. (1981). The primary mental ability. In M.P. Friedman, J.P. Das, & N. O’Connor (eds.), Intelligence and learning (pp. 87-102). New York: Plenum. Kuhl, J. (1990). Self-regulation: A new theory for old applications. Invited address to the International Congress of Applied Psychology, Kyoto, Japan, July. Kyllonen, P.C., Lohman, D.F., & Woltz, D.J. (1984). Componential modelling of alternative strategies for performing spatial task. Journal of Educational Psychology, 76,1325-1345.‘ Resnick, L.B. & Glaser, R. (1976). Problem solving and intelligence. In L.B. Resnick
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(ed.), The nature of intelligence (pp. 205-230). Hillsdale, NJ:Lawrence Erlbaum Associates. Simon, H.A. (1969). The sciences of the artificial. Cambridge, MA: MIT Press. Simon, H.A. (1976). Identifying basic abilities underlying intelligent performance of complex tasks. In L.B. Resnick (ed.), The nature of human intelligence. Hillsdale, NJ: Lawrence Erlbaum Associates. Snow, R.E. (1978). Theory and method for research on aptitude processes. Intelligence, 2,225-278. Snow, R.E. (1981). Toward a theory of aptitude for learning: Fluid and crystallized abilities and their correlates. In M.P. Friedman, J.P. Das, & N. OConnor (eds.), Intelligence and learning (pp. 345-362). New York Plenum. Snow, R.E. (1982). Education and intelligence. In R.J. Sternberg (ed.), Handbook of human intelligence (pp. 493-585). Cambridge: Cambridge University Press. Snow, R.E. (1986). On intelligence. In R.J. Sternberg & D.K. Detterman (eds.), What is intelligence? (pp. 133-139). Norwood, NJ: Ablex. Snow, R.E. (1989a). Aptitude-treatment interaction as a framework of research in individual differences in learning. In P.L. Ackerman, R.J. Sternberg, & R. Glaser (eds.), Learning and individual differences: Advances in theory and research (pp. 11-34). New York Freeman. Snow, R.E. (1989b). Cognitive-conative aptitude interactions in learning. In R. Kanfer, P.L. Ackerman, & R. Cudeck (eds.), Abilities, motivation and methodology (pp. 435-474). Hillsdale, NJ: Lawrence Erlbaum Associates. Snow, R.E. (1991). The concept of aptitude. In R.E. Snow & D.F. Wiley (eds.), Improving inquiry in social science (pp. 249-284). Hillsdale, NJ: Lawrence Erlbaum Associates. Snow, R.E. (1992). Aptitude theory: Yesterday, today and tomorrow. Educational Psychologist, 27,5-32. Snow, R.E. (in press). Abilities in academic tasks. In R.J. Sternberg & R.K.Wagner (eds.), Mind in context: Interactionist perspectives on human intelligence. Cambridge University Press: New York. Snow, R.E., Kyllonen, P.C., & Marshalek, B. (1984). The topography of ability and learning correlations. In R.J. Sternberg (ed.), Advances in the psychology of human intelligence, Vol. 2 (pp. 47-104). Hillsdale, NJ: Lawrence Erlbaum Associates. Snow, R.E. & Lohman, D.F. (1984). Toward a theory of cognitive aptitude for learning from instruction. Journal of Educational Psychology, 76,347-376. Spearman, C.E. (1927). The abilities of man. London: MacMillan. Sternberg, R.J. (1985). Beyond IQ: A triarchic theory of human intelligence. Cambridge: Cambridge University Press. Sternberg, R.J. & Wagner, R. (eds.) (1986). Practical intelligence. Cambridge, UK: Cambridge University Press.
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Swanson,J. (1990, April). The effectiveness of tutorial strategies: An experimental evaluation. Paper presented at the meeting of the American Educational Research Association, Boston, MA. Thomson, G.H. (1919). On the cause of hierarchical order among correlation coefficients. Proceedings of the Royal Society, A, 95. Thomson, G.H. (1939). The factorial analysis of human ability. London: University of London Press. Thorndike, E.L. (1921). Educational Psychology (three Vols.). New York: Teachers College, Columbia University. Thurstone, L.L. (1938). Primary mental abilities. Chicago: University of Chicago Press. Vernon, P.E. (1950). The structure of human abilities. London: Methuen. Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. Wood, D.J. (1980). Teaching the young child: Some relationships between social interaction, language, and thought. In D.R. Olson (ed.), The social foundation of language and thought (pp. 280-296). New York W.W. Norton.
Intelligence, Mind, ,and Reasoning: Structure and Development A. Demetriou and A. Efklides (Editors) 0 1994 Elsevier Science B.V. All rights reserved.
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Taking Stock of What There is: The Case of Cognitive Abilities* Johan Olav Undheim University of Trondheim, Norway INTRODUCTION It is true that several claims for the psychometricapproach to human intelligence have been shown to be unjustified. In fact, such unfounded claims are linked not only to vulgarized versions of intelligence findings, but even to great psychometricians: ability factors were labeled "primary" by Thurstone, indicating that one had somehow stumbled across mental building blocks; Guilford proposed a model indicating the "structure of intelligence", as if we were introduced to the periodic table; Cattell coined the terms "fluid and "crystallized intelligence, indicating that behavior measures somehow were able to distinguish between the raw and uncultured nature and the molding of knowledge. The field of psychometric ability research is also characterized by ongoing controversies: the virtues of this or that factor analytic solution; the proportion of heritability, and, in fact, the whole notion of heritability; the distinction of aptitude versus achievement or competence versus performance; the predictive value of ability measures for life accomplishments, etc. However, the fact that many claims have later been questioned and refuted, is true of all scientific endeavours. Also, controversies are common in wellrespected fields of inquiry. There are almost always growth and inevitable decline in the expectations for any approach. As will be discussed, there was a sense of diminishing returns and re-hashing of old stuff that led to the downturn of psychometric ability research in the 60's and 70's. Along came the informationprocessing alternatives, including the expert-novicetype of approach, emphasizing the importance of knowledge. Initially these new approaches were met with very high expectations.At present time, 15-20 years later, they are not so new anymore - and expectations have diminished somewhat. It is perhaps time to take stock of what we now seem to have of value in the psychometric approach to intelligence. I will not be arguing that all is well with psychometric research on abilities. Neither people inside nor people outside the field should be impressed with the * Author's address:Johan Olav Undheim, Department of Psychology, AVH, University of Trondheim, N-7055 Dragvoll, Norway.
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development of new theories and new instruments within this approach the last 20-30 years. In fact, I will start with pointing to some reasons why there was a need for new approaches in the 70's. However, it will be argued that psychometric ability research has played an important role even in these new approaches to individual differences.Also, new statistical techniques and measurement theories have some promise of solving at least some of the problems that led to the downturn of psychometric ability research. In any case, I will argue that the concept of ability is not at fault for the shortcomings of psychometric research, nor for the claims of some of its proponents. In fact, the concept is quite viable, having outlived most other concepts in psychology, and should continue to serve psychology well if used properly, that is, cautiously and tied in with empirical measurements. Critique of the psychometric approach For a long time, individual difference research on cognitive or intellectual functions was almost synonymous with factor-analyticresearch. Although once a prestigeous field of research, by about 1970 the factor analytic approach to intelligencewas looked upon with quite a bit of scepticism and the recruiting of graduate students to the area of individual differences was extremely difficult. There were at least two main causes for this situation: old instruments and diminishing returns. Analyzing correlations between performance on instruments (i.e. tests) that look almost identical to those developed by Thurstone before World War I1 was hard to justify and created little enthusiasm. For a while, Guilford's ambitious efforts of test construction created some interest, but the critique against his use of factor analysis (see Undheim & Horn, 1977) stopped further development almost cold - except in the area of creativity. Secondly, there were diminishing returns. There seemed to be little pay-off in doing another factor analysis. One might try a shot at establishing more firmly primary factor number 28, or extend factor analytic findings to younger ages. To be sure, there were the old questions of a possible change in the number of factors with age (often called the ability or factor differentiation problem) or that of possible decline of ability in adulthood and old age, or the question of differential heritability for ability factors, but they were all old problems and hardly apt to create enthusiasm in new generations of graduate students - and obviously very difficult and even elusive problems at that (for an update review on these old problems, see Sternberg, 1990, pp. 100-109). There were probably other causes for the state of affairs. Different factor analytic models were difficult to compare and to falslfy.Also, mental abilities as researched bv factoranalysis had little, if anything, to say about mental processes.The latter
Taking stock of what there is 31
is not only a critique of that approach, but also points to the reason why process analytic approaches came into vogue - the new approaches promising just that, a detailed understanding of the cognitive processes behind intellectual performance, and behind the individual differences that such performances show. Alternative approaches: Information-processing studies The information-processing studies were born out of experimental studies on cognition, and in response to the dominance of structure in the factor analytic approach, the emphasis has been on dynamic processes. Thus, while the factor analytic approach studied human reasoning by investigating dimensions of reasoning (e.g., inductive reasoning as separate from deductive reasoning), information processing approaches tried to extract components in reasoning tasks or it related performance on reasoning tasks to measures derived from experimental studies of reasoning. One may distinguish between two general approaches to the study of processes underlying individual differences in intelligence, the cognitive-correlatesapproach and the cognitive-componentsapproach &ail& Pellegrino, 1985; Sternberg, 1990). In the first approach, the one initially opening up this area of research, subjects high and low on some traditional intellectual measures are tested on tasks that contemporary information-processing psychologists believe involve certain basic processing skills. Also, one should point out that an approach often considered to be separate of the process analytic endeavours, characterized by an emphasis on the biological basis of intelligence, has some of its roots in the cognitivecorrelates approach. In the second approach, the cognitive-components approach, the aim is to develop processing models of complex cognitive tasks, finding ways to de-compose the tasks into simpler components. Initially, the two approaches were characteristic of endeavours into two different areas, verbal abilities and reasoning abilities. As time has passed, there has been a blending of these approaches and also applications to many areas of intellectual performance. A third approach often subsumed under information processing studies is characterized by expert-novice comparisons in some real life achievements, the domains of knowledge being as diverse as chess playing and physics. This approach may also be termed the cognitive-content approach or methodology, focusing on the content of the knowledge base and how that is brought to bear on the processes of comprehension, reasoning and problem-solving. These process analytic approaches brought about a revival of the field of individual differences, as seen by new journals devoted to the field, by the publication of numerous articles in traditional journals, and by the publication of many new books. Cognition gave the cognitive approaches to the study of intelligence a sense of unity, both in terms of purpose and in terms of methods
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to be used. The cognitive approaches to the study of intelligence vitalized the field of individual differencesand again put this area of study into the mainstream of psychology. However, after about 15 years of research, the sense of coherence and unity among cognitivists is no longer so evident. Cognitive analysts are arguing about levels of task analysis and about methods, much as factor analysts have argued about number of factors and rotational issues (Sternberg, 1990, p. 129).Also, while the cognitive psychologists entering the field of intelligence obviously had hopes for explanations rather than merely descriptions of intellectualdifferences, the process approach has not given the easy access to such that initially was envisioned. The dependence on ability factors in processing studies While the cognitive-correlatesand the component-approacheseach has provided much detailed knowledge about different aspects of cognitive functioning, they are both more intimately tied in with factor analytic ability research than their proponents initially were aware of, or cared to spell out. Both the cognitivecorrelates and the cognitive-components approach are based on the validity of psychometric abilities as representing important distinctions. The cognitivecorrelates approach depends on ability factors or single ability tests in the initial selection of subjects to compare - high verbal versus low verbal, good reasoners versus not so good, etc. In fact, these studies investigate the correlation between ability tests or factors and cognitive measures derived from experimental studies on cognition. The cognitive-componentsapproach also takes traditional ability tests as the starting point and decomposes these tasks by reaction time measures of sub-problems for each test. Moreover, many of the findings attributed to these approaches are actually rather slight extentionsof previous factor analytic findings. The cognitive-correlates approach has made much out of the fact that rather simple cognitive tasks correlated substantially with psychometric tests. This is not so new, cognitive speed tests having been shown to correlate with more complex ability tests long ago, and collectively to define primaries and a broad factor of intelligence. The eognitivecomponentsapproach has shown, for instance, that several tasks of inductive reasoning share many components, and similarly for deductive reasoning tasks. Also, components seem to have some, although not impressive, generality over some tasks and contents (as indicated by intercorrelation of component scores). Furthermore, speed of executing components correlateswith psychometric measures, "reasoning" components more so than others (Sternberg and Gardner, 1983). However, factor analysts would say years ago that, yes, inductive reasoning tasks must have much in common since they correlatehighly
Taking stock of what there is 33
and define a separate factor, as does deductive reasoning, although not as clearly. The fact that components of reasoning tasks correlate with total test scores is not so impressive, because correlations of at least some task parameters are being assured when decomposing traditional intelligence measures - as admitted by Sternberg, the most influential proponent of the cognitive component approach (Sternberg, 1981). Although Sternberg goes on to argue that the data of interest are in the pattern of correlations, not all would be impressed by the finding that a "reasoning" and a "comparison" component show the highest correlation with a traditional reasoning factor, considering the fact that those components represent the core of reasoning as traditionally viewed. Sternberg and Gardner (1983) do interpret their findings as providing some convergent and discriminant validity for the hypothesis of unities in inductive reasoning components - and for such components as individual difference "constructs". However, the fact that some components show reasonably high correspondingcorrelations is difficult to evaluate, considering that intercorrelations of total solution times for all tests are quite high to begin with. One may simply interpret this as reflecting the unity of inductive reasoning as measured by solution times, paralleling a similar unity in psychometric research using more complex problems and measuring solutions by the number of rights. Admittedly, there is some evidence for components as unities and individual difference "constructs", but the evidence is not very compelling, and it is difficult to argue that they in any way "explain" the psychometric factor constructs. Many cognitive researchers, and particularly those engaged in componential type research, have also suggested that the over-all efficiency of the intellectual system may be due to meta-cognitivefunctioning, higher-order control processes that are used for executive planning and decision-making in problem-solving. Sternberg and Gardner (1983) have proposed six metacomponents having to do with the recognition of the problem, the selection of lower-order components and of a strategy for their combination, the selection of representation, decisions regarding allocation of resources, and with solution monitoring. As pointed out by Siegler and Richards (19821, metacognitive research has been controversial from its inception. The metacognitive metaphor summons an image of a homunculus directing the operations of the information-processing system. Also, to many people the metacognitive construct is superfluous in that knowledge about when to, say, select a strategy, is embedded in the strategy itself (Siegler & Richards, 1982). While the ideas of metacognitive abilities are still attractive, how metacognition actually influences cognitive operations has rarely been specified and there has, in fact, been little hard evidence of metacognitive abilities independent of ability components. While one may argue that intelligence in a broad perspective must relate to what may be called higherorder control processes - such as the selection of strategies and the optimal
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allocation of time used on different processes - the sobering fact is that intelligence as measured by intelligence tests apparently involves relatively little of such higher-order thinking. True enough, the traditional paper-and-pencil psychometric tests are usually administered in such a way that, say, allocation of time may be of importance. However, measures of fluid intelligence based on paper-andpencil tests do correlate highly with fluid tests administered item by item as separate tasks, suggesting that strategies of time-allocation do not represent a large variance component in paper-and-pencil psychometric tests. The cognitivecodates approach started off investigating language and verbal abilities. Initially, the interest was concentrated around lexical processes. Hunt’s studies using a stimulus-matching paradigm suggested that verbal ability was related to lexical access time for a rather “elementary” process, letter names (Hunt, Lunneborg & Lewis, 1975).At first sight, we were now able to “explain” verbal ability. However, experimental cognitive psychology had already suggested several different accounts of lexical access. While lexical access variables would be examples of a ”bottom-up” approach, experimental research also suggests that “top-down” approaches are used, and that there is an interaction of the two approaches (see Baron, 1978; Rumelhart, 1977). Research suggests that highability readers use context information to their advantage, including the ”exclusion” of context when context-free word-recognition is faster (Perfetti & Roth, 1981). However, context effects also introduce the whole theme of knowledge-based approaches to ability. Thus, what started with elementary processes of cognitive tasks now has resulted in some measures that are as complex as the verbal tasks one started out to explain, in fact, some even seemingly more complex (text perception). While this in itself is not really a critique of the approach, it certainly shows that the process approach does not necessarily represent a more basic description relative to the psychometric approach. In any case, ongoing research in this vein is certainly very much tied in with research on verbal abilities. Choice-reaction time research involving micro-level analysis is often conceptualized within the area of the cognitive-correlates approach, but have come to live a life of its own. Its proponents prefer to theorize in relation to neurophysiological measures and concepts. This area of research has, to many cognitivists, come to epitomize the revitalization of old paradigms for studying intelligence. Reaction-time research of this kind has led to strong claims, suggesting, in fact, that such research endeavours are about to reveal the “nature” of intelligence. Using the paradigm of Galton, microlevel analyses of choicereaction time have developed on the basis of Hick’s law proposing that reaction time (RT)increases as a linear function of the increase in the amount of information in the array (i.e., number of choices). Results have been interpreted as supporting the implication of a limited channel
Taking stock of what there is 35
information-processing system in intelligence. Slow processing is assumed to lead to an incapacity to handle complex problems where a great deal of information has to be dealt with. Although initially impressive considering the failure of Galton and others to find any consistent relations between RT and intelligence, critics have argued that correlations in the order of .3 are far from demonstrating the ”true” nature of intelligence (Mine, 1991; Sternberg, 1985).Correlations of that order are found among all sorts of cognitive tests or tasks having acceptable reliabilities. In any case, the interpretations of these data differ widely. While some suggest interpretations in terms of “channel capacity” or basic CNS efficiency, Ceci has argued against this physiological view ( 1990a; 1990b).Ceci suggests that there are knowledge-base differences, i.e., while everyone may be familiar with the number 49, subjects may differ in how they represent it in memory - some may represent it simply as an odd number that is greater than 48 but less than 50, while other may represent it more elaborately in terms of cardinality, roots, etc. Ceci refers to some preliminary work showing that the more elaborately one represents a stimulus, the faster it can be recognized. Furthermore, the basis for this knowledge-base difference may be environmentaland motivational - persons less interested in academic/verbal games and activities end up knowing less about alphanumeric stimuli. Proponents of psychometric ability research have argued for an interpretation of the reaction time results along the line of primary or second-order factors representing perceptual speediness or memory abilities. Similarly, Sternberg (1990) has suggested that the relatively low correlations attained might be due to the psychometric test performances drawing on lower level perceptual and memory abilities in a peripheral way that do not in any way provide a theoretical grounding for the complex kinds of information processing called intelligence. The hierarchical view of intelligence of Gustafsson and Undheim (see Undheim & Gustafsson, 1987; Gustafsson & Undheim, in press) explicates this perspective in that every cognitive task is seen as composed of a variety of variance components, representing general intelligence (or fluid/analytical intelligence), verbal-educational knowledge (or crystallized intelligence),visuo-spatial ability, speediness, etc. Although some of the reaction-time studies have used tests traditionally characterized as fluid or analytical tasks, such as Raven’s matrices, any one task or test is composed of these components. According to this view, the interpretation of the relation between RT-measures and any one psychometric test is quite speculative. The implication from the hierarchical view is that one should rather study the relations to such variance components, obtainable as latent variables through the simultaneous analysis of several psychometric tests. To be true, there are reports of extremely high correlations of some RT variables or derivatives of such with ability measures (see Eysenck, 1986). In fact,
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correlations around .7 and .8have been reported, correlations being on par or actually higher than normally found between any two typical IQ tests. To Eysenck such findings seem to indicate a breakthrough in terms of a new perspective on the nature of intelligence.However, one should point our that in most cases such correlations have been corrected for both attenuation and imperfect reliability, the assumptions for such corrections possibly being questionable in these cases. Results should be replicated in more heterogeneous samples, with reliable measures, and with no capitalizationon chance in the way measures are combined for prediction purposes. Even if data turn out to be quite robust, however, there is the question of what comes first, the hen or the egg. One should certainly expect cognitive functioning to be reliably reflected in some kind of physiological measures, be it EEG, AEP, or other measures, such as blood flow. This does not mean that the physiological measures “explain” the cognitive measures, let alone the construct of intelligence. Actually, the extremely high correlation found, may, if replicated, argue against the view that such physiological measures reflect basic processes unaltered by only the most extreme environmental manipulation. This follows from the fact that the psychometric tests as such are clearly culturedependent. Thus, if the physiological measures correlate extremely high with such measures, they must themselves be culture-dependent. The knowledge-approach to cognitive functioning,also called the cognitive content approach, is more independent of ability findings. It does not often look at expert-novice relations in terms of test scores, but rather in terms of some life performance, including games and other leasure activities. However, one may argue that the results, the importance of a rich knowledge structure, are to some extent foreshadowed by factor analytic research, although the new approach has provided us with much richer details. Factor analytic approaches have long acknowledged “knowledge” factors among its repertoire. Variations of culturally modified and structured knowledge, or “crystallized intelligence, has always been included in traditional batteries of intelligence measures, and fluency factors have emphasized the importance of retrieval from some kind of long term memory. Thus, one might say that the importance of “elaborated knowledge structures is not so new. However, while the knowledge approach looks intensely at some rather limited domain of expertice, providing rich details in the chosen domain or area, ability research, by definition, takes more of a bird’s eye, looking at more generalized knowledge. In sum, the new alternatives actually depend heavily on the psychometric findings, and to some extent “re-discover” previous factor analytic findings, probably more so than their proponents initially had envisioned and sometimes would like to acknowledge.
Takingstock of what there is 37
On the concept of ability On the one hand, then, ability research and the concept of ability thus seems to have lived through the hard times. On the other hand, it is as if excuses for this state of affair are needed. This may partly relate to the controversies mentioned in the introduction, and to the embarrasing claims that some proponents of psychometric research have made. To many, the concept of ability is rooted in beliefs about heredity and stability, assuming that environment and context have little impact within the limits of “normal” variation. My point here is that most of what one often associates with the ability concept are historical connotations, and not necessary parts of the concept itself. The ability concept is rooted in the belief that intellectual performance may be analyzed by looking at dimensions across tasks. One may contrast individual differences as being looked upon by a problem solving approach - whether it be cognitive-components, expert-novice, or traditional problem solving and thinking approaches - with ability research. While the former approaches are initially interested in the solving of one or a few specific problems - defining parameters that influence the solution of each problem selected for study and seeking individuality in the subject’s approach to the specific problem - the ability approach intentionally seeks to partial out specific task variance in order to measure more generalized dimensions. The intentional summing of scores over items and over tests in the psychometric approach should be emphasized, because so many seem to think that this represents a short-cut substitute for detailed study (see Undheim, 1989).The two approaches should supplement, not supplant each other. While the problem solving approach informs us about reasoning, preferably individual differences in reasoning as well, in specific instances, there is the danger that categorization of thought processes becomes task specific. The psychometric intelligence approach is very much concerned with avoiding this danger of task specificity. One of its main objects is thus to tell us about how individuals differ in their general performance on intellectual tasks. There is then the danger that this knowledge becomes too summary and broad-pictured. But what is not true is that the one kind of approach tells the whole story. The ability concept is constructed and has developed on the basis of some empirical findings: positive correlationsamong several tasks considered intellectual and prediction of important accomplishements. On the other hand, the hereditarian position is in no way part of the assumptions of the ability concept. It is true that historically, many proponents of the psychometric view have been favoring this position, but neither across-task correlations nor continuity and prediction aspects, necessarily imply this view. Positive correlations are the basis for the across-task summation. The ability concept is not, however, based on the notion that all tasks correlate positively.
In fact, the discussion has centered on how many more or less independent
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generalized dimensions one would need to describe the co-variationamong tasks. While research supports the idea that many intellectual tasks do correlate positively, thus supporting a notion of a rather general intellectual factor, no one thinks that this is general to the universe of tasks thought to involve intellectual processes. The concept of ability is not dependent on any kind of universal generality. Secondly, the ability concept is rooted in the finding of continuity in development - as is all of psychology - and in finding a relation to subsequent performances on tests and to subsequent life accomplishments. The empirically shown stability of rank-orderings for ability measures, at least after the age of 2 or 3, and the relation to school achievements, has been essential to the rise of the industry of testing. However, the extent of such stability and the conditions under which rank-ordering of subject performance may change more or less, is an empirical question, similar to the extent of cross-task generalizability. It is certainly not assumed that all life accomplishments considered intellectual should be predictable by such measures. Thus, the discussion over, say, the prediction of success in the workplace by cognitive tests, or the relation between tests performance and the use of complex solution process for betting on the race track by ability measures (see Ceci, 1990a) is not adressing the validity of the ability concept as such. However, it does address the interpretation of ability as an indicator of "competence". It is quite unfortunate that the ability concept is often associated with the idea of "competence" as opposed to performance. As pointed out by Humphreys many years ago, the idea of aptitude as opposed to achievement is largely misleading. Although the measures of abilities are most often not so dependent on specific instruction as are academic achievement measures, test performances are certainly context-bound in many ways, and closely tied to general effects of schooling and literacy. So is the "structure" of intelligence, i.e. the weaving together of performances in abilities. There is nothing in the technique of factor analysis that somehow distinguishes between cultural molding and "hard-wired connections. Cattell (1971) illustrated this by suggesting that Bible knowledge and psalm singing might form a factor, because those who go to church get ahead in both, relative to those who do not. The high intercorrelations among academic subjects in school are undoubtedly inflated by communalities across school subjects in terms of discipline, attention, work habits, and the whole atmosphere of schooling - over and above what may be common in terms of cognitive requirements for, say, language learning and quantitative reasoning. Although the same Cattell argued that one may distinguish between "surface" traits and more basic "source" traits by heeding aspects of the factor analytic solution (e.g., "hyperplane" counts), any classification of ability traits in terms of, say, contextual versus physiological, is apt to be very problematical.
Taking stock of what there is 39 It follows that ability concepts cannot readily be used to “explain” other data. Misuse to this effect has certainly happened, and accusations of the psychometric approach for just that have been reiterated many times. Johnson-Laird, in his book on mental models, repeats this criticism, referring to, among others, Guilford as being “content to account for such differences ( i.e. individual differences) by appealing to “general intelligence” or some other factors derived from mental tests” ..and..”happy to treat some dimension derived from factor analysis of test performance as a primitive and unanalysed commodity that gives rise to the observed differences in reasoning ability” (Johnson-Laird, 1983, p. 65).Although it is true that factors have been thought of in this vein, these repeated accusations seem rather unfair (see discussion in Undheim, 1989). Most of our psychological concepts have been part and parcel of similar ”attributional” errors. Most of us, even psychometricians, are by now aware of the difficulties of arriving at any kind of explanation, except in a very shallow sense. Thus, while psychometric research purports to be classified as attempts at understanding mental activity, we do not think - and have not for a long time thought so - that explanations somehow magically pops out of the grinding known as factor analysis. Revival of psychometric ability research? While this may speak to the argument that there is not much new under the sun, and that the ability concept may have a life, when stripped of the unnecessary historical clothing, it does not in itself bolster the argument that ability research is on good footing. Are there any reasons to believe that such research is in a better shape than before? I think there are some reasons to believe so: statistical advances in multivariate analysis and an accompanying theory of measurement. The development of path analysis models, as exemplified by Joreskogand Sorbom’s (1981)linear structural relations analysis (LISREL) seem to have solved some of the main problems of factor analysis, namely problems associated with reliability/specificity, rotational problems, and the exploratory nature of traditional factor analysis. This has paved the way for a measurement theory based on this technology of teasing out multilevel components in behavioral measurements, hierarchical order analysis (Gustafsson, 1984,1988; Undheim & Gustafsson, 1987; Gustafsson & Undheim, in press). The new methods of linear stucture analysis promise to rid factor analysis of some of its main problems, bringing it in line with other hypothesistesting statistical methods. Also, the new model of hierarchical analysis promises a solution to the level of analysis problem that has plagued the factor analytic approach. Although the old British tradition, as well as the Cattell-Horn broad factor approach, may be said to be hierarchical in the sense that they include ability dimensions of different levels of generality, neither of them tried to, and
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had good tools for, partialing out influencesfrom one level in relating organizations at another level. The new linear structural analysis allows one to decompose task performance into variance components such as a general factor (if evidenced in the data at hand), residuals of broad factors, residuals of narrower factors, and specificity/unreliability. Gustafsson (1988) discusses the advantages of such covariance analyses and demonstrates the use of such decomposition in a prediction study; Undheim and Gustafsson(l987) re-analysed cross-sectional data on abilities using this approach, and Gustafsson and Undheim (in press) reexamined ability development. The implication of the hierarchical structure approach is that no single measurement (i.e., test) ever measures a single ability, because performance is affected by variance from sources located at each of the levels in the hierarchy. Such analyses have implicationswithin the field of psychometricwork as well as implicationsfor individual difference studies where ability concepts are utilized - and thus for almost all studies of intellectual functioning. As for studies within the field, one is led to a reevaluation of development and stability of cognitive functions. This may be exemplified by the Gustafsson and Undheim finding (in press) that in Swedishstudents aged 13 to 16, the ability of Visualization (residual visual-spatial factor when other components are taken out) was perfectly stable over these years (in a correlationalsense),while the visual-spatial tests themselves did not correlate more highly than other tests over the three years, apparently due to the influences of these other components. In studies focusing on cognitive correlates or components, it will be important to distinguish between relations to one or the other level of ability conceptualization. I also think that these new developments may pave the way for new theorizing about intelligence as such. The hierarchical studies of ability factors (Undheim, 1981; Undheim & Gustafsson, 1987; Gustafsson & Undheim, in press) clearly indicate that reasoning is the central construct of intelligence - as true for small children as for youngsters and adults. The invariant qualities of the central core of reasoning needs to spelled out, but the idea of such invariance will have to be reconciled with reasoning as knowledge-dependent in all of its manifestations. With the general finding of positive correlationsin mind, one might hypothesize that all intellectual tests directly or indirectly involve portions of such reasoning. However, the residual latent variables, such as visualization and verbal ability, when the general reasoning factor has been partialed out, are independent of general intelligenceas defined by this reasoning construct. While this follows by necessity from the hierarchical analysis and any kind of partialization, it is suggestive of quite independent functions.Other kinds of psychometric research more strongly suggest such functional independence, the evidence being particularly compelling for reading and spelling as "technical" acquisitions.The existence of students with dyslexia, children and youngsters with good reasoning
Taking stock of what there is 41
abilities and very poor reading or spelling proficiency - and of others with very poor reasoning having no problems reading or spelling correctly - indeed point to independent functions. Illustrating this point, a recent study of high-ability youngsters in Trondheim, identifying the 7% top students on fluid ability measures, i.e. reasoning ability, included several students with severe reading or spelling difficulties (Undheim, Norovik, Gustafsson & Undheim, in preparation). The important point here is that this view of independent functions is not contradictory to the observed positive correlationsamong measures of language proficiency and reasoning. In fact, it is about time that evidence from learning disabilities, gifted individuals and prodigees, brain-damaged individuals, and even idiot savants and autists is juxtaposed with the evidence from correlating measures of large groups of individuals. Howard Gardner exemplifiesone who draws attention to the former and his book on frames of mind (Gardner, 1983) is a rich source for such information; but he does not try to integrate the totality of psychometric findings (most studies of dyslexia and of giftedness are psychometric by any definition of the word!). There is evidence, then, for general intelligence characterized by reasoning and problem solving - a construct which permeates almost all measurable intellectual tasks - while at the same time one may hypothesize some rather independent functions or "modules", such as written language acquisition, some visuo-spatial functions, memory and retrieval functions,etc. If Gardner wants to call such functions "intelligences", he may do so, but the conceptualization of intellectual "abilities" would be quite different from that of his original theory since these "residual" functions are much more specific and circumscribed than the Gardner idea of linguistic "intelligence", spatial "intelligence", and so forth. What is suggested here is that any one test and life-like performance will require one or more such functions as well as reasoning and problem solving skills resulting in positive correlations with other tasks. However, the independence is strong enough to provide cases having large discrepancies, say, between reading and fluid ability reasoning. This is not the right place for more than this suggestive outline of where psychometrictheorizing about intelligence may go.
Ability research and beyond Sternberg (1990) uses the metaphor of geographical maps in discussing psychometric ability research, indicating that the possibilities and limitations of this approach to intellectualperformance are similar to the kind of answers maps may give about a geographical region. He goes on to discuss other metaphors of mind, such as the computer metaphor of process analytic studies, as well as other approaches to intelligence (epistemological, biological, sociological, and anthropological). While in agreement about factor analytic type research in
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general, this paper departs somewhat from Sternberg’s view in trying to show that the concept of ability extends far beyond the traditional mapping business of factor analysis. In fact, the ability concept has been a useful and, in fact, integral parts of most other approaches taken to individual differences. The point, then, is - to keep within the metaphor - that you need a map, whatever else you are doing in a region. The map itself cannot answer but a fraction of your questions, but without it, your knowledge of what is going on at any one point does not have geographical reference. Sometimes you need a large-scale map, sometimes you need a small-scale map (see Gustafsson, 1988), but sooner or later you will need one or the other kind of map - and most likely, you have used the map without knowing it. It is unfortunate that the map designers have thought that maps are the only things worth designing and testing. Also, it is unfortunate that many mapdesingers have fought each other, thinking that there is only one right map. Likewise, map-designers have thought that everything is unchangeable, just because maps are fairly accurate for a long time, or at least, many maps are. Finally, they have made many unreasonable claims about what a map can do for you. While this is true, this does not make a map less essential -you know where you are and where you can go from there.
CONCLUSION The paper is organized so that attack and defense of the psychometric approach interchange. While accepting some and discarding other parts of this critique, the author retraces to the basic measurement definition of an ability - generalized dimensions of performance on cognitive tasks. One of the main concerns of this psychometric approach has been to partial out specific variance of each task. The summing of scores over items and over tests in the psychometric approach has the intention of doing just that, avoiding the danger of task specificity. An alternative to this approach with an equally long tradition in psychology is the area of problem-solving. Focusing interest in the solving of one or a few problems, the problem-solvingapproach tries to define parameters that influence the solution of each problem selected for study. To the extent that the problemsolvingapproach is interested in individual differences, it seeks individuality in the subjects’ approach to the specific problem. The modern version of this is the information processing approach, also called the computational approach. While this may give a detailed picture of individual differences, there is the danger that the resulting categorization of thought processes becomes too task specific. The summing of items and tests of the psychometric tradition is not a short-cut substitute for a more detailed study, but an intentional and well-founded way of arriving at generalized dimensions. There is, of cource, the possibility
Taking stock of what there is 43
that this knowledge becomes too summary and broad-pictured for the questions at hand. What is not true is that the one kind of approach tells the whole story. In the last part of the paper, the metaphor of making geographical maps was discussed, the metaphor originally introduced to explain aspects of psychometric ability research by Sternberg (1990). Let us now switch to an agricultural one. The present paper is based on the conviction that there are fruits to be harvested by cultivating old fields. While the information processing approaches undoubtedly revived the study of intelligence and produced fruits of their own, and other approaches may promise some harvest to come, there is no reason to throw away the obtained and obtainable harvest on the old field. In fact, the dishes that have been served to us, even quite recent ones, have always included many ingrediances from the psychometric field - whether the cooks were aware of it or not - and future dishes are likely to need such ingrediances as well. REFERENCES
Baron, J. (1978).The word-superiority effect:Perceptual learning from reading. In W.K. Estes (ed.), Handbook of learning and cognitive processes, Vol. 6 (pp. 131-166). Hillsdale, NJ: Erlbaum. Cattell, R.B. (1971). Abilities:Their structure, growth, and action. Boston: Houghton Mifflin. Ceci, S.J. (1990a). On Intelligence - more or less: A bioecological treatise on intellectual development. Englewood Cliffs, NJ: Prentice Hall. Ceci, S.J. (1990b). On the relation between microlevel processing efficiencyand macrolevel measures of intelligence: Some arguments against current reductionism. Intelligence, 14,141-150. Eysenck, H.J. (1986). The theory of intelligence and the psychophysiology of cognition. In R.J. Sternberg (ed.), Advances in the psychology of human intelligence, Vol3. Hillsdale, NJ: Lawrence Erlbaum. Gardner, H. (1983).Frames of mind: The theory of multiple intelligences. New York: Basic Books. Gustafsson, J.E. (1984).A unifying model for the structure of intellectual abilities. Intelligence, 8,179-203. Gustafsson, J.E. (1988).Hierarchical models of individual differences in cognitive abilities. In R.J. Sternberg (ed.), Advances in the psychology of human intelligence. Hillsdale, NJ: Lawrence Erlbaum. Gustafsson, J.E. & Undheim, J.O. (in press). Changes in broad and narrow factors of intelligence:Stability of factors, developmental relations among factors, and changes relative to verbal activities in 12-15year-olds. Journal of Educational Psychology. Hunt, E., Lunneborg, C., & Lewis, J. (1975).What does it mean to be high verbal?
44 J.O. Undheim
Cognitive Psychology, 194 - 227. Johnson-Laird, P.N. (1983). Mental models. Cambridge: Cambridge University Press. Joreskog, K.G. & Sorbom, D. (1981). LISREL V. Analysis of linear structural relationships by maximum likelihood and least squares methods. Research report 81-8. University of Uppsala, Department of Statistics. Kail, R. & Pellegrino, J.W. (1985).Human intelligence: Perspectives and prospects. New York: Freeman. Kline, P. (1991). Intelligence: The psychometric view. London: Routledge. Perfetti, C.A. & Roth, S. (1981).Some of the interactive processes in reading and their role in reading skill. In A.M. Lesgold & C.A. Perfetti (eds.), Interactive processes in reading. Hillsdale, NJ:Erlbaum. Rumelhart, D.E. (1977). Toward an interactive model of reading. In S. Dornic (ed.), Attention and performance, Vol. VI (pp. 573-603). Hillsdale, NJ: Erlbaum. Siegler, R.S. & Richards, D.D. (1982). The development of intelligence. In R.J. Sternberg (ed.), Handbook of human intelligence. Cambridge: Cambridge University Press. Sternberg, R.J. (1981).Intelligence and nonentrenchment. Journal of Educational Psychology, 73,l-16. Sternberg, R.J. (1985).General intellectual ability. In R.J. Sternberg (ed.), Human abilities: An information-processing approach (pp. 16).San Francisco: Freeman. Sternberg, R.J. (1990). Metaphors of mind. Cambridge: Cambridge University Press. Sternberg, R.J. & Gardner, M.K. (1983). Unities in inductive reasoning. Journal of Experimental Psychology, 112,1,80-116. Undheim, J.O. (1981).On intelligenceI1 A neo-Spearman model to replace Cattell's theory of fluid and crystallized intelligence. ScandinavianJournal of Psychology, 22,181-187. Undheim, J.O. (1989). On the measurement of individual differencesin intelligence and problem solving. In I.A. Bjrgen (ed.), Basic issues in psychology: A Scandinavian contribution. Bergen, Norway: Sigma Forlag. Undheim, J.O. & Gustafsson, J-E. (1987). The hierarchical organization of cognitive abilities: Resorting general intelligence through the use of linear strutural relations (LISREL).Multivariate Behavioral Research, 22,149-171. Undheim, J.O. & Horn, J.L. (1977).Critical evaluation of Guilford's structure-ofintellect model. Intelligence, 1,65-81. Undheim, J.O., Nordvik, H., Gustafsson, K., & Undheim, A.M.(in preparation). Academic achievement of high-ability students in an egalitarian education: A study of able 16-year-old students in Norway.
Intelligence, Mind, and Reasoning: Structure and Development A. Demetriou and A. Efklides (Editors) 0 1994 Elsevier Science B.V. All rights reserved.
45
Hierarchical Models of Intelligence and Educational Achievement* Jan-Eric Gustafsson University of Gtiteborg, Sweden
INTRODUCTION Two important aims of education are to disseminate knowledge and skills in particular domains, and to develop general skills of learning and thinking, even though the relative emphasis on these two categories of objectives has varied over time and different educational philosophies (Glaser, 1984; Resnick, 1987). Problems associated with attainment of these aims have been in focus in much educational research, but the research efforts have been hampered by the problem that it is difficult to distinguish the different types of educational outcomes in anything but taxonomic classifications. Assessment of knowledge and skills in particular domains is difficult, and identification of general, domain-free, skills of learning and thinking is even more difficult. The problems appear even more intricate when it is realized that acquisition and application of domain-specific knowledge and skills must be influenced by general skills, and that general skills can only be demonstrated in particular contexts. To the extent that questions about relations between general cognitive abilities and acquisition of domainspecific knowledge have at all been approached in empirical research, it would not seem that this research has been successful in clarifying the relations. One thesis of the present paper is that this is at least partly because the research has been plagued by fundamental methodological and theoretical problems, which above all concern the definition and identification of the constructs which refer to ability and performance. The paper has a strong psychometric, differential psychological, orientation. This is virtually the only approach which has tried to approach the problem of general cognitive skills and competencies. It may be noted, however, that recent cognitive science research has indicated the need to introduce concepts which refer to general skills of reasoning and higher order thinking. Resnick (1987), for example, concluded that competence in problem solving in different domains share certain characteristics, such as: 'elaborating and reconstructingthe problem in a new form; looking for consistencies * Author'saddress:Jan-EricGustafsson, Departmentof Education and Educational Research, University of Guteborg, Box 1010, S43126 Mtilndal, Sweden.
46 J.-E. Gustafsson and inconsistencies in proposed solutions; pursuing implications of initial ideas and making modifications rather than seeking a quick solution and sticking with onek initial idea; reasoning by analogy to other, similar situations.These similarities, long noted in discussions of intelligence ...and problem solving ... lead naturally to the question of whether there might not be some general thinking skills that would produce improved ability to learn across many traditional curriculum areas.’ (Resnick, 1987, p. 424). However, even though some differential psychologists have operated with concepts like “general mental ability” and ”general intelligence”, these concepts certainly have not been generally adopted (cf. Ceci, 1990).In the first part of the paper the major schools of thought in differential psychology will be described, and an attempt is made to formulate a model which allows for both general and specific cognitive competencies. This model is then applied in two small empirical studies.
GENERAL AND SPECIFIC COGNITIVE ABILITIES The development in the field of differential psychology may be described as a movement from an emphasis on general ability to an emphasis on narrow abilities. Spearman (1904a, 1904b) contributed the basic psychometric tools, such as factor analysis and models for dealing with errors of measurement, and he also showed empirically that it is possible to identify an ability broad enough to influence performance on any cognitive task. The contributions of Binet and Simon (19051, Terman (1916), and others who developed the first generation of intelligence tests demonstrated that it is possible to measure such a broad cognitive ability with relatively simple means. The notion of general mental ability has been severly criticized, however. Thurstone’s work (e.g., 1938,1947) provided an early and important basis for questioning the existence of a general factor. When Multiple Factor analysis, guided by the principle of Simple Structure, was applied to large observational materials, overwhelming support was obtained for the position that several narrow abilities are needed to account for individual differences in intellectual performances. For quite some time after Thurstone‘s pioneering research, the major line of development in ability research was characterized by replication and extension of the Primary Mental Abilities (PMAs). Carroll (1989) lists no fewer than 400 studies in this vein, which have resulted in a seemingly endless proliferation of factors of ability. Thus already in 1951, when French presented the first survey of factor analytic findings, the list encompassed some 60 factors of ability and achievement. Later reviews (e.g., Cattell, 1987; Ekstrom, French & Harman, 1976; French, Ekstrom & Price, 1963; Guilford, 1967; Guilford & Hoepfner, 1971; Horn, 1977; Pawlik, 1966) have subtracted some of the factors on this list, but have also
Hierarchical models of intelligence 47
added quite a few. It seems, however, that there is disenchantment with the PMAs. Several critics have pointed at the limited utility of Multiple Factor analysis for describing the structure of ability. Humphreys (19621, for example, argued that the basic problem is "... the tendency to think of the factors as basic or primary, no matter how specific, or narrow or artificial the test behavior may be that determines the factor". In the limit, each factor is identified by a set of parallel tests, which implies that factor analysis identifies as many dimensions as there are types of test items. Undheim (1981) expressed a similar point of view in even stronger words: "... the widespread application of multiple factor analysis in research on abilities seems to have carried factor analysis far beyond its descriptive and conceptual limitations as a research tool, resulting in an ever increasing number of factors of 'the mind"' (p. 251). In practical applications too the value of the PMAs has been questioned (e.g. Thorndike, 1985). Differential aptitude batteries seem not to have differential predictive power for achievement in different subject-matter areas, for example (Carroll, 1982; McNemar, 1964). The research on aptitude-treatment interactions (AT11 is another example of a field in which narrow ability concepts have failed to live up to expectations. In their large review of ATI-research Cronbach and Snow concluded: 'whereas we had expected specialized abilities rather than general abilities to account for interactions, the abilities that most frequently enter into interactions are general. Even in those programs of research that started with specialized ability measures and found interactions with treatment,the data Seem to warrant attributing most effects to a general ability.' (Cronbach & Snow, 1977, pp. 496-497).
These demonstrations of the ubiquitous importance of general ability indicate that the position of narrow abilities may have to yield for research approaches which rely on the concept of general mental ability. It would, however, be desirable to achieve some kind of integration between the two positions. Such possibilities are offered by the hierarchical approach, which allows simultaneous consideration of general and specific abilities. Below a brief review is made of the hierarchical approach to describing the structure of abilities. Hierachical models of the structure of intelligence The hierarchical approach to the structure of intelligence certainly is not new, and in the British research on intelligence it has been the dominating one. Already Spearman (1927) claimed,to be employing such an approach, but it was not until the contributions by Burt (1949) and Vernon (1950) that more full-grown hierarchical models were presented. The impact of these models on theories and
48 J.-E. Gustafsson
methods in differential psychology has been rather limited, however. Since about the mid-70s there has been a rersurgence of interest in broad factors of ability, primarily as a function of disenchantment with the results obtainable with the PMAs. As an alternative "... theorists gradually adopted a hierarchical model of abilities which, while allowing for both broad and narrow abilities, clearly emphasized the role of general ability." (Lohman, 1989, p. 334). The most popular hierarchical model is the theory of fluid and crystallized ability developed by Raymond B. Cattell and John Horn. It may be noted, however, that important contributions of formulation, dissemination and development of the theory has been made by other researchers as well (e.g., Cronbach, 1984; Snow, 1980,1981). The theory was first formulated by Cattell (1943) who argued that there is not one general factor of intelligence, but two. However, clear empirical support was not demonstrated until considerably later (e.g., Cattell, 1963; Horn, 1968; Horn & Cattell, 1966). Through factorization of tests or factors representing primary abilities, Cattell and Horn have identified several second-order factors, or broad abilities. The two dimensions of most central importance in the Cattell and Horn formulation are fluid intelligence (Gf)and crystallized intelligence (Gc), and the whole theory is often referred to as Gf-Gc theory. Both these dimensions reflect the capacity for abstraction, concept formation, and perception and eduction of relations. The Gc dimension, however, is thought to reflect individual differences associated with systematic influences of acculturation, and is central in tasks of a verbal-conceptual nature. The Gf dimension is thought to reflect effects of biological and neurological factors, and factors such as incidental learning. This dimension is most strongly shown in tasks that are either new or very familiar to the examinees. In the early formulation of Gc-Gf theory Horn and Cattell (1966) identified some three or four additional second-order factors: General Visualization (Gv), General Speediness (Gs)and General Fluency (Gr). In later research reported by Horn and collaborators (e.g., Horn, 1978,1980,1986,1989; Horn & Stankov, 1982; Stankov & Horn, 1980) the list of second-order factors has, however, been considerably expanded, and a hierarchical model based on levels of functions has been proposed. The Horn (1986) model organizes the abilities within an information processing hierarchy with levels of sensory reception, associational processing, perceptual organization and relation eduction, which model bears strong resemblance with a hierarchical model proposed by Burt (1949) model (cf. Horn, 1978, p. 115). The factors of Gc and Gf are found at the level of relation eduction. The level of perceptual organization provides input to the Gf-Gc processes, and includes Gv, and a factor of General auditory (Ga) competence, reflecting capacities for dealing with the complexities of sound. This level also includes the dimension of Gs. The level of association processing includes two dimensions representing memory
Hierarchical models ofintelligence 49
capacities. One of these, short-term acquisition and retrieval (SAR), reflects the capacity to store and retrieve information over such short periods of time as a minute or two,while the other, tertiary storage and retrieval (TSR), identifies an ability to retrieve information stored a considerable time before the measurement. At the lowest level - the one of sensory reception - one factor represents the acuity of visual sensory detectors (vSD), and another represents the acuity of auditory sensory detectors (aSD). Cattell (1971,1987)also has developed the Gf-Gc theory into a rather elaborated hierarchical model which uses concepts quite different from those used by Horn. The so called ‘Triadic‘theory includes abilities of three different kinds. “General capacities” (e.g., Gf, Gs, and Gr) ”are limits to brain action as a whole, and appear as general factors across all cognitive performances’’(Cattell, 1987, p. 366).Another class of abilities is referred to as ‘provincial powers’ and correspond to sensory area factors, such as visualization, auditory structuring ability, and motor and kinesthetic abilities. The third class of abilities is referred to as ‘agencies’. These “... take their shape largely from cultural and general learning, and are the agencies through which fluid intelligence and the powers express themselves.” (Cattell, 1987, p. 366). The agencies largely correspond to primary abilities. According to the triadic theory ”... any actual instance of cognitive behavior is reduced ... to the joint action of three distinct types of ability.... The triadic theory is thus a statement both about the specific nature of each of the three kinds of components, and about their tendency commonly to combine in joint action in any actually observed behavior.” (p. 366; emphasis in original). It would carry too far to analyze in detail the differences and similarities between the different formulations of hierarchical theories. These models represent integrations of results from many studies and they have not been tested in full in any single empirical study. The models should, therefore, be conceived of as alternative conceptual frameworks to be developed in further research. During the ‘80s a series of studies has been conducted in which confirmatory higher-order factor analytic techniques have been used to compare different models of the structure of abilities, with a special emphasis on hierarchical models (Gustafsson, 1984,1988,1989; Gustafsson, Lindstrbm & Bjsrck-Akesson, 1981; Undheim & Gustafsson, 1987; Undheim, 1981). This research has resulted in a model which comes close to the hierarchical model proposed by Vernon (19.501, but which is also close to the Cattell-Horn model. In brief summary the model has the following main components (see Figure 1): At the lowest level there are abilities similar to the PMAs identified within the Multiple Factor tradition. The intermediate level identifies factors which closely correspond to the broad abilities within the Cattell-Horn model. Among the handful of factors identified at this level, three seem to be of particular importance. Fluid intelligence (GO, which subsumes primaries such as Induction (I), General
50 J.-E. Gustafsson
Reasoning (R), and Cognition of Figural Relations (CFR); Crystallized intelligence (Gc),which is most strongly shown in the primary factors Verbal Comprehension (V) and Cognition of Semantic Relations (CMR); and General Visualization (Gv), which is loaded by primary abilities such as Visualization (Vz), SpatialOrientation (SR) and Flexibility of Closure (CO.
Figure 1. A hierarchical model
At the highest level the model includes a factor of general intelligence (g), on which all the broad abilities have loadings. A rather striking result, however, is that the loading of Gf in g consistentlyhas been found to be unity, which implies
Hierarchical models of intelligence 51
that the g-factor is equivalent with fluid intelligence. This hierarchical framework is compatible with most previously presented models of the structure of intelligence, even though these tend to be limited by a focus either on narrow abilities (e.g. Thurstone and Guilford) or on a single broad ability (e.g. Spearman).Among the previous models it seems that only the Vernon model is a full-fledged hierarchical model with factors ranging in breadth from a completely general factor down to very narrow factors, which account for performance in very limited domains. It must be observed, however, that the threelevel structure displayed in Figure 1 is quite arbitrary in the sense that the order at which a particular factor appears varies from study to study: depending upon how densely or sparsely a domain is sampled as many or as few levels as is wished may be obtained. So far hierarchicalmodels have mainly served the function of taxonomic systems which have helped reduce the complexities of the results obtained in the research on cognitive abilities. Use of hierarchical models for purposes of classification and description of abilities and tests certainly is worthwhile but there may be reason to take one step further and formulate a stronger version of the hierarchical approach. In a strong hierarchical model the relations between factors at the different levels are actually taken into account and the influence from higherorder factors is partialled out from the lower-order factors. In any higher-order (HO) model fitted with exploratory or confirmatory factor analysis the proportion of variance in the observed variables accounted for by the factors at the different levels may be computed (Schmid and Leiman, 1957). Such a decompositionof the observed score variances produces a pattern in which the g-factor accounts for variance in all the observed variables, and factors at lower levels in the hierarchy account for variance in successively smaller classes of observed variables (see Gustafsson, 1988, pp. 56-57). This transformation thus makes it clear that higher-order factors are not abstract constructions at a larger distance from the observed variables; a higher-order factor simply influences performance over a broader domain than does a lower-order factor. The strong hierarchical model thus implies that performance on any task is influenced by several sources of variance of varying degrees of generality. According to this approach task performance thus typically is factorially complex, and performance on any task always reflects a mixture of general and specific cognitive factors. In order to understand the factors affecting task performance it is thus necessary to achieve a decompositionof task variance in these components of differentdegrees of generality. However, technical as well as conceptual reasons make the ordinary HO-approach to hierarchical model fitting less than perfectly suited for achieving such decompositions. In the first study to be reported here an alternative approach to hierarchical variance decomposition is, therefore, investigated.
52 J.-E. Gustafsson
STUDY I: DECOMPOSING TASK VARIANCE IN STRONG HIERARCHICAL
MODELS What is needed is a technique which directly and in one step specifies the relations between latent variables (factors)of different degrees of generality and observed variables. In principle it is easy to specify a hierarchical confirmatory model with a set of orthogonal factors, some of which are related to many observed variables, and some of which are related to few observed variables. This type of model thus treats a lower-order latent variable as nested within the higher-order latent variable, and it will be referred to as an orthogonal model with nested factors (NF-model, see also Gustafsson & Balke, in press). Such models are close to the hierarchical group-factor techniques developed and used in the British research on abilities (e.g., Burt; 1944, Vernon, 1961).These models have not been much used in ability research elsewhere, however, because of a reputation for being less than perfectly objective. The hierarchical groupfactor analysis is carried out by assessing loadings on a general factor first, and then analyzing residual correlations in groups of tests. However, it is well known that the nature of the general factor may change with the composition of the test battery, and if the general factor changes, the residual factors change as well. These models thus are afflicted by the same problem as is principal factor analysis when used to identify the general factor (cf. Jensen, 1982).The criticism of these approaches for being arbitrary and subjective(e.g., Horn, 1989) seem quite correct. However, use of confirmatory methods and reliance on the previously established identity between Gf and g may make it possible to identify an invariant general factor (GI in NF-models. In the study to be reported below NF-models are fitted to a rather large test battery. In order to investigate the issue of invariance of the G-factor a model is fitted to a sub-set of the variables as well. For the data to be considered here, a higher-order model with factors at three levels has previously been fitted (Gustafsson,1984).So the study also allows comparisons between the HO- and NF-approaches to formulating hierarchical models.
Method The data to be analyzed here are part of a larger study designed to investigate structural issues of intelligence (Gustafsson et al., 1981; Gustafsson, 1984). During 1980 a sample of students (N=981)in the 6th grade (12-year-olds)was given a battery of aptitude and achievement tests. At different occasions these subjects have since been followed up, but the present study will only consider the first wave of measurement. The test battery comprised 13aptitude tests and 3 standardized achievement
Hierarchical models ofintelligence 53
tests and was designed to measure the broad abilities Gc, Gf and Gv, along with some 10 narrow factors corresponding to Thurstone's primary mental abilities and to factors in the Guilford model. The aptitude variables are described in great detail elsewhere (Gustafsson et al., 1981; Gustafsson, 1984), and summary information about the tests is presented in Table 1.In the previous work a rather elaborate hierarchical model with factors at three levels was fitted for the complete set of variables, with some of the tests divided into half-tests. On the basis of this model hypotheses have been formulated about which factors should be included in an NF-model (see Table 1; and consult Gustafsson and Balke, in press, for an extended discussion). Table 1 Aptitude variables included in the analysis Test name
Label
Opposites - odd items Opposites - even items Swedish Achievement English Achievement Auditory Number Span Auditory Letter Span Mathematics Achievement Number Series I1 Letter Grouping I1 Raven - odd items Raven - even items Metal Folding - odd items Metal Folding - even items Group Embedded FiguresTest Hidden Patterns Copying Card Rotation Part I Card Rotation Part I1 Disguised Words Disguised Pictures
op-0 Op-E Sw Ach Eng Ach ANS ALS Ma Ach NS LG Ra-0 Ra-E MF-0 MF-E GEFT HP co CR-I CR-I1 DW DP
Expected factors G G G G G G G G G G
G G G G G G G G G G
Gc' Gc' Gc' Gc' Gc' Gv' Gv' Gv' Gv' Gv' Gv' Gv' Gv' Gv' Gv' Gv'
V'
v
Ms' Ms' Num Ach Num Ach' CFR'
CFR' VZ' VZ' Cf Cf
S' S' S' CS' CS'
Results The modelling of the aptitude variables'has been done in such a way that a
54 J.-E. Gustafsson
sequence of increasingly complex NF-models has been fitted. Table 2 presents results from statisticaltests of the goodness-of-fit of the models, along with various fit indices (GFI, AGFI, PGFI;see Mulaik, James, Van Alstine, Bennett, Lind & Stilwell, 1989). In these, and all other analyses reported in this paper, the matrix of product-moment correlationshas been analyzed with the LISREL VI program (version 6.13, included in the SPSS-X system under VM/CMS).
Table 2 Results from tests of fit of NF-models for the aptitude variables
Model Factor included 1 2 3 4 5 6 7 8 9
10
G +Gv' +Gc' +V' +Ms' +NumAch'
+CFR' +VZ'
+s'
+CS'
X2
3437.90 2458.26 1929.27 1808.59 1599.63 1507.80 917.65 519.29 385.37 292.43
Fit of model df AGFI 170 160 156 155 154 153 152 151 150 149
.616 .699 .763 775 .795 .803 .860 .916 ,940 ,953
GFI
PGFI
.690 .771 324 .834 .850 .856 399 .939 .957 .967
.559 .587 .612 .616 .623 .624 .651 .675 .684 .686
Change df
x2
979.64 10 528.99 4 120.68 1 208.96 1 91.83 1 590.15 1 398.36 1 133.92 1 92.94 1
Model 1includes only one factor of ability (G)and as may be seen in the Table the fit of this model is quite poor. In Model 2 Gv' is included as another, orthogonal, factor. This factor is assumed to influenceperformance on the 11tests hypothesized to measure Gv' (see Table 1).Since it is assumed that the two half-tests of Mental Folding have the same loading on Gv' Model 2 has 10 degrees of freedom less than Model 1. However, the value of the chi-square test-statistic is almost 1000 units less than for Model 1, which shows that the introduction of Gv' does cause a very highly significant improvement of fit. In Model 3 a third factor (Gc') is introduced in such a way that it is assumed to be orthogonal to the other two factors. The Gc'-factor is hypothesized to be related to 5 tests (with equivalence restrictions imposed for the Op half-tests), and it does effect a substantial improvement of fit. In Models 4 to 10 the narrow factors assumed to influence two tests each are successively introduced under the assumption of orthogonality of factors. In order for these models to be identified it is necessary that the factor loadings of the two variables are constrained to be equal. These factors therefore consume 1 df each. As may be seen in Table 2 the factors are all very highly significant.
Hierarchical models of intelligence 5s
However, when attempts were made to introduce the Cf-factor (see Table 1) the model failed to converge, which indicates that it is not possible to include both Gv' and Cf' in the model. With the exception of Cf all the factors hypothesized in Table 1 may thus be identified in the IW-model. It may also be noticed that the fit of the most elaborate NF-model (Model 10) is quite good (seeTable 2). The value of the chi-square teststatistic is, of course, too high according to traditional criteria, but even for this relatively large sample the chi-square value is only about twice as large as the degrees of freedom, which may be taken to indicate an acceptable level of fit (cf. Loehlin, 1987).The values of the different Goodness-of-Fit Indices also indicate a good fit between model and data.
Table 3 Loadings of the aptitude variables on the ability factors Test
G
Gv'
Gc'
V'
Ms'
Num
CFR
Vz' S'
Cs'
Ach'
OP-0 Op-E Sw Ach Eng Ach ANS ALS Ma Ach NS LG Ra-O Ra-E MF-0 MF-E GEFT
HI? co CR-I CR-I1 DW DP
.54 .53 .70 .64 .27 .35 .73 .74 .70 .53 .57 .48 .49 .56 .54 .51 .42 .48 .30 .21
.44 .44 .64 .49
.46 .46 .65 .65
.18 .06 .09 .33 .33 .36 .50
.35 .35
.70 .70 .66 .66
.54 .38 .38 .12 .20
.63 .63
.54 .54
Table 3 presents the loadings of the aptitude variables on the latent variables in this model, which will be referred to as the Half-test model. The values presented are standardized factor loadings, and since all latent variables are orthogonal to one another the amount of variance explained by a factor is given by the square
56 J.-E. Gustafsson
of the loading. The G-factor accounts for variance in every test. However, even though the G-factor does have a relation with every kind of intellectual performance measured by the test battery, the strength of the relationship varies greatly. High relations are obtained with the Inductive reasoning tests Number Series (.74)and Letter Grouping (.70).The standardized achievement tests are also highly correlated with the G-factor, and particularly so the Mathematics Achievement test (.73) and the Swedish Achievement test (.70).To interpret these numbers correctly it must be noted, however, that the estimates are influenced by the reliability of the test. The standardized achievement tests are long ,and therefore reliable, while some of the other tests are quite short and unreliable. This is, of course, in particular true for the half-tests, in which the errors of measurement do account for a large proportion of variance. For other tests the relationship with G is very low, even when the tests are highly reliable. For example in the Disguised Picture test only about 4 per cent of the variance is accounted for by the G-factor, and in the other test designed to measure the Speed of Closure factor (Disguised Words) only about 9 per cent of the variance is due to G. For the other spatial (or Gv-) tests in the battery the G-factor accounts for between 20 and 30 per cent of the variance. There are quite a few spatial tests in the battery, and they are all influenced by the broad spatial Gv’-factor. The Gv’-factoraccounts for up to about 30%of the variance in some tests (i.e., Hidden Patterns, GEFT) but only a few per cent of the variance in some tests (i.e., DW and DP). The Gc’-factoraccounts for variance in the school achievement variables and in tests with verbal content. The highest loading on Gc’ is obtained with Sw Ach, but Eng Ach and the Opposites halftests have quite high loadings as well. This indicates that Gc’ as it is defined here reflects verbal-educational knowledge (cf. Undheim, 1981). The results presented above were obtained from analyses of the set of 20 variables included in the original analysis. However, several of the tests were entered as half-tests, and it would be more natural to fit an NF-model to the fulllength tests. A model has, therefore, been fitted which encompasses 16 variables (Full model). In order to illuminate the issue of factorial invariance, another model has been fitted as well. This model (Reduced model) only includes 7 observed variables, namely those selected to represent Gf, Gc’, and Num Ach’. The purpose is, of course, to see if the parameter estimates in the Reduced model are the same as those in the Full model. The two models were fitted as NF-models, with the relevant factors from the original NF-model included. The Full model encompasses 6 latent variables (G, Gv’, Gc‘, Ms’, Cs’, and Num Ach’). Although the chi-square test was highly significant the fit of the model must be judged acceptable (chi-square=230.97,
Hierarchical models of intelligence 57
df=89, p< .OO,GFI=.971).The Reduced model includes three factors (G, Gc', and Num Ach') and it has an excellent fit (chi-square=14.74, df=9, pe .lo, GFI=.996). Table 4 presents the standardized loadings of the Full and the Reduced models. If the results in the Full-model are first compared with the estimates from the Half-test model (see Table 31, it is found that the estimates are quite close for all the variables that are included in both models. As may be expected, tests entered as half-tests in the Half-test model obtain higher estimates in the Full model. This comparison thus indicates that identical variables do get invariant estimates in models which are partially different. The Reduced model contains much fewer variables than does the Full model. In spite of this, however, the results presented in Table 4 show that the loadings estimated within the Reduced model do not in any case deviate more than .02 from those estimated within the Full model. This is thus a striking demonstration that the loadings estimated within an NF-model are invariant from one model to another. Table 4 Standardized loadings for two NF-models for full-length tests
Full model G
OP Sw Ach Eng Ach ANS ALS Ma Ach NS LG Ra MF GEFT HP
co
CR DW
DP
.60 .73 .66 .28 .36 .74 .75 .70 .60 .53 .58 .55 .53 .49 .33 .22
Gv'
Gc'
Ms'
Reduced Model Cs' NumAch
.47 .61 .49
G
Gc' NumAch'
.60 .73 .65
.47 .60 .50
.72 .75 .70 .60
.22
.63 .63 .20
.36 .36
.10
.38 .38 .49 .53 .39 .12 .22
.53 .53
.38 .38
58 J.-E. Gustafsson
Discussion The NF-model fitted to the test battery in the present study contains a smaller number of factors than the previously fitted HO-model, which makes it a more parsimonious model. In addition, the NF-model has the advantage of allowing more straightforward interpretations. In this model the G-factor is easily seen to be general in the sense that it influences performance on each and every aptitude variable. In the HO-model, in contrast, the general factor stands in a more remote and indirect relationship with the observed variables. Models of ability which include a general factor have been criticized for defining a non-invariant G-factor, the nature of which changes with the composition of the test battery. However, the results presented here indicate that the NF-models define a general factor which seems to be almost perfectly invariant over the three models (i.e., the Half-test model, the Full model, and the Reduced model), the largest of which contains 20 variables and the smallest of which only includes 7 variables. The reason for this invariance is, of course, that the model is specified without any residual Gf-factor. This causes the G-factor to coincide with the Gf-factor, and to be as invariantly defined as any latent variable within a regular HOanalysis. It must be noted, however, that if an NF-model is fitted to a set of variables and such a constraint is not imposed the general factor will be as poorly defined as in a principal factor analysis. The analyses presented here thus show that it is possible to decompose the variance in performance on a task, or on a class of tasks, in components of variance from sources of different degrees of generality. The G-factor affects each and every task; the broad factors Gv’ and Gc‘ each influence a rather broad range of tasks; and there are factors which only influence a few tasks. According to this model each test (or task) reflects several different abilities. For the Opposites halftests, just to take one example, there are four separately identifiable sources of variance: the G-factor (29%),the Gc’-factor (19%),the V’- (and 0p’-) factor (21%), and error (30%). This complexity of the observed variables indicates that it is necessary to adopt a multivariate approach to measurement (cf. Gustafsson, 1989).It also indicates that efforts to induce and understand changes in learning and performance may be analyzed from a partially new point of departure. In order to illustrate the latter line of thinking another study will be presented briefly.
STUDY 11: SOURCES OF VARIANCE IN MATHEMATICS ACHIEVEMENT The dimensional complexity identified in test performance in the previous study is, of course, not only to be found in psychological tests: performance on
Hierarchical models of intelligence 59
any cognitive task may be analyzed in terms of multiple sources of variance of varying degrees of generality (cf. Gustafsson, 1988, pp. 58-65). These sources of variance in performance are, of course, interesting from an educational point of view since some represent domain-specificsources of variance and others represent general, domain-free, sources of variance. The purpose of the present study is to illustrate a possible approach to such a decomposition of individual differences in mathematics performance, and to relate it to educational variables. The data to be analyzed here are part of the newly started National Evaluation program in Sweden. In 1989 data were collected from some 3500 pupils in grades 2 and 5. Several different subject-matterareas were covered and a rather extensive set of tasks was given to each pupil, with a total testing time that in grade 5 exceeded 20 lessons. In mathematics alone more than two hours was used to present the pupils with a wide range of tasks (Ljung & Pettersson, 1990). In addition data was collected from several other sources: the class teacher was asked about teaching practices; the school was described; and various environmental variables were collected, just to mention a few of these additional sources of information. A subset of the sample (some 500 pupils in each grade) also was given a set of inductive reasoning tasks in order to measure Gf (Westerlund & Ullstadius, 1991). A part of this informationwill be analyzed here in order to illustrate the potential benefits of a hierarchical decomposition of variance to separate domain-specific and domain-general influences on performance. It must be observed, however, that the analysis is very preliminary and tentative and that the study should be taken more as a methodological excercise than a substantively oriented contribution.
Method The analysis will focus upon arithmetic only, and even here a subset of the items will be focussed upon. In the first step models will be fitted for these items, which models are then elaborated to include the Gf-factor as well. The latent variables within these models are in the final step of the analysis employed as dependent variables in an analysis using teacher reports of frequenciesof teaching activities as independent variables. Variables The mathematics tasks comprised a very large number of items (Ljung & Pettersson, 1990).For the purposes of the present analysis items measuring three aspects of mathematics competence have been concentrated upon. The first type
60 J.-E. Gustafsson
of items are Problem Solving (PS) items. There are several types of problem solving items, such as relatively simple everyday problems, multistep problems, problems requiring conceptual understanding, and problems which require creative solutions. These items are all word problems, and an example is: From 1896 there have been Olympic Summer Games every fourth year. In 1916,1940 and 1944 the games were cancelled, because of the World Wars. How many Olympic Summer Games have taken place up to and including 1988? Another type of item aims at investigatingthe pupils’ grasp of number concepts (Number Sense, NS). There were several different types of items in this category, such as the following: Eighthundredninety crowns is twice as much as 425Cr 445Cr 465Cr 485Cr 505Cr Which whole number is closest? 4.8 = 8.73 = +
Make an estimate and put the decimal point in the right position 0.75 + 12.40 + 9.55 2270
... The third type of items involves arithmetic operations (Numerical Calculations, NC). Below some examples of items in this category are presented: What is
3 080 + 14 120 =
... Which number is missing? Write the number on the line so the result is correct 12=7+ 21 / =3 ...
Within each of these three categories the items were randomly allocated to three sub-scales. In this way 9 scales were constructed (PSI-PS3,NSI-NS3, and NCI-NC3). The PS-scales contained 6,12 and 6 items, respectively; the NS-scales consisted of 5,4 and 3 items, respectively; and the NC-scales contained 7,7 and
6 items.
Hierarchical models of intelligence 61
As has already been mentioned a sub-set of the pupils was also given a set of non-verbal inductive reasoning tasks. Among these were 28 Series items, in which figural, numerical or verbal series problems were presented. There were also 26 items of a type inspired by the so-called Bongrad problems described by Hofstadter (1979).In such items there are two groups of six elements each. The elements in each group share a characteristic, which also forms a contrast between the two groups. In a simple task of this kind one of the groups may, for example, consist of squares and the other group by circles. The present version of these items, which are called Opposed Groups, are constructed as multiple-choice items. A more detailed presentation of the Series and Opposed Groups tests is given by Westerlund and Ullstadius (1991). For the present study the two item types were scrambled and randomly allocated to four sub-scales with 13 or 14 items each. These sub-scales (Gfl-Gf4) will be used as observed variables in the models. In a questionnaire the class teachers were, among other things, asked to provide estimates of the frequency of different kinds of teaching activities. From this questionnaire two questions have been selected, namely: How often do the pupils in your class work with: Mental arithmetic (in groups and/or singly)? Estimates (in groups and/or singly)? For both these questions the response alternatives were: Practically every lesson, once a week, once a month, rarely or never. The first variable will be called MentArith and the second variable Estimates. Subjects The mathematics items were administered to 164 grade 5 classes with in all 3504 pupils. However, because data was collected at several occasions there was some attrition. Thus, some of the analyses reported here are based upon a sample of 3421 pupils. Most of the analyses are, however, conducted on a smaller sample (N=488). This is because the Gf-tests were only administered to some 20 5th grade classes. Analyses presented by Westerlund and Ullstadius (1991)indicate, however, that this sub-sample is reasonably representative. All the models which include the Gf-variables have been conducted on the smaller sample. Results In the first step of the analysis of data a sequence of models has been fitted for the mathematics items. An obvious traditional model for these data is a model with three correlated factors (i.e., I%, NS and NC), each indicated by three sub-
62 J-E. Gustafsson
scales. Such a model fits quite well, particularly after a relation is allowed between the NC-factor and the NS3-scale (chi-square= 112.2, df=21, p < .OO, GFI=.993, N=3421). The model (the Oblique model) and estimates of parameters are presented in Figure 2.
.78
+ NS 1
i
NS
+ NS3
+ NCI
NC
NCI
,
i NG
Figure 2. The Oblique model for the mathematics scales
As may be seen in the Figure 2 the loadings of the scales on the factors tend to be high and even. The only exception is the NS-factor, which tends to have lower loadings. The reason for this is that there were few items in all these scales, so the amount of error variance is large. There is little doubt, however, that all the hypothesized factors are identifiable. However, the factors are very highly intercorrelated. The correlations range between .74 and .90 which indicates the presence of a factor common to all three aspects of mathematics performance. Another model has, therefore, been fitted in which a general mathematics
Hierarchical models ofintelligence 63
factor (G-MATH) has been introduced, along with orthogonal specific factors, to represent the different aspects of mathematics performance. The modelling started with the GMATH factor after which the specific factors were successively added. Addition of the NS- and NC-factors improved fit considerably, but there was no need to introduce a specific PS' factor. This indicates that the Problem Solving factor coincides with the G-MATH factor, in the same way that Gf coincides with the general cognitive factor. The model, which will be referred to as the NF-Math model, is presented in graphical form in Figure 3.
Figure 3. The NF-Math model for the mathematics scales
This model has a very good fit (chi-square=67.9, df=18, p c.00, GFI=.996, N=3421). The G-MATH factor has strong relations to almost all the sub-scales, and particularly so to the PS- and NC-scales, where it accounts for some 50 to 60
64 J.-E. Gustafsson ?6 of the variance. The amount of variance accounted for by G-MATH is lower in the NS-scales (around 25 %), but the contribution from this factor still tends to be higher than the contribution from the NS'-factor. For the NC-scales it is also true that the amount of variance contributed by the NC-factor is considerably smaller than the amount contributed by the G-MATH factor. Thus, while the Oblique model emphasizes the differentiation of the three aspects of mathematics competence, the NF-model identifies general mathematics competence as the major source of individual differences in all the different areas of performance, even though it also allows for the more specific sources of variance.
i
Figure 4. The NF-Gf model for the mathematics scales
Hierarchical models of intelligence 65
The G-MATH factor is likely to be complex in its turn, however. It is reasonable to assume that a part of the variance in this factor is due to a specific mathematics factor,and that another part is due to general cognitive ability, which is important in other areas as well. In order to redefine the G-MATH factor to represent only the specific mathematical component (G-MATH) a model has been constructed which includes the 4 Gf-scales as well. This model, which will be called the NFGf model, has been estimated from the sub-sample with scores on the Gf-tests. It has a general factor (GI, which has relations to all the observed variables, in adition to the three factors in the NF-model in Figure 3. The parameter estimates presented in Figure 4 show that G-MATH and G are equally important as sources of variance in the PS- and NC-scales, with loadings around .50. It is interesting to note that in the NF-Math model G-MATH was found to account for about 50% of the variance in the PS-scales. In the NF-Gf model this variance is equally distributed over the two components. The G-factor accounts for a smaller amount of variance in the NS-scales (510%)but again the contribution is quite similar from G-MATH and G. The contribution from the specific factors NS’ and NC’ is virtually indentical in the NF-Math and NF-Gf models. In the next step of the analysis instructional variables have been related to the latent variables within the three different models presented above. These models have been estimated for the sub-sample with scores on Gf-tests, and all the models have been fitted as individual level model. From a statistical point of view this is, of course, incorrect since the instructional variables are class-level variables. It would, in principle, be possible to fit a latent-variable model at the class- and individual levels simultaneously using techniques recently developed by MuthCn (1991). However, since the purpose of the present study only is to illustrate implications of different ways of conceptualizing and modelling differences in performance, the complexities involved in such multilevel modelling have temporarily been put aside. Table 5 presents correlations between the instructional variables and the latent variables within each of the three models. Only correlations which are significant according to the LISREL-analysisare presented, but it must be remembered that these significance tests are likely to give inflated values. In the Oblique model the MentArith variable has a relationship with all latent variables, and the Estimates variable has a rather substantial correlation with the NS-factor. In the NF-Math model the pattern of correlations with the MentArith variable is quite different for some of the variables: There is no correlation at all with the NSfactor and the correlation with NC’ is stronger than it was with the NC-factor. The correlation between Estimates and NS’ is even stronger in this model than it was in the Oblique model. In the NF-Gf model, finally, the results are quite similar to those obtained in the NF-Math model, except that the relation between
66 J.-E. Gustafsson
MentArith and G-MATH' is stronger than the relation between MentArith and G-MATH. The results obtained with the three models appear in certain respects to be quite different. The differences in pattern of results seems, however, to be explainable. In the Oblique model a correlation is found between NS and MentArith, but in the other models there is no relationship between MentArith and NS. The reason for this is, of course, that in the Oblique model the G-MATH variance is confounded with the NS' variance, which causes the relation between MentArith and G-MATH to appear as a correlation between NS and MentArith in the Oblique model. No such relation is expected, however, so in this respect the results from the two NF-models do make more sense than the results from the Oblique model.
Table 5 Relations between educational variables and latend variables within three models for mathematics achievement NF - Math
Oblique
Ment Arith Estimates
PS
NS
NC
.19
.13 .40
.29
G-Math NS' .17
NF - Gf NC' .37
.65
G
G-Math' NS' NC' .25
.36 .66
In some cases the residualized latent variables do give considerably higher estimates of correlations than do the unresidualized variables. This is true for the relationship between NS' and Estimates (.65)as compared with the relationship between NS and Estimates (.40);for MentArith and NC (.29) versus MentArith and N C (.37); and for MentArith and G-MATH (.17) versus MentArith and GMATH (25).The reason for the higher correlations with the residualized factors is that in these variables a part of the irrelevant variance has been partialed out. Thus, the reason why MentArith accounts for twice as much variance in G-MATH' than in G-MATH is that the Gf-factor accounts for about 50 % of the common variance in G-MATH. However, it must be remembered that such simple relations only hold true when there are no relations with the higher-order factors. In the present case there were no such relations, and none were expected, but in other situations there may be both positive and negative relations between instructional variables and the more general sources of variance.
Discussion The sequence of models presented here demonstrates that sources of variance in mathematics performance can be analyzed and conceptualized in models with
Hierarchical models ofintelligence 67
different degrees of complexity. In the Oblique model (Figure 2) the variance in performance on the NC1-tasks, for example, is accounted for in terms of one NCfactor (66%)and error (specificityand random error; 34%).In the NF-Math model the variance in the NCI-scale is decomposable into one component due to GMATH (52%),one component due to NC‘ (19%)and error (29%).In the NF-Gf model, finally, the variance in the NC1-scale is decomposed into a G-component (21%), a G-MATH component (31%),an NC’ component (14%)and error (34%). It cannot be claimed that any of these models is more correct than the others. However, the models do have quite different conceptual implications.The results obtained when instructional variables are related to the different latent variables also show that the empirical pattern of results is quite different in the different models. It is of course not possible to draw any general conclusions from the present, admittedly very limited, study. It would appear, however, that the pattern obtained from the NF-Gf model is the most reasonable and interpretable one. This model identifies a relatively strong relationship between MentArith and NC’ which might be interpreted as a possible instructional effect. There is also a weak relationship between G-MATH and MentArith. Such a relation may appear for many different reasons: there may be a direct instructional effect; teachers with advanced mathematics pupils may use this instructional approach more than others; or it may appear because general teacher experience causes both better pupil performance and higher frequency of use of mental arithmetic. This model also identifies a strong relationshipbetween use of Estimates in the teaching and the NS-factor, which may be hypothesized to be another direct instructional effect. It is, of course, important that the relations identified within a model are reasonable and interpretable. Equally important, however, is the absence of relations which are not hypothesized or reasonable. The NF-Gf model demonstrates that there is no relationship between G and the instructional variables, nor is such a relationship expected in the present data. According to the NF-models there is no relationship between MentArith and NS’ while the Oblique model says that there is a correlation between these variables. Again, it seems that the absence of relation is a more trustworthy and reasonable result.
GENERAL DISCUSSION The major message of the present paper is that individual differences in cognitive performance should be understood in terms of a several sources of variance, some of which are broad and some which are narrow. Even though no conclusive proof has been presented that this decomposition can be effected in a correct way in actual data, the empirical results are encouraging. It does seem possible to identify an invariant general factor in NF-models through inclusion
68 J.-E. Gustafsson
of Gf-measures in the model, and the decompositionof mathematics performance into a general mathematics factor, close to problem solving, and more specific factors also seems reasonable. The results imply that the measures employed to assess educationalachievement invariably confound more narrow, domain-specific, effects with general, domainfree, effects. The approach sketched upon here promises that future research on educational efforts to improve both general skills of learning and thinking and achievement in particular domains may be carried with a higher degree of conceptual and empirical precision. It must be emphasized, however, that the present approach is based upon a particular set of assumptions, and that it cannot provide answers to more than certain kinds of questions. The fact that the approach is a differential one implies that only domains in which there are individual diffferences in performance may be fruitfully approached. The differentialapproach also implies that the analysis is structural rather than process-oriented, and that the concept of ability plays a central role. As is clarified by Undheim (the present volume) the ability concept makes it possible to describe, and perhaps also to understand, performance consistencies which span several domains. This is achieved through partialling out specific task variance as far as posssible, which is typically done through summation of scores over items and over tests. In this way more generalized dimensions are identified, which capture a part of the variance in specific tasks, but which always leave a part of the variance unaccounted for. In contrast, research which uses an information-processingor cognitive science approach, of which there are several examples in the present volume, typically attempts a more complete specification of the processes involved in solving particular tasks. This generally provides considerablymore detailed informationabout the tasks studied, but at the expense of generality and easy use of concepts which refer to across-task consistencies. The differential and the information-processing approaches thus are complementary, and to a large extent they do provide answers to diifferent questions. It is essential to understand that the individual-differenceapproach is a group centered approach, and that the central concepts tend to lose their meaning when brought down to the individual level. Thus, the statement, say, that the G-factor accounts for 36%and Gc’ for 22% of the variance in the Opposites test only has meaning as a statement which refers to a group of persons (in this case virtually unselected 6th-graders).When interpreted at this level it is statement which gives valuable information about the Opposites test, and it also provides us with some further information of value for the interpretation of G and Gc‘. However, the statement should not be interpreted to mean that any single person uses a certain proportion of G and a certain proportion of Gc’ to solve vocabulary tasks.
Hierarchical models ofintelligence 69
It is true that the factor analysis model, when formulated as a regression equation, does specify an individuals' performance to be a weighted sum of the individuals' abilities, acccording to a linear,-additive,compensatory, model (see, e.g., Harman, 1967). As a model for task performance at the individual level, this formulation does not make much psychological sense, particularly since we don't even want to make the assumption that abilities exist within persons as entities (cf. Snow and Lohman, 1989). However, as has been shown by Carroll (1993) violations of the assumptions of the factor analytic model are not necessarily serious, as long as we do not interpret the results as indicating that the linear, additive, model is true for each individual in the sample. It seems, however, to be an interesting challenge for further development to develop models, both at the individual level and at the group level, which do not make assumptions about linearity and additivity. Any model which is to be judged psychologically reasonable must probably specdy a dynamic relationship between domain-specific knowledge and more general learning and thinking skills. Glaser (1984) has expressed the following view: ' ... improvement in the skills of learning, such as required on aptitude and intelligence tests, takes place through the exercise of conceptual and procedural knowledge in the context of specific knowledge domains. Learning'and reasoning skills developnot as abstract mechanismsof hkristic search and memory processing. Rather they develop as the content and concepts of a knowledge domain are attained in learning situations that constrain this knowledge to serve certain purposes and goals' (p. 99).
The theoretical system called 'experiential structuralism' which has been developed by Demetriou and Efklides (see, e.g., the chapters by Demetriou and Efklides in this volume) may possibly provide a framework for such a theoretical development. One attractive aspect of this theoretical system is that the distinction between a general processing system and a set of specialized structural systems, seems to be compatible with the distinction between general and specific abilities made here, and it also proposes an interesting theory of the mechanisms of change. The relations between knowledge and skills in particular domains, such as arithmetic, and the systems specified within the theory of experiential structuralism yet remain to be worked out, however, and much empirical research, using both additive and non-additive models, seems to be needed to clarify the intricate interrelationships among the systems.
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McNemar, Q. (1964). Lost: Our intelligence? Why? American Psychologist, 19, 871-882. Mulaik, S.A., James, R.L., Van Alstine, J., Bennett, N., Lind, S., & Stilwell, C.D. (1989). Evaluation of goodness-of-fit indices for structural equation models. Psychological Bulletin, 3,430-445. Muthh, B.O. (1991). Multilevel factor analysis of class and student achievement components. Journal of Educational Measurement, 28,338-354. Pawlik, K. (1966). Concepts and calculations in human cognitive abilities. In R.B. Cattell (ed.), Handbook of multivariate experimental psychology. Chicago: Rand McNally. Resnick, L.B. (1987). Instruction and the cultivation of thinking. In E. De Corte, H. Lodewijks, R. Parmentier, & P. Span (eds.), Learning and instruction: European research in an internationalcontext, Vol. 1.Oxford: Leuven University Press and Pergamon Press. Schmid, J. & Leiman, J.M. (1957). The development of hierarchical factor solutions. Psychometrika, 22,53-61. Snow, R.E. (1980). Aptitude processes. In R.E. Snow, P.-A. Federico, & W.E. Montague (eds.), Aptitude learning and instruction. Vol. 1.Cognitive process analyses of aptitude (pp. 27-63). Hillsdale, NJ: Lawrence Erlbaum Associates. Snow, RE. (1981).Toward a theory of aptitude for learning. I. Fluid and crystallized abilities and their correlates. In M.P. Friedman, J.P. Das, & N. OConnor (eds.), Intelligence and learning. New York: Plenum. Snow, R.E. & Lohman, D. (1989). Implications of cognitive psychology for educational measurement. In R.L. Linn (ed.), Educational Measurement. New York: Macmillan. Spearman, C. (1904a). General intelligence objectively determined and measured. American Journal of Psychology, 15,210 - 293. Spearman, C. (1904b).The proof and measurement of association between two things. American Journal of Psychology, 15,72-101. Spearman, C. (1927). The abilities of man. London: Macmillan. Stankov, L. & Horn J.L. (1980). Human abilities revealed through auditory tests. Journal of Educational Psychology, 72,Zl-44. Terman, L.M. (1916).The measurement of intelligence. Boston: Houghton-Mifflin. Thorndike, R.L. (1985).The central role of general ability in prediction. Multivariate Behavioral Research, 20,241 - 254. Thurstone, L.L. (1938). Primary mental abilities. Psychometric Monographs, No. 1. Thurstone, L.L. (1947). Multiple factor analysis. Chicago: University of Chicago Press. Undheim, J.O. (1981). On intelligence IV: Toward a restoration of general intelligence. Scandinavian Journal of Psychology, 22,251-265.
Hierarchical models of intelligence 73
Undheim, J.O. & Gustafsson,J.-E. (1987).The hierarchical organizationof cognitive abilities: Restoring general intelligence through the use of linear structural relations. Multivariate Behavioral Research, 22,149-171. Vernon, P.E. (1950). The structure of human abilities. London: Methuen. Vernon, P.E. (1961). The structure of human abilities. London: Methuen 2nd ed. Westerlund, A. & Ullstadius, E. (1991). Prov for mtning av allmanna fardigheter i iirskurs 2 och 5. Konstruktion och analys av instrument inom den nationella utvarderingen. Rapporter friin institutionen f6r pedagogik, No. 1991: 20.
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Intelligence, Mind, and Reasoning: Structure and Development A. Demetriou and A. Efklides (Editors) 8 1994 Elsevier Science B.V. All rights reserved.
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Structure, Development, and Dynamics of Mind: A Meta-Piagetian Theory" Andreas Demetriou and Anastasia Efklides Aristotelian University of Thessaloniki, Greece Our theory aspires to accommodate the architectureand development of human intelligence, mind, and reasoning. For reasons of convenience, from this point onwards, we shall use the term "mind to refer to all of these three aspects of human knowing because, as it will be argued below, it is the most inclusive. As a theory about the architecture and the dynamics of the mind, it involves propositions, assertions, and hypotheses about (a) the structural organisation of human knowledge acquisition and problem solving devices and capabilities, (b) the condition of these devices and capabilities at different ages, and (c) the causes and mechanisms which are responsible for their change along with age. Our theory has originated in the Piagetian tradition. However, during its evolution along the years it interacted closely -and, we hope, fruitfully- with the psychometric and the cognitive tradition. In fact, our theory aspires to function as a frame that would facilitate the integration of the developmental,the psychometric, and the cognitive approach to the study of human mind and intelligence. Thus, we would like to spell out the relations between our theory and these three major traditions of psychology. Classical Piagetian theory has been the startingpoint of our research endeavour. That is, our original aim was to work within the Piagetian system in order to understand human intelligence (Demetriou, 1983; Demetriou & Efklides, 1979, 1981). As the anomalies of this system soon became apparent (Demetriou & Efklides, 1988),we started working on our own model of cognitive development. Llke other neo-piagetian models (Case, 1985; Fischer, 1980; Halford, 1988; PascualLeone, 1970; all of these models are presented in Demetriou, 19881, this model aimed to preserve the strong points of this theory and remedy its weaknesses. Thus, our model is still close to classic Piagetian theory in at least two respects. First, our system endorses the Piagetian assumption that human intelligence is the means and the product of the self-regulated and constructive interaction of the person with her environment (see Piaget, 1971).Second, a large part of the Authors' address: Department of Psychology, School of Philosophy, Aristotelian University of Thessaloniki, Thessaloniki 540 06, Greece.
76 A. Demetriou and A. EMides cognitive phenomena which we investigate in our laboratory are those originally brought to focus by Piaget, such as categorical thought, mathematical thought, causal thought, the emergence of awareness, etc. In as far as method is concerned, our theory is in some respects closer to the developmental tradition and in some other respects is closer to the psychometric tradition. That is, we usually test relatively large numbers of subjects by group tests in which many different aspects of thought activity are represented. However, the construction of these tests is inspired by epistemological-developmental rather than psychometric concerns. For instance, the tests are addressed to diffmnt cognitive operations related to the domains of thought mentioned above, such as abstraction and integration of properties (categorical thought), numerical operations (mathematical thought), isolation of variables (causal thought), etc., and not to dimensions of ability, such as fluid or crystallised intelligence, which have been the focus of interest in the psychometric tradition. Moreover, the structuring of item difficulty in our studies is criterion rather than norm referenced. That is, it is directed by assumptions regarding the developmental status or the processing complexity of the cognitive process represented by an item rather than by the success rates attained by different groups of a given population on the item. Testing in the psychometric tradition is based on the assumption that thought activity is organised along a number of specifiable ability dimensions which can be used to differentiate individuals. In turn, it is assumed that individual differences are signs indicating the boundaries between cognitive structures. That is, the fact that some individuals perform better, for example, on mathematical tasks and others on spatial tasks is interpreted to indicate that the processing of these two task categories is based on different processes. We do accept this assumption. This is equivalent to saying that we assume that the patterns of individual differences generated by a psychometrically designed study which involves tasks inspired by the developmental or the cognitive tradition are signs of the boundaries between the cognitive structures which attracted the interest of developmental and cognitive psychologists. The data we obtain are usually analysed by a multiplicity of methods. A major part in this process is always reserved for factorial approaches, especially modern confirmatory factor analysis and structural equation modelling. Of course, traditional developmental methods such as clinical interviews and longitudinal examinations, or experimental methods, such as training experiments, are used to cross-validate hypotheses about structure and development (Demetriou, Efklides, & Platsidou, 1993a; Demetriou, Gustafsson, Efklides, & Platsidou, 1992; Efklides, Demetriou, & Gustafsson, 1992; Shayer, Demetriou, & Prevez, 1988). In as far as the interpretative constructs are concerned, the system is also eclectic. Depending upon the specific theoretical needs, it draws upon the
Structure, development and dynamics of mind 77 developmental and the psychometric tradition or upon modem cognitive science in general or information processing in particular. For instance, one needs to invoke notions developed in the developmental tradition, such as the need for mental cohesiveness and the removal of inconsistencies in order to explain the emergence of new cognitive structures. However, if one is to explain differences in the rate of development between individuals it might be better to invoke notions such ,as differential sensitivity to external stimulation or differences in learning ability offered by psychometric theories of intelligence. Finally, if one is to explain performance differences across classes of tasks it might be better to invoke notions such as information processing complexity, representability, etc. In conclusion, our theory is inspired by the assumption that developing mind can only be understood if the strong points of the developmental, the psychometric, and the cognitive tradition are allowed to converge and become integrated into a comprehensive system. In the first part of this chapter we will present the propositions of our theory about the structure of human mind. That is, the structural systems described by the theory and the laws governing their organisation will be summarised. The second part will focus on development. That is, we will summarise the major developmental landmarks of the various structures to be described in the first part of the chapter. Based on this summary we will present our basic assumptions about the dynamics of development. That is, we will propose a model aiming to explain why and how development occurs. The relations between our theory and other theories of intelligence and cognitive development will be discussed in the concluding part of the chapter. THE ARCHITECTURE OF DEVELOPING MIND
T h e principles of cognitive organisation The five principles to be presented below are regarded as the general laws which govern the relations of mind with the environment and the relations between the various systems and subsystems of mind. In other words, the principles aim to capture the organisationalforces whose operation results in the inter-connection or the fusion of particular mental elements (i.e., knowledge acquisition, representation, and processing schemes or components) into broader and more efficient functional systems and in the preservation of these systems along both the phylogenetic and ontogenetic time. These are the domain-specific systems and the domain-free self-awareness and self-regulation system to be described below (see Demetriou & Efklides, 1988; Demetriou et al, 1993a).
78 A. Demetn’ou and A. EMdes The principle of domain specificity
This principle is based on two fundamental assumptions.First, reality is variable and multifaceted. It consists of elements which bear on properties differing in physical identity and functioning.The particular nature of the properties defining the elements constrain the ways in which these elements may be inter-related. A set of elements bearing on the same type of properties and connected by the same type of relations constitutes a reality domain which is psychologically different from other domains involving elements with different properties and relations. Second, the person and reality are structurally tuned. This implies that the person tends to organise his interactions with reality into domains of thought that preserve the dynamic and figural peculiarities of different reality domains. It is in this sense that these domains of thought are regarded as specialised. That is, they originate from and they direct the person’s interactions with special reality domains. Thus, we call these domains of thought specialised structural systems (SSSs). The principle of formal-procedural specificity According to the principle of domain specificity, the SSSs are domains of thought mapped onto different reality domains. Therefore, the mental acts, operations, or processes characterising each of the SSSs must be able to encode, recover, preserve, reproduce, or extend the elements and relations that define the reality domain onto which each SSS is mapped. If this were not the case, reality domains might be confused by the thinker. This would lead to misapplication of SSSs, with all the ensuing negative consequences. Therefore, different SSSs are characterised by different properties regarding all four important aspects of problem solving. Namely, the representation of problem space (for example, it is binary-propositional in the verbal-propositional SSS but holistic-imaginal in the spatial-imaginal SSS); the definition of the information unit relevant to the problem (for example, words or numbers whose meaning is specified according to a commonly accepted code of conventions in the case of the verbal-propositional or the quantitative-relational but spatial coordinates in the case of the spatial-imaginal or figural properties in the case of qualitative-analytic); the definition of the operations to be performed on the units (one may contrast here the operations on numbers to operations such as mental rotation applied on spatial problems); and the evaluation of the outcome obtained (for example, propositional arguments are evaluated on the basis of logical truth often inspite of observable reality whereas images are evaluated on the basis of realistic or other aesthetic criteria).
Structure, development and dynamics of mind 79 The principle of symbolic bias This principle is a direct derivative of the two first principles. That is, each SSS is biased toward those symbolic systems or subsystems which are more conducive than others to the representation of the properties and relations of each SSS’s reality domain. Moreover, each SSS is biased toward that symbolic system which allows the efficient application of its own operating processes onto the elements of the reality domain concerned. For instance, spatial relations are better preserved in images rather than in numbers. Quantitative relations are better preserved in numbers rather than in images. It needs to be noted here that a symbolic system may be related to more than one SSS. For instance, it is trivial to claim that quantitative relations may be expressed in numbers, words, or images. Thus, the choice of a symbol system by an SSS depends upon the moment‘s particular needs or preferences. It is reasonable to assume that selecting a given symbol system always is a cost and benefit enterprise. That is, some possibilities will be lost in favour of others. The principle of subjective equivalence-distinctnessof abilities A mind which is structurally (first principle),computationally (second principle), and symbolically (third principle) variable and multifaceted usually operates under conditions of uncertainty, especially when there are no ready-made action plans directly cued by reality. This is usually the case with problem-solving situations. Under these conditions, efficient cognitive functioning raises the problem of how the person comes to make reasonably correct decisions about the structure, computational procedure, etc., she is required to bring to bear on the problem. The present theory assumes that the developing person is programmed to experience his cognitive experiences in a way that is accurate enough to enable her to make the differentiations required for decisions as to the most a p propriate course of mental or overt action vis-a-vis the particular characteristics and demands of the problem at hand. Therefore, this principle implies that cognitive experiences which differ between each other according to the three principles above are felt or cognized by the person as distinct of each other. Otherwise, they are felt or cognized as functionally similar or equivalent.These feelings and cognitions continually contribute to the creation, recreation, and expansion of a mental map of one’s mind to which one might refer whenever the present moment’s decisions need to be mindfully informed by the decisions made in the past.
The principle of developmental variation The four principles above conjointly determine the general characteristics of
80 A. Demetriou and A. Emides development. That is, that development is bound to produce at one and the same time intra- and inter-individual variation as well as commonalities due to the very nature of the subject-object relations and the organisation of the subject himself. Advancing time covaries, by definition, with increasing experience. However, the time twhich is devoted to interaction with a given reality domain is necessarily withheld from possible interactions with other reality domains. Therefore, the knowledge of and interaction facility with this domain would be privileged relative to the other domains with respect to time f. However, there will always be experience of experience.That is, the organism gets to know how it is connected to reality, how it can attribute reality elements to representations of reality, and, at last, how it feels to have a processing system activated and running. This implies that any organism-reality interaction generates at one and the same time domain-specific and organism-specific knowledge and skills. The latter type of knowledge and skills are transferable over different domains. It is unlikely that a person would either distribute his time evenly across different reality domains or never come across a given domain. Two implications follow from this assumption. On the one hand, intra- and inter-individualvariation would be the rule in development. On the other hand, it is probable that there would exist a certain range to this variation. This range depends upon both the operation of the self-understanding and management factors noted above and the operation of constraint related to the processing potentials characterising a given individual in relation to other individuals or the same individual at different ages. The structures of mind The five principles provide for a multidimensionally organised mind. In particular, their joint operation would generate structures which would be domain, procedurally, and symbolically specific.Moreover, there should be a self-awareness and self-regulation structural system. This system would, on the one hand, be autonomous of the structures referred to before and, on the other hand, would "know" and interact with these structures. Finally, the functioning and development of all of these structures would depend upon the constructional characteristics of the human mind. These are reflected in the ways information is stored and processed in the system. The Specialised Structural Systems
7Ae qualitative-analytic SSS. This SSS is concerned with qualitative reality. Specifically, this SSS is the basic production mechanism underlying the
Structure, developmentand dynamics of mind 81 construction, representation, and processing of categoricalstructures. Therefore, this SSS is oriented to the processing of similarity-difference relations. That is, this is the system enabling the thinker to go from isolated properties of stimuli to the knowledge structures to which these properties are related. Evidently, the aim is to give meaning to the properties of reality elements presently observed in relation to relevant knowledge constructed in the past in order to help the organism make decisions which are important vis-a-vis a given goal. The decision of an animal to run away or attack another animal or to eat or avoid a plant based on the identification of a given characteristic may be considered as one of the most fundamental expressions of this SSS. As a processing system, this SSS is primarily analytical.That is, its functioning is based on the specificationand disentangling of the various properties that may co-define the objects of reality. Once this is.possible, the various properties can be treated as “pure” objects of thought activity. That is, as the building blocks which can be used by the mind in order to build conceptualsystems which capture the semantic and logical relations between these properties and hence of the objects represented (e.g., the ”greenness”, or ”redness”, or the “squareness”, or “circularness” of objects are combined to build the concepts of green squares, red squares, green circles, and red circles etc.). As a representational system, the qualitative-analytic SSS is biased to figural representationor to the declarativeaspect of language which seems able to encode the properties of things as well as the class relation between properties. An example in this regard is the “natural k i n d terms (e.g., “cat”, “animal”, etc.) which are apt to reveal the class inclusion relations between categories belonging to the same class hierarchy. The q uantita tive-relational SSS.Reality has clear quantitative properties which are independent of knowing systems -be they animals, humans, or robots. Reality elements -be they atoms, stones, humans, or stars- tend to aggregate or separate so that they increase, decrease, divide or multiply in space or time. Thus, the quantitativerelationalSSS is concerned with the representationsand processing of these aspects of reality. As such, it is relational in nature because any quantity Q exists in relation to other quantities Qk1. As an operating system, the quantitative-relational SSS involves abilities which enable the thinker to (rekonstruct the quantitative relations between reality elements varying along one or more dimensions as well as to inter-relatethe dimensions themselves. As a representationalsystem, the quantitative-relational SSS is biased to a symbolic medium which enables the thinker to focus on quantitative properties and relations and disregard those properties and relations which are irrelevant to quantitative processing. Thus, this system involves the following component abilities. Abilities of quantitative specificationand representation.Counting acts, such as pointing, bringing in, removing, and sharing may be taken as the overt
82 A. Demetriou and A. Eflrdides manifestations of these abilities. These enable the thinker to specify the basic quantitative relations mentioned above (i.e. increase, decrease, and redistribution). That is, to grasp and represent the relations which connect the single elements of reality once these are mentally deprived of all of their identifying properties. Abilities of dimensional-directional construction. They refer to operations enabling the person to specify different types of quantitative relations. For instance, increase or decrease which may be regular or irregular, linear or curvilinear, etc. These abilities underlie the dimensionalization of reality and they should be regarded as the building ground on which the concept of variable is constructed. Abilities of dimensional-directional coordination.These enable the thinker to grasp and specify inter-dimensional relations. Thus, these abilities are the basis of complex mathematical thinking such as proportional reasoning. The causal-experimental SSS. The relations between objects and persons usually change. In this dynamic state of the world, some objects or persons sometimes function as the cause of change and others as the recipient of causal effects. Sometimes the cause-effect relations are clear and directly available to the senses. Frequently, however, causal relations are masked by the presence of unrelated elements. In fact, causal interactions may be so concealed (like the interactions between planets or particles within atoms) or conspicuous and immaterial (like the effects exerted on human behavior by desires, ambitions, evil or good feelings) that they would never strike onto the senses. The concealed interactive reality structures constitute the domain of the causal-experimental SSS. That is, this SSS is directed at disembodying cause-effect relations out of broader networks of phenomenally relevant but essentially irrelevant relations in regard to a phenomenon, and at building models representing these networks of relations. In the sake of this aim the following component abilities are involved. Combinatorial abilities form the cornerstone of this SSS. This is so because they function as the means used by the person in order to exhaustively define the broader coexistence structure on which the person would have to operate. Hypothesis formation abilities enable the person to induce predictions about possible causal connections on the basis of data patterns. The predictions must be taken by the person, at least implicitly, as propositions to be verified or falsified by experimentation. fiperimentation abilities enable the person to "materialise" hypotheses in the form of complementary experiments.This is equivalent to finding ways of giving actual form to the world of the possible. The isolation-of-variables ability is probably the best example of this set of abilities. Model construction abilities enable the person to properly map the results of experimentation with the original hypothesis in order to arrive at an acceptable interpretative framework or theory. The verbal-propositionalSSS. This SSS is concerned with the formal relations
Structure, development and dynamics of mind 83 between mental operations rather than with the relations between the objects denoted by the propositions involved in a propositionalargument. The identifymg characteristic of this SSS is the ability to differentiate the contextual from the formal elements of a series of statements and operate on the latter. Thus, although it involves deductive or inductive reasoning as the other SSSs, efficiency in this SSS is not closely related to other domains of cognitive activity which may also involve deductive or inductive reasoning (cf. Demetriou & Efklides, 1988).This is so because relations in other SSSs may directly be cued by the context in which the thinker operates. In the case of this SSS it is not the context but the type of relation between the propositions which is important. For instance, we have found that the basic logical relations of conjuction, implication, transitivity, etc., function as the basic building blocks of this system. The reader is referred to Efklides, Demetriou, & Metallidou (this volume) for a further discussion of the structure and development of this SSS. The spatial-imaginalSSS.This SSS is directed to those aspects of reality which can be visualised by the "mind's eye" (Kosslyn, 1978) as integral wholes and processed as such. Evidently, this SSS comes out of and directs the activities which are related to location and orientation in space. Therefore, its component abilities are applied within a mental space structured on the basis of the spatial coordinates which structure real space. Thus, this system involves cognitive abilities such as mental rotation, image integration, and image reconstruction. These abilities preserve on the mental level the actions that one can execute on real objects in space. Design for the validation of SSSs and organisational principles The SSSs "...are dynamic, multilayered, and multi-dimensional entities that involve very general, ever-present core operators, subfield operators, and processing skills as well as the products of their past operations. These products are conceptions and misconceptions, beliefs and misbeliefs, ideas and ideals, about the world with which the person is interacting. That is, we view our SSSs as the means through which people construct foundational theories about the physical, the biological, and the social world" (Demetriou, Efklides, Papadaki, Papantoniou, & Economou, 1993b, p. 193-194). All of these operators, skills, concepts, and beliefs are coordinated under the organisational principles to function in the concerted way that is required if the person would be able to cope with the complex demands posed by the reality domain to which an SSS is affiliated. Theories which are rather exact in their specification of the constructs they are concerned with, like this theory, are perfectly suitable for confirmatory testing.
84 A. Demetriou and A. EWdes Design for the validation of the individual SSSs
In this type of research one first devises sets of tasks addressed to each of the components presumably involved in the SSS one wants to investigate.The second step is to address these tasks to a sample of subjects which is developmentally variable enough to allow the presumed differentiation between components to be expressed in the pool of performance patterns to be observed. Finally, one would have to write a model that would prescribe how performance in the task battery must be structured. In more technical terms, performance on tasks representing the various components of an SSS would have to be structured in the following three types of factors: a) A set of ability specific factors that would be taken to represent each of the component abilities. Evidently, each of the tasks presumably addressed to a component ability would ideally have to be related only to the factor designed to represent this component. b) There should also be one first-order general factor that would be related to all tasks. This factor would represent the common core shared by all component abilities. c) There should also be a second-order general factor which would have to be related to all first-order component-specific factors. This factor would capture the intercoordination of the components into the SSS under study.
Figure 1. The model that would fit performance on four tasks addressed, in pairs, to two componentsof the same 555. Note: The symbols cr, cm, and pr stand for the common core operations of an 555, the componentsof an SSS, and the principles coordinating components into an SSS, respectively.
Figure 1shows how a model fitting the structure of our SSSs would look like.
Structure, development and dynamics ofmind 85 It needs to be stressed here that this model was independently tested in studies that investigated the structure of the qualitative-analytic(Demetriou & Efklides, in preparation), the quantitative-relational (Demetriou, Platsidou, Efklides, Metallidou, & Shayer, 19911, the causal-experimental (Demetriou et al., 1993b1, the verbal-propositional(Efklides,Demetriou, Metallidou, this volume) and the spatial-imaginal SSS (Loizou, 1992). Design for the validation of principles
A study that would aim to validate the operation of organisationalprinciples across SSSs would have to be considerably more complex than a study designed to verify the organisation of an individual SSS. This kind of study would have to be able to demonstrate the power of each principle to chanellize performance on tasks independently of the power of other principles. Violating this assumption would imply that the principles may be reduced to each other. This would, in turn, indicate that each of the principles cannot be taken as an independent causal agent responsible for the patterns of performance observed.
Figure 2. The model that would validate the operation of principles. Note: The symbols SSS and SYh4 stand for the specialized structural systems and symbolic
systems, respectively.Latin numerals refer to different tasks.
86 A. Demetriou and A. Eiwides Under the assumption above, the minimal design for the validation of organisational principles would have to involve tasks made to represent at least two principles. In turn, each of the principles would have to involve tasks representing at least two of the constructs each of the principles is presumably able to differentiate.An example of this minimal design is depicted in Figure 2. It can be seen in the model shown in this figure that there are eight tasks addressed to one SSS and eight tasks addressed to another SSS (SSS and SSS, may stand for any of the five SSSs described by the theory). Four the tasks addressed to SSS, and four of the tasks addressed to SSS are biased to be represented and processed through a given symbolic system &M, and the other four tasks addressed to each of the two SSSs are biased towards a different symbol system SYM, (SYM and SYM, may stand for any symbol system such as language, mathematical symbolism, or pictorial-figural symbolism). Under these specifications, the model that would fit performance on the 16 tasks would have to involvq four principle-specificfactors. Specifically, the four SSS,-SYM, and the four SSS,-SYM, tasks would have to load on one factor that would stand for SSS,. The four SSS,-SYM, and the four SSS,-SYM, tasks would have to load on another factor that would stand for SSS,. Also, the SSS,-SYM, and the SSS,-SYM, tasks would have to load on a third factor that would represent SYM, and the SSS,-SY$ and SSS,-SyM, tasks would have to load on a fourth factor that would represent the SYM, symbolic factor, respectively. Finally, all 16 tasks would have to be related to a common general factor. This would represent the operation of two domain-free systems invoked by the theory. Thus, the SSS, and the SSS, factors may be taken as an index of the power of the prinaple of domain specificity to differentiate between groups of tasks presumably addressed to different domains. Likewise, the SYM, and the SYM, factors may be taken as an index of the power of the principle of symbolicbias to systematically affect performance over and above the forces related to the structure of domains. This model was validated in several studies that involved different SSSs and differentsymbolic systems (Demetriou & Efklides, in preparation; Demetriou et al., 1993a).
01
The Hypercognitive System Structure This system involves models, rules, and strategies underlying self- and taskmonitoring, self-understanding, and self-management. This system is regarded as the interface between (a) cognition as a whole and reality, (b) any of the SSSs, and (c) the processing system to be described below and the SSSs. Thus, what has come to be known as metacognition (Flavell, 1979)is part of our hypercognitive system. The reason we opted to coin a new term is that the term "metacognition" conveys the assumption that the functions associated with it come after cognitions.
Structure, development and dynamics of mind 87 In fact, it has been shown (Demetriou& Efklides, 1989) that these functions may as well come before or concurrently and shape cognitions. Thus, our term is superior to the old one because it is neutral in this regard. Moreover, our term is more accurate as it refers to functions applied on the other cognitive systems. This system seems to exert its control on the functioning of intelligence at two different levels. At a macro-developmentallevel, hypercognition frames the person’s general orientation to how reality is to be represented and processed. Thus, at this level, the system refers to the person’s general theory of intellectual functioning.This may involve three integral components: (a) A model of cognitive organisation and functioning.This model specifies knowledge and beliefs about the structure and functioning of mind. Thus, it specifieswhat cognitive functions exist (e.g., that there is memory which is distinct from thought or that there are different types of thought such as our SSSs). This model also specifies how the various functions can be efficiently used (e.g., rehearsal is effectivefor a short list of digits but organisationaccording to meaning is preferable for a long shopping list involving many categories of products). (b) A model ofintelligence.This model involves knowledge and beliefs about what is considered intelligent or wise behavior in a given environment. Thus, this model specifies how one‘s intellect is to be employed in order to attain the goals and objectives one sets to oneself in accord with the rules and principles shared by one’s culture. (c) A model of one’s cognitive self:This model rests at the intersection of the two models summarised above. It involves the person’s beliefs about his strong and weak points as a cognitive system. It also involves one’s personal strategies and skills in activating and using the various cognitive functions, systems, and operations one possesses. At a micro-developmental level the hypercognitive system controls on line cognitive functioning. As such this system is involved in making decisions of two different kinds. First, decisions as to the SSS-task affiliation.This is a family of decisions aiming to ensure that (a) the right SSS and (b) the most relevant taskspecific schemes will be brought to bear on the task at hand. Second, decisions regarding the appropriate and efficient use of these schemes as well as of the processing system and other cognitive functions. Design for the validation of the hypercognitive system The principle of subjective equivalence-distinction of abilities states that cognitive functioning continually contributes to the creation and refinement of a mental map of cognitive functions and SSSs. This map may be used by the person during on-line processing when she needs to make decisions about the
88 A. Demetriou and A. Emides
appropriate course of action. Therefore, this map must reflect the objective structure of the cognitive system. It is only under this condition that the hypercognitive system would be able to function as the interface between SSSs and reality or among any of the SSSs. A study that would be able to test the assumption of correspondence between the objective and the subjectivestructure of cognition needs to satisfy the following requirements. First, it would have to involve tasks addressed to at least two SSSs. These tasks would have to be performed by the subjects to be involved in the study. The scores reflecting their performance would be used to identify the objective structure of the abilities employed by subjects when processing the tasks. Second, the subjects must be asked to make evaluations of one or more aspects of their performance on the tasks. For example, they may be asked to specify the facility they felt when processing the tasks or to evaluate the success of the solution they provided on each of the tasks. These metacognitive scores would be used to identlfy the subjective structure of the experience generated when applying the various abilities.
Figure 3. The structure of performance and subjective evaluation of difficulty and success on tasks representing four SSSs.
In terms of structural modelling, both the objective and the subjective scores would have to be structured in SSsSpecific factors representing the SSSs addressed by the tasks used in the study. Figure 3 shows the model that would have to fit
Structure, development and dynamics of mind 89 the data to be generated by this kind of study. Variations of this method were used in a series of studies (Demetriou & Efklides, 1985,1989) and they always demonstrated that the subjective structure of abilities does constitute a veridical reflection of its objective structure. An alternative and probably more refined method for uncovering the thinker‘s metacognitive map was used by Demetriou et al. (1993a, Study 3). In this study subjects first solved tasks addressed to three SSSs. They then were presented with specific descriptions of a variety of mental functions and skills. These were either domain-free functions, such as long-term memory, short-term memory, attention, and reasoning, or SSS-specificprocesses, such as isolation-of-variables, proportional reasoning, and mental rotation. The subjects were asked to indicate the degree to which they used each of the general functions and each of the SSSspecific skills when solving each of the tasks addressed to the three SSSs represented in the study. Confirmatory factor analysis and a series of other analyses showed clearly that the general cognitive functions tended to be perceived by the subjects as differentially related to each of the SSSs. Moreover, each set of SSS-specific skills were perceived as more closely related to its own rather than to other SSSs. The Processing System Structure According to our theory, the processing system is a “dynamic field where information is represented (i.e., encoded and kept active), protected (i.e., refined, dissociated, or disassociated from interfering information), and processed (i.e., connected, compared, transformed, or combined) over an as yet undefined time interval that is required by the thinker in order to make sense of the information” (Demetriou et al., 1993a, p. 25) in order to attain a current mental goal. The functioning of this system may be analysed in terms of three dimensions: sped ofprocessing, control ofprocessing,and storage. Speed of processing basically refers to the minimum speed at which a given mental act may be efficiently executed. Speed of processing is a basic parameter of cognitive functioning because of the very nature of our cognitive system. Specifically, it is well known that memory traces tend to decay either because of the plain passage of time or because of the interference of other stimuli (Baddeley, 1991).This implies that the thinker must be able to complete the processing related to the moment’s current goal before the activation of any of the units involved falls below a certain threshold. Control of processing refers to a mechanism which functions under the guidance of the task-goal like a filter permitting only goalrelevant schemes to enter processing space. Control is important as a parameter
90 A. Demetriou and A. Efilides
of processing because it regulates what information is to be attended, inhibited, rejected, or put into a waiting state under the time and activation limitations of our cognitive system noted above. That is, the more efficient this mechanism is the more probable it becomes that the mind will grasp or effect the interconnections needed at the appropriate time. Storage refers to the maximum number of schemes that the person can keep active above a minimum level of trace strength for the time needed in order to grasp their meaning and/or relations as suggested by the moment’s current goal. The theory claims that the three components of the processing system are interrelated. The faster a person is as a processor, the more information units she will be able to process in a given standard time unit. Therefore, the more efficient she will eventually be in sorting out the goal-relevant from the goal-irrelevant units. A possible reason for this positive correlation between speed and control of processing is that fast processing enables the cognitive system to complete the processing acts needed at a given moment before irrelevant representations get activated. Alternatively, fast processing may give time to the thinker to work on both, representations already judged to be goal-relevant to the moment’s current goal and on representations that might be relevant to the next moment’s goal. Thus, fast processing either minimises the need for control or provides free time to the thinker that she can spend for control of information in parallel to the execution of the processing acts suggested by the moment’s current goal. In turn, the more efficient one is in regard to speed and control of processing the better one would be in using her storage potential. This is so because the right information units will occupy this potential for the minimum time required to grasp the concept defined by these units and assemble the response needed under conditions of minimum interference. Moreover, fast and efficient processors may have the time to rehearse and associate information. Evidently, these functions minimise forgetting. In conclusion, these three parameters of the processing system may be considered as complementary functional manifestations of the processing capabilities of the brain of a given person at a given age. Specifying these parameters for a person is equivalent to showing her optimum potentialities under conditions of effortful performance. That is, under conditions in which grasping a concept or relation presupposes that the flow of information in the system should stay above a certain threshold and there are certain minimum coactivation requirements of the dimensions defining a concept if it is to be grasped as such. In a sense, the processing system is the factory of both the abilities involved in the various SSSs and the self-monitoring and self-regulation concepts, strategies and skills involved in the hypercognitive system. Specifically, in order to be acquired, SSSs-specific abilities must either be copied, constructed, or reconstructed by the thinker himself. Moreover, if a knowing system is to have
Structure, development and dynamics of mind 91 awareness it must possess a more basic system which generates cognitive and other experiences along with its moment to moment functioning. Design for the validation of the structure and functioning of the processing system According to our theory, processing and understanding is a multilayered edifice which may be likened to an inverted pyramid so that each higher layer necessarily involves all lower ones. Speed of processing lies at the basis of the pyramid. There are tasks which can be defined in terms of only this parameter because no control, storage, or any specialised skill is needed in order to be errorlessly performed. These tasks require from the subject to execute a well learned and already automated response to a simple, clear, and easily recognisable stimulus. Reading a single word may be taken as an example of this class of tasks. The tasks at the next level of complexity can be defined in terms of both speed of processing and control of processing. Asking the subject to recognise as fast as possible the ink colour of a word which has a different meaning (e.g., the word BLUE written in red ink) is an example of this kind of tasks. Evidently, when we see a word we are used to reading it rather than recognising the ink colour in which it is written. Thus, in order to identify the ink colour, the subject must first inhibit (i.e., put under control) the tendency to read the word. However, this kind of tasks does not require any short-term storage because once a property of the stimulus is selected as the goal-relevant property only one response is possible and this is stored in long-term memory. Performance on classical working memory task, such as the backward digit span task, can be defined in terms of speed and control of processing and, of course, in terms of storage. The reasons for the dependence of working memory on speed and control of processing were analyzed above. Finally, simple problem solving tasks, such as arithmetic problems, can be defined in terms of at least four dimensions: namely, speed and control of processing, working memory, and the mathematical skills related to the four basic arithmetic operations. On top of this level other dimensions may, theoretically, be added adinfiniturn, depending upon the complexity of the tasks concerned. For instance, problem solving in algebra would require, in addition to the four dimensions specified above, a fifth.oneconcerned with the manipulation of algebraic expressions, etc. The model below summarises the analysis of the edifice of processing advanced Level 4 S+C+M+SSS Level3 S+C+M Level2 S+C S Level 1
92 A. Demetnou and A. Efldides above. That is, if the symbols S, C, M, and SSS stand for speed of processing, control of processing, working memory, and SSS-specificskills, respectively, the tasks at each higher level necessarily involve the dimensions defining all lower levels plus the dimensions characteristic to this level. Therefore, a study that would aim to test if this analysis is valid would have to involve tasks distinctly representing each of these levels. Examples of these tasks were given above. The reader may have recognised that Stroop-like tasks (Stroop, 1935) may be used to tap the two basic levels of the processing system. Any tasks addressed to working memory may be taken to indicate the third level and any SSS-specific tasks that require mindful processing would indicate the fourth level.
Figure 4. The hierarchical model that would fit performance on a series of tasks designed to tap the successive levels of the cognitive edifice. Note:The symbols S, C, M and 0 stand for speed of processing, control of processing, memory, and arithmetic operations, respectively.
This design is an ideal case of the nested-factor modelling pioneered by Gustafsson (1988, this volume). This is so because, in this case, the nesting of the lower level constructs within the higher level constructs is an integral aspect of
Structure, development and dynamics ofmind 93 the task construction itself rather than a simple restriction of a measurement model imposed from without. In effect, Figure 4 shows the ideal model that would have to fit performance on sets of tasks representing each of the four layers of the processing edifice. That is, a processing speed factor would have to be related to all tasks. A control of processing factor would have to be related to all but the speed of processing tasks. A storage factor would have to be related to the working memory and the SSS-specific tasks. Finally, an SSS-specific factor would have to be related only to the tasks addressed to the SSS represented in the study. It should be noted that we validated this general model in a number of studies. The analysis above is based on Study 5 presented in Demetriou et al. (1993a).In her doctoral thesis, Platsidou (1993) has extended this general model in order to test each of the four layers of processing across three different symbol systems (verbal, numeric, imaginal). She showed that this model captures processing across all three symbol systems, although some differences were noted between systems in the relative strength of the various dimensions. Demetriou, Platsidou, Sirmali, & Tsakiridou (in preparation) replicated Platsidou’s findings in middle and old age. Finally, in her doctoral thesis, Zhang (in preparation) has validated this model in China using Chinese language characters. THE CHARACTER AND DYNAMICS OF DEVELOPING MIND It is next to trivial to ascertain that all parameters of mind described above undergo massive changes from birth to maturity. In fact, some parameters continue to change until the very end of life. In our view, the grand task of the modem theory of cognitive development is, first, to uncover and explain how change in one component or parameter of the cognitive system propagates to other components or parameters. A second major task is to understand how change in a given component, once activated, acquires a self-sustained momentum which ensures that this component will be elevated to a higher level of functioning, to a considerable extent independently of the condition of other components. In this section we will sketch a general model of developmental causality that aims to open discussion about these two major issues. To facilitate the reader to grasp the thrust of the model we will first outline the developmental course of the general and the specialised systems discussed above. Major trends in development The development of the processing system Figure 5 summarises our studies of the development of the three parameters
94 A. Demefiiou and A. Elwides of the processing system. It can be seen in this figure that all three parameters of the processing system improve significantly throughout childhood and adolescence and they peak between 20 and 30 years of age. It needs to be noted, however, that the greatest improvement in the speed of processing and the control of processing occurs from 9 to 11 years of age. The improvement observed in these parameters from 15 to 25 years was comparatively limited. Unfortunately, the evidence on the development of speed and control of processing in younger ages is practically non existent. 1300
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Figure 5. Changes in speed of processing, control of processing, and working memory as a function of age and SSS.
There is more evidence on the development of working memory. Case (1985) and Pascual-Leone (1970) have shown that short-term memory span is no more than one unit of information (e.g., one word or digit, etc.) at the age of three years and it systematically grows thereafter until it levels off at about the end of adolescence. Our studies summarized in Figure 5 show that there is a monotonic improvement in working memory from one age level to the next throughout the period from 9 to 20-30 years of age. Finally, it must be stressed that all parameters
Structure, development and dynamics of mind 95 were found to regress systematically from middle to old age so that between 60 and 70 years of age they approximated the values obtained by the ll-year-old preadolescents. The development of the hypercognitive system The hypercognitive system also changes extensively in all of its components. In so far as the model of cognition is concerned, awareness moves from a global to a differentiated conception of the cognitive system and from the surface to the processing characteristics of cognitive functioning.That is, children at the age of 2-3 years think about the world but they do not think about their thinking (Flavell, 1988). At the age of 4 years children begin to understand that reality and the representations they may have about it may not coincide. Thus, they are transformed from condition theorists to representation theorists (Perner, 1991). According to some authors, it is this transformation that enables children to differentiate between reality and appearance. After the age of 5-6 years children begin to systematically differentiatebetween mental functions, such as memory, attention, thinking, etc. However, they do not use this knowledge to regulate their cognitive behavior before they are about eight years old or older. At the beginning of adolescence the person becomes able to circumvent the content characteristics of tasks and identify their operational/procedural characteristics. Likewise, it is only from this age onwards that the thinker becomes able to differentiate between SSSs according to how each is related to different general cognitive functions such as short-term memory, long-term memory, attention, etc. (see Demetriou & Efklides, 1989; Demetriou et al., 1993a).However, it is not before the end of adolescence that the person formulates a more or less complete and differentiated theory of cognitive organization. Similar changes were observed in the understanding of the nature of intelligence and in the image of one’s own cognitive self. However, no further reference will be made to these changes because of space limitations. The development of the SSSs Space limitations do not allow presentation of the development of all five SSSs even in rough outline (see Demetriou & Efklides, 1987; Demetriou et al., 1993a). Thus, the development of only two SSSs will be summarised below. That is, the quantitative-relational (Demetriou et al., 1991)and the causal-experimental SSS (Demetriou et al., 1993a, 1993b). The aim is to provide the basis for the causal model of development to be outlined in the next section. In the period between three and five years of age, quantitative thought functions
96 A. Demetriou and A. Efklides on the basis of what Resnick has called proto-quantitativeschemas (Resnick, Bill, & Lesgold, 1992). For instance, a global concept of numerosity can be used by the child in order to derive solutions to simplified one-to-one correspondence tasks (see Gelman & Gallistel, 1978).Overt quantifying acts, such as pointing or finger counting, are very powerful as a means for quantifying the world even until the age of seven years. The ability to mentally execute the basic arithmetic operations is established during the primary school years. At the beginning it is limited to apply only one operation on two numbers and it gradually expands so that it can involve all four operations and many numbers. If defined on the basis of the number of the operations to be executed, this ability develops in four levels. These are acquired, one almost every second year, in the period from about 7 to 12years. Proportional reasoning first appears as an ability to grasp intuitively supported proportional relations at 11-12 years. It gradually ascends through a sequence of four levels until it becomes able, at the age of 14-15 years, to grasp complex and counterintuitive relations. Interestingly enough, however, the development of the algebraic reasoning spans over the whole period from about 8 to 15years. At the beginning it enables subjects to specify quantitative relations on the basis of well defined elements and it culminates in the ability to specify relations by coordinating undefined structures on the basis of their logical relations. Thus, the development of the ability to execute the four arithmetic operations appears at the beginning to alternate with the acquisition of the lower developmental levels of algebraic reasoning. The development of proportional reasoning appears to alternate with the highest levels of algebraic reasoning (Demetriou et al., 1991). The causal-experimentalabilities are interpatterned in a similar way. That is, up to the age of 5-6 years causal understanding can go no further than provide descriptions of observable reality. That is, it can create representations which mostly preserve the order of events in time. Trial-and-error predominate as a means for studying cause-effects relations. In the period from 7 to about 10 years causal-experimentalthought begins to be transformed from descriptive to theory guided. However, theories at this period are nothing more than implicit theories in action (Karmiloff-Smith& Inhelder, 1974). It is not before the age of about 11 years that thought acquires a proper experimental orientation to answering questions regarding causal relations. According to our studies (Demetriou et al., 1993b),combinatorial abilities appear at about 11 and they are consolidated at about 15 years of age. Simple experimentation and hypothesis formation abilities appear together around 1213 years of age and they continue growing until college years. Model construction abilities, i.e., the abilities enabling one to integrate hypotheses with experimental data into a unified theory, appear around the age of 15years and their application may be problematic even at the graduate level. Signs of a "personal epistemology"
Structure, development and dynamics ofmind 97 regarding the causal structure of the world were not observed before late adolescence. These involved a grasp of the limits of both the mechanisms an experimenter uses to produce empirical evidence and the models to which experimentation may eventuate. That is, that experimentation is prone to error due to the presence of confounding variables and that the models are, to a large extent, heuristic tools which are, in principle, always refutable. In conclusion, all systems and subsystems of mind appear to change systematically from birth to maturity. It is a matter of fact that the products of change are more visible to the observer at some age phases than at other phases. For instance, the changes occurring in the first two years of life culminate in the ability of the child to use conventional symbolic systems; the changes occurring throughout childhood culminate in the ability of the young adolescent to think about his models of the world than just about the world. Thus, in the section below we will attempt to explain how the changes in individual components are orchestrated so as to boost each other and result in the grand macroscopic changes that captured the attention of both the developmentalists and the laymen. Networks of change
The theory postulates that developmental causality is a synergic force. Specifically, it assumes that a change in any of the three kinds of systems already described may be a cause of changes in any of the other systems. This is so because the systems are functionally tuned to each other. Therefore, a change in any of them is a disturbance factor which puts the dynamic tuning of the whole system in jeopardy. The direction of change is dictated by the system that has changed first. That is, this system would tend to pull the other systems in the direction toward which it has already moved. An attempt will be made below to highlight how synergic developmental causality may be operating. Of course, it needs to be stressed here that the theory recognizes that a causal chain of changes may be initiated by endogenous (e.g., maturation), individual (e.g., discovery or invention), or exogenous factors (e.g., imitation or teaching). The interested reader is referred to Demetriou et al. (1993a) for a discussion of how these factors may activate a causal chain. First, a chain of developmental changes may be initiated by a change in the most basic components of the processing system and gradually escalate to ever higher layers of the cognitive edifice until to affect the most advanced components of the hypercognitive system. The model shown in Figure 6 summarizes the results of a short-term longitudinal study that involved measures of the three components of the processing system and one of the components of an SSS, namely the ability to mentally execute the four arithmetic operations which belongs to the quantitativerelational SSS.In this study the four components were
98 A. Demefriouand A. Elwides
TIME 1
TIME 2
Figure 6. Causal relations between the speed of processing, the control of processing, the memory, and the arithmetic operations factors across the two testing occasions. Note: The symbols S, C, M, 0 stand for speed of processing, control of processing, memory and arithmetic operations, respectively.
Structure, development and dpamics of mind 99 measured at two times separated by a sixth-month interval. Two conclusions are clearly suggested by the model shown in Figure 6. First, the high autoregressions obtained (i.e., the regression of each factor identified at the second testing on its corresponding factor identified at the first testing) suggest that each of the four components is a dynamic module that to a large extent draws on itself in order to change along the dimension of time. Second, the presence of paths going from each module at the first testing to all higher level modules at the second testing indicates that change tends to spread, as assumed by the theory, from the more basic to the most advanced modules of the system. This upward escalation of change is in line with the assumptions put forward above about the relations between the different layers of cognitive organization. That is, it indicates that the faster flow of information that results from an increase in processing speed above a certain threshold makes it more necessary than before to screen incoming information. Thus, the system works in the direction of improving control of processing. In turn, an improvement in handling the flow of information in the system makes it able to better exploit its available storage space or capabilities. These changes in processing capacity open the possibility to construct new SSSspecific skills which could not be constructed before. A chain of changes may be initiated by a change in the hyperaognitive system. For instance, the acquisition of a new rehearsal or organizational strategy may first affect the handling of the processing system and then spread to the various SSSs. Case (1972) has shown that a simple change in the strategy that directs the person to attend only goal-relevant and disregard redundant information may increase dramatically the probability of success on tasks based on working memory because it brings the task within the range of the processing potentials of the subject. Finally, an improvement in an SSS-specificskill may cause a series of changes in the two general systems. For instance, the practice with arithmetic operations provided by school may lead the child to discover her storage limitations. In turn, this may motivate her to develop strategies that would overcome these limitations. These strategies may, on the one hand, raise the child’s self-monitoring and selfregulation facility. On the other hand, they may eventuate in more efficient handling of processing capacity. The causality governing changes within each of the various SSSs s e e m also to be synergic. This is suggested by the developmental inter-patterning of the quantitative-relational and the causal-experimental abilities summarized in the section above. Specifically, the reader is reminded that in the case of the quantitative-relational SSS the four levels of arithmetic operations formed one block which was followed by the block of the four levels of proportional reasoning. The four algebraic developmental levels were spaced in such a way that they overlapped with both the arithmetic operations and the proportional reasoning
100 A. Demetriou and A. Emides
levels. Likewise, the model construction abilities started to get off the ground once combinatorial thought had been consolidated. However, the development of experimentation and hypothesis formation abilities appeared to be co-extensive with both of these two consecutive sets of levels. We have assumed that the abilities which interlock other abilities during development may be operating as the catalyst which enables the system to shift from the state of functioning characterizing the lower block of levels to that characterizing the higher one. That is, it has been assumed that basic quantitative constructions which can be built by the application of the basic arithmetic operations are decontextualized by being encapsulated in symbolic structures through algebra. This process enables quantitative constructions to remain functional and develop by raising them from the plane of first order representations, such as numbers, to the plane of representations of representations, such as the letters which stand for numbers. This model also captures the network of dynamic interactions in the development of the causal-experimental SSS: Applying this model to the development of the causal-experimental SSS, we would argue that combinatorial abilities of the lower levels serve to set up the mental space in which the first hypotheses can be formulated. At a subsequent phase, hypothesis formation abilities enable the young adolescent to fix the combinationshe or she conceives in structures that can function as frames that can direct his or her manipulations of reality. Thus, systematic experimentationbegins to be possible. Once it is acquired, experimentation acts in two directions. On the one hand, it provides strategies that can be put into the service of the combinatorial ability itself. As a result, the construction of the higher level combinatorialabilities is facilitated.On the other hand, it generates a data space that has to be understood. Evidently, a good way to gain an understanding is to map this data space onto the space of the hypotheses that served as the starting point of experimentation. This is the beginning of model construction. In turn, when model construction advances to a certain level, it functions as a frame for the conception of more complex hypotheses and consequently for the design of more sophisticated experiments. These then may loop back by providing the material, external or mental, for the construction of more complex model, and so on and so forth" (Demetriou et al., 1993b, p. 495).
Figure 7 shows the general causal model that was found to fit the dynamic patterns of change summarized above. It needs to be mentioned here that this model also captures the dynamic interactions between different SSSs (Demetriou & Efklides, in preparation). Paths a, b, and c in this model stand for strong, moderate, and weak effects, respectively.Thus, the model represents the condition in which two systems or subsystems exchange interactions at the beginning, they then interchange in influencing and being influenced by the other system or subsystem until they arrive at a phase at which there is no traceable interaction
between them.
Structure, development and dynamics of mind 101
Component 1
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Figure 7. The general model of interaction between components within or between Ssss. Note:The symbols a, b and c, stand for strong, moderate, and weak effects, respectively.
The nature of development According to the analysis above, development is possible because of the multisystemic and multistructural nature of the mind. That is, a change in any component of the mind triggers a whole set of changes aiming to re-institute the functional tuning between the component that has changed and those related to it. Thus, any change in the system is regarded as a potential radiator of growth pressures on its neighbouring components. The eventual result is of course a function of several crucial factors. Specifically,the nature of change depends upon the specific system that initiates a chain of changes, the extent of these changes, and the condition of the other systems at the given time period. This last factor is important because it determines the readiness of the other systems to move from their present state and follow the forerunner. For instance, developmental theorists agree that a change in the general processing system raises the general potential of the organism to assemble general strategies and grasp the relations between SSS-specific units which could not be seen at the previous functional level of the processing system (see Case, 1985; Fischer, & Farrar, 1988; Halford, 1988; Pascual-Leone & Goodman, 1979). The sequences of developmental events summarized above are consistent with this interpretation. Nevertheless, the analysis of individual change patterns of the subjects tested in our Stroop experiments shows that a change in the speed or control of processing does not always result in changes in the specialized structural systems. It was also found that no subject with a working memory span of less than four units was able to solve proportional reasoning tasks or design simple experiments in order to test a hypothesis. However, not all of those who have attained this storage capacity were able to solve these tasks. This evidence is congruent with the assumption that the massive changes that
102 A. Demetriou and A. Efklides
have been associatedby developmentaltheory with major stage shifts are possible when the changes in one of the systems accumulate up to a certain level, and then a change in another system occurs that functionsas a catalyst which triggers the reorganization of mind as a whole at a new representational or structural level (Demetriou et al., 1993a).The changes occurring at crucial developmental turning points such as those leading from sensorimotor to representational intelligence at about the age of two years or from denotational to suppositional representations at about the age of 10-12 years seem to be of this variety. However, once a major change has occured, each of the various systems tends to draw upon itself as it moves to approach its final state. This is the developmental pattern shown in Figure 7. This pattern brings the discussion to the second issue raised at the beginning of the section on development. Specifically, why do interactively generated changes in the different systems of mind gradually tend to become autonomous and self-sustained?.Threecomplementary reasons seem responsible for this phenomenon. First, even when activated from outside, the rate and forms of change in a system will largely be dependent on the state and the peculiarities of each of the components involved in the system as well as on the system's organisation as such. For instance, how fast change can propagate in a system depends on the penetrability of each component to influences coming from neighbouring components but also from the amenability of the between components relations to change. In turn, these inertial constraints of a system depend upon earlier habitual patterns associated with its functioning. This point leads to the second reason. Specifically,however it has been initiated, the change of a system will be effected in interaction with the domain of the environment the system is affiliated to. Therefore, the peculiarities of each system's domain together with the opportunities the person has to interact with this domain at the times which are critical for the change to survive and spread is very important. Finally, the consolidationand propagation of change within a system depends upon the relations between this system and the two general systems. That is, on the one hand, it depends upon the way in which the components make use of the processing resources available at the given phase. On the other hand, it depends upon decisions the person herself or himself will make in consultation with the models she or he holds about intelligence, cognition, and the self, when she or he feels the change. Is then development a continuous or a discontinuous process? It is both. If viewed from the point of view of its end-products, development is discontinuous. That is, a major representational shift such as those mentioned above may be seen as a cutting point which demarcates the end of one developmental cycle and the beginning of another. However, if viewed from the point of view of the dynamics underlying structural changes, development appears to be continuous rather than discontinuous. This is so because of the very nature of mind itself.
Structure, development and dpamics ofmind 103 Being both an open and self-regulated system, it is always in a state of microadaptations. Thus, to the extent our measures are refined enough to spot these micro-adaptationsbetween different blocks of mental units, development would be shown a continuous process. This conception of development as being continuous and discontinuous at one and the same time brings our theory close to the modem analysis of development in terms of dynamic systems theory (van Geert, 1991) and catastrophe theory (van der Maas & Molenaar, 1992). We would anticipate that lending the two approaches to interact would highlight phenomena that at present remain obscure. On the one hand, catastrophe theory, for example, provides the framework and the methods that may be used to spot what change in what component can lead to a major (catastrophic) transformation of the mind. On the other, our theory provides well defined parameters and domains of mind on which one can test the general catastrophe models to see how they apply on different aspects of cognitive development. CONCLUSIONS: THE DYNAMIC LOOP OF MIND, INTELLIGENCE, AND REASONING
The theory presented in this chapter is concerned with the structure and development of all three aspects of human cognition to which this volume is devoted. Namely, mind, intelligence, and reasoning. In this section we will spell out how we conceive of the relations between these three aspects of human cognition and briefly discuss the relations between our theory and the other theories and research presented in this volume. It is trivial to ascertain that intelligence refers to the ability of living beings to learn about the environment, to learn how to use this knowledge in their interactions with the environment, and to learn how to learn. We would fully agree with Piaget (1971)that the ultimate aim of this learning business is to enable the organism to foresee and precorrect errors. That is, to provide the organism with potential action plans for problems that the environment might pose. Piaget believed that the more intelligence approaches this aim, the more it comes to obey the rules of one grand structure, namely the structure of the INRC group and the lattice that supposedly govern the organisation of formal operations. We believe the opposite. Specifically, we claim, in full agreement with Snow (this volume), that intelligence is able to attain this aim because it is multifaceted, multileveled, and hierarchical. Our SSSs are some of the facets of intelligence. We view these facets as systems mapped onto the structure of the world. They frame and facilitate the acquisition, organisation, storing, and use of knowledge as they provide ready made pathways to the interaction with different facets of the world. At the same time, however,
104 A. Demetriou and A. Efklides the operation of these systems chanellizes learning so that it may hinder transfer from the one field of knowledge to the other. Limited transfer is not as bad as many educators would think. In fact, it may protect learning systems from unduly mixing up the results of learning. Our SSSs are modular. However, we are not yet sure if they are modular in the Fodorian sense of being hard-wired or in the sense that they are only conceptually modular. Snow (this volume) believes that intelligence involves only conceptual modules. There is evidence to suggest, however, that very young infants do possess capabilities pertinent to our SSSs (e.g., Landau, Spelke, & Gleitman, 1984; Starkey, Spelke, & Gelman, 1990).This evidence might be taken to support a Fodorian conception of modules. However, we prefer to take Karmiloff-Smiths (1991)stance and assume that what may be hard-wired in our SSSs are particular attention biases that direct the organism to attend to, store, and process particular patterns of information in particular ways. Then it is experience and development that will shape the biases into meaning-making and problem-solving operations, rules, and strategies, and, of course, concepts. Thus, our SSSs may at one and the same time be hard-wired, experiential, and conceptual. Only future research can specify how experience shapes unformed attention and processing biases into cohesive operational-conceptual systems. The processing system, the set of the SSSs, and the hypercognitive system may be seen as the three grand levels of the human knowing system. However, each of the three grand levels is itself a multileveled enterprise. This structure is demonstrably -both experimentally and psychometrically- hierarchical as we, Gustafsson (this volume) and many other students of intelligence have shown. However, there are many differences between our theory and other theories of intelligence, either traditional or modern. These differences are concerned with the specification of both the specialized abilities and the levels of the hierarchy. Regarding the first, our theory is the only one to define specialized abilities in reference to types of relations in the environment; thus, the systems we describe do not fully coincide with the systems described by more traditional theories of intelligence. Regarding the second, our theory is the only one to involve mind as a clearly defined construct that interacts with the constructs that reside at the other levels. Below we shall elaborate only on the later. Knowing and intelligence as defined above is not confined to humans. However, not all knowing systems possess mind. According to our theory, mind is the ability of a knowing system to know itself and other knowing systems. As such, it is both a product of intellectual activity and a means of further activity. Specifically, the theory takes for granted that human brain can feel and register its own knowing activities as well as the products of these activities. In so doing it stores knowledge about both its own properties and functions and about its contents. That is, it accumulatesknowledge about knowing and knowledge about
Structure, development and dynamics ofmind 105 knowledge. This knowledge can then be used to direct both the knowing activities as such as well as the knowing of knowing activities. Mind so defined is the sine qua non condition for learning to learn. According to our theory, mind involves a structural or architectural aspect and a procedural or computational aspect. In as far as structure is concerned, the minimal assumption that one can make about mind as defined here, is that it would tend to preserve the organisational characteristics of the knowingactivities which give birth to it and which then come under its government. The results presented in this chapter, and in the chapters by Efklides, Demetriou, & Metallidou, by Fabricious, and by Moshman do validate this assumption. In so far as process is concerned, we have not progressed much beyond Piaget’s (1974) assumptions about reflective abstraction. That is, we do not really know how feelings and experiences of knowing emanate, how they are encoded, registered, and transformed so as to result in the construction and continuous refinement of the map of one’s mind activities and processes. The assumptions advanced by Efklides et al. and by Fabricious provide some clues in the right direction. Reasoning is the basic tool of intelligence and mind. That is, reasoning refers to the processes employed by the thinker in order to specify if and how a given piece of information either given in the environment or generated by thought is acceptably related to other pieces of information already taken as the basis of processing. Deduction, induction, and analogy seem to be the basic types of reasoning. It is not our aim to embark on them here. Four chapters in this volume (i.e., the chapters by Efklides et al., Langford, Moshman, and Smith) are concerned with reasoning. We only want to point out that the three types of reasoning mentioned constitute the basic inferential mechanisms underlying the functioning of all five SSSs and mind. It is plausible to assume that the functioning of the more fundamental components of the processing system is also based on these inferential mechanisms. The functioning of these mechanisms themselves may be based on semantic principles, on logical principles, or on mental models -”or” here is meant to be inclusive. However, we know next to nothing about how each type of reasoning is used by each of the systems of the knowing hierarchy specified by our theory. We believe that a large part of the confusion in understanding reasoning is due to the assumption that it is either over and above domains (Piaget) or conceptually bound (the conceptual change movement). Our theory takes the middle ground. It argues that the functioning of domains generates patterns of mental activity which, when projected onto mind, become reasoning patterns. These can then be used for further more efficient functioning of the domains and so on and so forth. Thus, future research will have to focus on the interplay between the various types of reasoning and the systems and subsystems of the knowing hierarchy during development. In conclusion, intelligence is tool and product of adaptation. Mind is tool and
106 A. Demetriou and A. Efklides product of the functioning of intelligence. Development is the force that makes mind to gradually emanate from the functioning of intelligence and then play its orchestrating functions. In this process reasoning is a means whose power increases the more it comes under the direction of mind. From another point of view, one might view the human mind as the tool and product of a bi-directional process that leads to the personalization and socialization of intelligence. As a result of this process one becomes increasingly able to tune his or her intelligence with his or her own capabilities, talents, and ambitions and the possibilities, the rules, the needs, and the expectationsof his or her society and culture. As a result, intelligence turns into wisdom and reasoning into rationality. On the one hand, this development is possible because of the multistructural nature of our knowing system that makes the dialogue necessary both within and between minds. On the other hand, the forms that this dialogue can take along with development is constrained by the structural and functional limitations of the human processing system. REFERENCES Baddeley, A. (1991). Working memory. Oxford: Oxford University Press. Case, R. (1972). Validation of a neo-Piagetian capacity construct. Journal of Experimental Child Psychology, 14,287-302. Case, R. (1985).Intellectualdevelopment: Birth to adulthood.New York: Academic Press. Demetriou, A. (1983).Psycho-logical development of the structures of concrete thought: Experimental studies on the thought of children aged from 4 to 10 years (Scientific Annals of the School of Philoshophy, Suppl. No 39). Thessaloniki: Aristotelian University Press. Demetriou, A. (ed.) (1988).The neo-Piagetian theories of cognitive development: Toward an integration. Amsterdam: North-Holland. Demetriou, A. & Efklides, A. (1979).Formal operational thinking in young adults as a function of education and sex. International Journal of Psychology, 14, 241-253. Demetriou, A. & Efklides, A. (1981).The structure of formal operations: The ideal of the whole and the reality of the parts. In J.A. Meacham & N.R. Santilli (eds.), Social development in youth: Structure and content (pp. 20-46). Basel: Karger. Demetriou, A. & Efklides, A. (1985). Structure and sequence of formal and postformal thought: General patterns and individual differences. Child Development, 56,1062-1091. Demetriou, A. & Efklides, A. (1987).Towards a determination of the dimensions and domains of individual differences in cognitive development. In E. de Corte, H. Lodewijks, R. Parmentier, & P. Span (eds.), Learning and instruction:
Structure, development and dynamics of mind 107 European research in an international context, Vol.1 (pp. 41-52).Oxford: Leuven University Press and Pergamon Press. Demetriou, A. & Efklides, A. (1988).Experiential Structuralism and neo-Piagetian theories: Toward an integrated model. In A. Demetriou (ed.),The neo-Piagetian theories of cognitive development: Toward an integration (pp. 173-222). Amsterdam: North-Holland. Demetriou, A. & Efklides, A. (1989).The person’s conception of the structures of developing intellect. Genetic, Social, and General Psychology Monographs, 115,371-423. Demetriou, A. & Efklides, A. (in preparation). Structure and development of qualitative-analytic ability. Demetriou, A., Efklides, A., & Platsidou, M. (1993a).Experiential structuralism: A frame for unifying cognitive developmental theories. Monographs of the Society for Research in Child Development, 58 (Serial No. 234). Demetriou, A., Gustafsson, J.-E., Efklides, A., & Platsidou, M. (1992). Structural systems in developing cognition, science, and education. In A. Demetriou, M. Shayer, & A. Efklides (eds.),Neo-Piagetian theories of cognitive development: Implications and applications for education (pp. 79-103). London: Routledge. Demetriou, A., Platsidou, M., Efklides, A., Metallidou, Y., & Shayer, M. (1991). The development of quantitative-relational abilities from childhood to adolescence: Structure, scaling, and individual differences. Learning and Instruction: The Journal of the European Association for Research in Learning and Instruction, 1,19-43. Demetriou, A., Efklides, A., Papadaki, M., Papantoniou, G., & Economou, A. (1993b). Structure and development of causal-experimental thought: From early adolescence to youth. Developmental Psyclology, 29,480-497. Demetriou, A., Platsidou, M., Sirmali, K., & Tsakiridou, E.(in preparation). Processing capacity, working memory, and domain-specific thought processes from 7 to 70 years of age. Efklides, A., Demetriou, A., & Gustafsson, J.-E. (1992).Training, cognitive change, and individual differences. In A. Demetriou, M. Shayer, & A. Efklides (eds.), Nec-Piagetian theories of cognitive development: Implications and applications for education (pp. 122 - 143). London: Routledge. Fischer, K.W. (1980). A theory of cognitive development: The control and construction of hierarchies of skills. Psychological Review, 87,477-531. Fischer, K.W. & Farrar, M.J. (1988). Generalizations about generalization: How a theory of skill development explains both generality and specificity. In A. Demetriou (ed.), The neo-Piagetian theories of cognitive development: Toward an integration (pp. 137-171). Amsterdam: North-Holland. Flavell, J.H. (1979). Metacognition and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychologist, 34,906-911.
108 A. Demetriou and A. Efklides Flavell, J.H. (1988). The development of children’s knowledge about the mind: From cognitive connections to mental representations. In J.W. Astington, P.L. Harris, & D.R. Olson (eds.), Developing theories of mind (pp. 244 - 267). Cambridge: Cambridge University Press. Gelman, R. & Gallistel, C.R. (1978). The child‘s understanding of number. Cambridge, MA. Harvard University Press. Gustafsson, J.-E. (1988, April). Broad and narrow abilities in research on learning and instruction. Paper presented at the Minnesota symposium on learning and individual differences: Abilities, motivation, methodology. Minneapolis, USA. Halford, G.S. (1988). A structure-mapping approach to cognitive development. In A. Demetriou (ed.), The neepiagetian theories of cognitive development: Toward an integration (pp. 103-136).Amsterdam: North-Holland. Karmiloff-Smith, A. (1991).Beyond modularity. Cambridge, MA: MIT Press. Karmiloff-Smith, A. & Inhelder, B. (1974).If you want to go ahead, get a theory. Cognition, 3,195-212. Kosslyn, S.M. (1978). Measuring the visual angle of the mind‘s eye. Cognitive psycho lo^, 10,356-389. Landau, B., Spelke, E.S., & Gleitman, H. (1984). Spatial knowledge in a young blind child. Cognition, 16,225-260. Loizou, L. (1992). Structure and development of spatial - imaginal abilities. Unpublished Master Thesis. Thessaloniki, Department of Psychology, Aristotelian University of Thessaloniki. Pascual-Leone, J. (1970).A mathematical model for the transition rule in Piaget’s developmental stages. Acta Psychologica, 32,301-345. Pascual-Leone, J. & Goodman, D. (1979). Intelligence and experience: A neoPiagetian approach. Instructional Science, 8,301-367. Perner, J. (1991). Understanding the representational mind. Cambridge, MA: MIT Press. Piaget, J. (1971). Biology and knowledge. Edinburgh Edinburgh University Press. Piaget, J. (1974). The grasp of consciousness: Action and concept in the young child. Cambridge, MA: Harvard University Press. Platsidou, M. (1993). Information processing system: Structure, development and interaction with specialized cognitive abilities. Unpublished Ph.D. Thesis. Thessaloniki, Department of Psychology, Aristotelian University of Thessaloniki. Resnick, L.B., Bill, V., & Lesgold, S. (1992). Developing thinking abilities in arithmetic class. In A. Demetriou, M. Shayer, & A. Efklides (eds.), Nediagetian theories of cognitive development: Implicationsand applications for education (pp. 210-230). London: Routledge. Shayer, M., Demetriou, A., & Prevez, M. (1988). The structure and scaling of
Structure, development and dynamics of mind 109 concrete operational thought: Three studies in four countries. Genetic, Social, and General Psychology Monographs, 114,307-376. Starkey, P., Spelke, E.S., & Gelman, R. (1990). Numerical abstraction in human infants. Cognition, 36,97-127. Stroop, J.R. (1935). Studies of interference in serial verbal reactions. Journal of Experimental Psychology, 18,643-662. van Geert, P. (1991).A dynamic systems model of cognitive and language growth. Psychological Review, 98,3-53. van der Maas, H.L.J. & Molenaar P.C.M. (1992).Stagewise cognitive development: An application of catastrophe theory. Psychological Review, 99,395-417. Zhang, X.K., (in preparation). Children's cognitive development as a function of processing capacity in different cultures and semantic environments: A crosscultural study in China and Greece. Ph.D. Thesis. Thessaloniki, Department of Psychology, Aristotelian University of Thessaloniki.
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The Older Child’s Theory of Mind* William V. Fabriciusa and Paula J. Schwanenflugelb aArizona State University, USA bUniversity of Georgia, USA The topic of what children know about the mind has recently become a very lively and important one (e.g., Astington, Harris, &Olson, 1988; Frye & Moore, 1991; Perner, 1991; Wellman, 1990). The great bulk of the research and theory have been directed toward younger children, specifically children under the age of about 6 years. The central questions here are when and how do children acquire the essential components of our everyday adult mentalistic psychology, or “folk psychology.” This research has dealt with important issues such as when young children are able to understand the representational nature of beliefs, that human behavior is caused by beliefs and desires, and even that mental phenomena are distinct from physical phenomena. However, comparatively little work has been done to investigate further developments in children’s beliefs about how the mind works once they have an understanding of these basic elements. There is much that we need to know about these later developments. For instance, What are the similarities and differences that children see among different types of mental activities such as memory, comprehension, attention, and inference? How do concepts of these mental activities change with age, and what might explain those changes? How does children’s developing theory of mind relate to their acquisition of cognitive strategies, and to their intelligence as assessed by psychometric techniques? In this chapter we will focus on the work that we have begun to do on later developments in children’s theories of mind that addresses some of these questions. Research on later developments in children‘s theory of mind forms a link between the current work on young children’s acquisition of the basic components of a theory of mind, and the earlier work on metacognition, which tended to focus on children’s knowledge about variables that affect different types of mental activities, such as memory or attention. The earlier work on * Preparation of this chapter was supported by NICHD grant # HD - 28796. * Author’s address: W. V. Fabricius, Department of Psychology, Arizona State University, Tempe, AZ 85283 - 1104, USA
112 W.V. Fabricius and P.J. Schwanenflugel
metacognition, however, suffered from two limitations with respect to the current questions. One limitation was to focus almost solely on children’s acquisition of certain cognitive ”facts;” for example, that it is more difficult to remember many things than few things, or that rehearsal helps you remember. As Fabricius and Wellman (1983) put it, “What this research fails to capture are the child’s further ideas about how memory variables work .... We know little of children’s larger knowledge of memory, their theories that qualify and organize the effects of different influences on memory performance” (p. 15). The other limitation was that researchers characteristically looked at children‘s knowledge and beliefs about, for example, memory or attention in isolation, without much attempt to interrelate them and address what Wellman (1985)called the neglected question: ”What is the child’s larger view of human information processing that lies behind the understanding or misunderstanding of the operation of specific variables” (p. 186)? In the present chapter, we first present our research on children’s early theories of memory. In this work we studied their explanations for how memory variables work. Next, we discuss our research on older children’s larger theory of mind. Here we study developmental changes in children’s concepts of a wide range of mental activities. The findings from these two sets of research suggest to us that older children are engaged in an extended process of developing a constructivist theory of mind, and in the final section we present our current ideas about how this development might occur.
EARLY THEORIES OF MEMORY Our first indication that it might be profitable to study children‘s naive theories about memory came from a study (Fabricius & Hagen, 1984)in which we wanted to see if 7- and 8-year-old children who were aware that sorting pictures into related groups would help one remember the pictures later, would be more likely to use a sorting strategy than other children who were not aware of that fact. To assess children‘s awareness, we used an approach suggested by the kind of phenomena reported by Nisbett and Wilson (1977). Nisbett and Wilson argued that adults were more likely to report their naive theories about what caused their behavior, than to report the actual experiences that did influence them. We reasoned that if all children in a sample were given experience of sorting improving their recall, then only some of those children would report that sorting in fact was the causal factor that influenced their recall. They would be the ones whose naive theories about memory included sorting as a relevant causal factor. Other children, analogous to the typical subject in one of Nisbett and Wilson’s studies, would report other kinds of things that they believed influenced their recall, such as looking at the pictures, trying hard, guessing, etc. Using this approach, our findings were clear. Children who were aware that
The older child’s theoxy of mind 113
sorting improved recall were in fact the ones who tended to use sorting as a strategy. But in their own way the other children, those who were not aware that sorting improved recall, showed how strongly they too were affected by their naive theory. Their behavior was a good example of what Perner (1991) has recently described as ”being in the grip of a theory.” When we asked them, these children knew quite well that they had recalled more on trials when they had sorted. They also remembered that they had sorted the pictures on those trials. But they were unwilling to attribute their improved recall to sorting. These Nonattributors, as we will call them, were clearly in the “grip” of a theory about memory that constrained what they would consider as plausible variables that could affect memory. We can appreciate the strength of this grip when we recall that one of the frequent criticisms (e.g., White, 1980) of Nisbett and Wilson’s studies was that they relied on between groups comparisons. One group of subjects would be exposed to some experience that influenced their behavior, while a control group was not exposed to the experience. Critics argued that people would be much more likely to report the actual causes of their behavior if they were allowed to observe their behavior covarying with the presence and absence of the crucial experience. Children in our study did observe their behavior covarying with the presence and absence of sorting, but to no avail for the Nonattributors, who constituted about half of the 7-year-olds, and 25%of the 8-year-olds. We also noticed something else intriguing in this study. Most of the children who did attribute improved recall to sorting could give explanations for how sorting works to help them remember. These children said that sorting pictures during study time led them to cluster the pictures during recall. They described clustering either as one item automatically making them think of a related item, or as their deliberate attempt to try to think of items belonging to one category at a time. For example, one child said that “I knew it had to be some kind of fruit, so I didn’t think of everything else in the world, just fruits.” Moynahan (1973) had originally reported a similar finding. What is interesting about these explanations is that they appeal to mental processes as mechanisms to explain how sorting works. This suggested to us that we could study children’s explanations of how memory strategies work and perhaps get more insight into the content of their theories about memory. We did this in Fabricius &Cavalier (1989). There were two goals in this study. The first was to see what kinds of explanations children would give for how a labeling strategy works. The second goal was to see if children’s explanations would predict whether or not they used a labeling strategy. In this study, we used some careful controls. Most importantly, we wanted to identify a subset of children all of whom reported that labeling improved recall-in other words, children who attributed recall to labeling. And within
114 W.K Fabricius and l? J. Sch wanenflugel
that subset, we wanted to identify different groups of children depending on the types of explanations they offered for how labeling worked. This would allow us to determine whether it was attributions or explanations that predicted children’s later strategic use of labeling. However, there was a potential problem in finding children who attributed recall to labeling without having an explanation for how labeling works. In the previous study, most 7- and 8-year-oldswho attributed recall to sorting also gave explanationsof sorting. This suggested that older children might tend to attribute recall only to causes that they considered plausible, that is, causes for which they had explanations. However, the causal reasoning literature shows that when children do not have prior causal theories-such as in artificial situations, or in natural situations where they have not yet developed a causal theory-they will attribute effects to causes for which they have no explanations by using causal rules such as covariation, and similarity between the causal candidate and the effect to make their attributions (Kassin, 1981). Young children would only have begun to develop causal theories about memory. Thus we reasoned that it would be possible to find children between the ages of 4 and 6 who differed in whether or not they had explanations for how labeling affects recall, but who were otherwise similar in that they both would attribute recall to labeling. The task involved two sessions. In Session 1, we elicited children‘s attributions and explanations of labeling. We showed children pictures one at a time. There were 3 or 4 pictures to each set. There were labelingtrials, followed by a counting trial. On the labelingtrials, all children said the name when they saw the picture, and as soon as they did the picture was put face down and the next was shown. (If they didn‘t start out by saying the name of the pictures, we encouraged them to.) At the end, they were asked to recall the pictures. On the final countingtrial, children were told to count the pictures instead of saying the names (to prohibit labeling). All children recalled more on the labeling trials than on the counting trial, and so we could determine whether children attributed their increased recall to labeling, and whether and how they could explain how labeling worked. We were able to classify children into four levels of awareness of labeling, as shown in Table 1. Nonattributorsdid not think that labeling affected their recall. The rest did attribute improved recall to labeling. They fell into three groups. As expected, there was a group of Attributors With No Explanations, who could not identify any causal mechanisms by which labeling works to improve recall. Most said they did not know how labeling worked. There was a group who gave Perceptual/Behavioral Explanations. They said that labeling worked because it allowed other perceptual or behavioral activities to occur. There were three types of such explanations. The most frequent was “More Time.” These children said that labeling helped them recall more because it gave them more time than counting to look at each picture. Other children (“Same Response”) said that
The older child k theory ofmind 115 labeling helped them recall more because they simply had to reiterate the names they had just said, and that counting meant they had to say numbers first and then names. Finally, one child ("Hear Names") said that labeling helped her recall more because it allowed her to hear the names, and counting did not.
Table 1 Number of children at each of the four levels of awareness of labeling by age in session 1, and relation between level of awareness and use of labeling in session 2 USE OF LABELING AGE
LEVELS OF AWARENESS Mental Explanations ........................... Perceptual/Behavioral Explanations: More Time ........................................ Same Response ................................ Hear Words ...................................... Attributors with No Explanations .... Nonattributors ..................................... a
Trial 1
Trial 2
4
5
6
0-la
2+b
0-1
2+
2
2
7
7
4
1
10
0 1 0 6 15
2 0 0 6
;)
14
5
4
5
4
1 3
7
8
24
8 13
8 19
7 18
Observed to use labeling during 0 or 1 observation interval out of 6. Observed to use labeling during 2 or more observation intervals.
Finally, children who gave Mental Explanations said that labeling worked because it helped them keep thinking about the pictures after they had said the names. They said for example that labeling helped them "keep thinking about it," or it helped them "say it in my mind," or it helped them say it "over and over," or "two times in my mind." Session 2 occurred at least a week later. The purpose was to assess children's spontaneous use of a labeling or rehearsal strategy. We gave these same children a dozen pictures to study in any way they wanted for 1 minute, and we observed their study behaviors. As Table 1 also shows, on the first trial of Session 2, there was no difference among the groups in terms of the number of children who tended to use labeling. But on the second trial, after they had experienced the difficulty of trying to recall all of the pictures, almost all of the children who had given Mental Explanations began labeling. There was essentially no change among the other three groups. Thus, children who appealed to mental processes by which labeling worked were the ones who tended to use it. This suggests that in general, children's e ~ p l a ~ t i ~ ~ - ~ of how memory strategies work can give insight into important aspects of their beliefs about memory, and in particular that children who gave Mental
116 W.V.Fa bricius and P.J. Sch wanenflugel
Explanations had a different idea about how memory works than did the other children. Further confirmation of this came from another study with 6-year-olds (Fabricius, Zwahr, & Roberds, in preparation). In this study children were asked about a matching strategy of pairing pictures into thematic relations, such as "hamburger" and "plate." In Session 1 of this study, we gave children sets of 8 pictures to put on 4 stands, 2 pictures to a stand. On matching trials, we gave them pictures composed of matching pairs, and they put the matching pairs together either spontaneously or after a slight prompt. Then they were asked to recall them. On the final nonmatching trial, the pictures did not match. All children recalled more on the matching trials than the nonmatching trial. Again there were some 6-year-olds who failed to attribute recall to the matching strategy (Nonattributors).There was a second group who attributed recall to matching but could not offer any explanations for how it worked (Atfributors With No Explanations). The one difference in this study was that we got no Perceptual/ Behavioral explanations. No children said that matching helped them remember more because it gave them more time to see the pictures. That was because in this task it turned out that children actually had more time to see the pictures on the nonmatching trial, because they were initially surprised they didn't match and they hesitated before putting them on the stands. Finally, there were again those who attributed recall to the strategy and offered Mental Explanations of how it worked to help them remember. These explanations were like the clustering explanations described earlier. Children said that matching the pictures helped them remember because when they remembered one picture of the pair, it made them think of the other picture, or when they couldn't think of the matching picture right away they could just try to think of all the kinds of things that might be related to the first picture until they got it. For example, one girl said that matching the pictures of horse and saddle together helped her because, "if I forgot what went with horse, I could just think about walking around the barn till I saw a saddle, and then I'd get it." Results showed that as before, it was explanations and not attributions that predicted use of the strategy in Session 2. Seventy-five percent of children who gave Mental Explanations used sorting, whereas only 15%of the children in the other two groups did so. These results suggest how children's theories about memory may change with age. In children's early conception of memory, they may think that memory is affected only by how well the information is initially perceived or acquired. We can call this an Mormation Acquisition theory of memory. In this theory, the relevant causal-explanatory factors would be those that influence information acquisition, such as the time spent, the amount of information to be acquired, and the effort expended in attending to the information. These are in fact some
The older child k theoy of mind 117
of the earliest memory variables that children appreciate. Children who gave Perceptual/Behavioml Explanations of labeling reflect this Information Acquisition theory. As causal factors, they cited time, being able to both see and hear the information, and whether the information they acquired (labels vs. numbers) was the same as what they had to recall. Children who could not give explanations of labeling and matching (Attributors With No Explanations) also reflected this theory, because when they talked about other activities that helped them recall they cited looking at the pictures, trying to see them well, trying to take their time, etc. In children’s later conception of memory, they may think that memory is primarily affected by how the information that they have acquired is processed further. We call this an Information Processingtheory of memory. In this theory, children would be able to appreciate the effects of mental processes such as rehearsing, clustering, associating mental images and labels, and elaborating. Children who gave Mental Explanations reflect this theory of memory. What is different in this new theory is that children appeal to a new set of causalexplanatory mechanisms that can affect memory; namely, mental processes. They may discover these new mechanisms when they begin to monitor their memory processes more closely, to observe the intermediate steps in more detail, and to discover for instance that repeating information keeps a fading trace alive, or that one item can cue a related item, and that both processes can be expanded with directed attention. From this point, we have begun to explore three issues regarding children’s theories about memory. Do these theories exert causal influence on children’s choice of memory strategies? Are there individual differences in children’s theories about memory? How do these theories relate to intelligence? In regard to the first issue, we conducted a training study (Fabricius, Zwahr & Roberds, in preparation) with 5- to 6-year-olds to determine whether children who did not give Mental Explanations for a particular strategy, and who tended not to use the strategy, would begin using the strategy if they were told Mental Explanations for how it worked. Children were given either one or the other of two different types of training about how a matching strategy works to help them remember. One type (Mental Explanations) involved telling children the same things that children who spontaneously give Mental Explanations tend to say. The other type (Time Explanations) involved telling children that matching worked because it gave them more time to look at the pictures. Because of the way we set the task up in this study, children did see the pictures longer when they matched them. Children who had not spontaneously given Mental Explanationsin Session 1of this study were randomly assigned to either Mental or Time Explanation training. As predicted, Mental Explanation training led to increased strategy use, and
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Time Explanation training did not. This demonstrates that children’s explanations of how strategies work can determine their strategy choice. Importantly, all children in both training groups were told that matching helped them remember as part of their training. But having a conception of how it works in terms of the mental processes it facilitates was necessary for them to begin using matching as a strategy. Regarding whether there are individual differences in children’s theories of memory, on the one hand, the fact that some &year-olds give Mental Explanations while others do not might reflect the fact that the former had just acquired those explanations sooner, and that in a year or two the others would catch up. On the other hand, those differences at 6 years of age might reflect relatively stable individual differences. To investigate,we did one of the first longitudinal studies in this area (Fabricius & Zwahr, 1990). We recontacted and tested almost 90%of two original samples of 6-year-olds three years later, when they were 9 years of age. We combined those children who had given Perceptual/Behavioral Explanations and those who had given No Explanations into one group. This gave us 3 groups: a group of 14 9-yearolds who had given Mental Explanations of either a labeling or a matching strategy when they were 6-years-old, a group of 17who had attributed recall to the strategy behavior, but who could not give a Mental Explanation of how it worked (Attributors), and a group of 10 who had been unwilling to attribute recall to the strategy behavior (Nonattributors). Children who had given Mental Explanations at age 6 tended to outperform the other 2 groups at age 9 on several measures of memory performance and strategy use. We also distributed a parent questionnairethat asked, among other things, about children’s overall performance in school, and children with Mental Explanations were reported as generally having better grades than the other groups. These findings suggest that young children’s knowledge about how memory strategies work reflects relatively stable individual differences. The ability to predict performancebased on the child’s knowledge about memory was especially strong considering that it spanned three years and different tasks. This brought up the third issue: How do these theories relate to intelligence? Perhaps children who have an Information Processing theory of memory at age six are more intelligent in many areas, as assessed by standard intelligence tests. We continued our longitudinal study by testing the children again at age 10 on the Wechsler IntelligenceScales for Children -Revised, and standardized school achievement tests (Woodcock-Johnson-Revised, Tests of Achievement). Children who had given Mental Explanations at age 6 tended to score higher on both assessments. In summary, children‘s early acquisition of an Information Processing theory
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about memory appears to be a causal determinant of their strategy use, to reflect at least somewhat stable individual differences, and not to be a trivial acquisition, because it is the higher intelligence children who tend to acquire this theory. LATER THEORIES OF MIND
We have recently begun to broaden the forgoing research by examining the development of children’s larger theory of the mind, in which their theory of memory is embedded. The approach we have used is to examine the concepts that children and adults have about different types of mental activities, concepts such as Memory, Comprehension, Selective Attention, and Inference. There was good reason to assume that studying the organizationand structure of concepts of mental activities would give us insight into people‘s underlying theories of mind. Murphy and Medin (1985) have argued that concepts are embedded in deeper, underlying theories. According to this theory-based approach to concept formation, people’s naive theories in a domain constrain concept formation in two ways. First, theories specify which features or properties are relevant bases for categorizing entities. For example, adults’ naive theory about biology specifies that the relevant features for the concept Bird are such features as “has two legs,” “has wings,‘‘ “has feathers” and are not other kinds of potential features such as “is nonradioactive,” or “is heavier than air”. And second, theories specify how concepts are related to each other. For example, Susan Carey (1985) argues that 10-year-oldsand 4-year-olds represent different relations among such activities as eating, breathing, growing, dying, and being male or female. The whys and wherefores of these activities for 4-year-olds involve individual wants and desires, and social convention. But 10-year-olds have acquired a new naive theory-a theory of biology-which allows them to see different, biological, relations among those activities. In sum, we have examined concepts of mental activities in order to look for developmentalchanges in the features used to form concepts,and in the similarities and relations seen as important among concepts. Observing changes in the differentiation and organization of concepts of mental activities we felt would give us insight into the underlying theories of mind responsible for those changes in conceptual structure. In our first study (Fabricius, Schwanenflugel, Kyllonen, Barclay, & Denton, 19891, we asked subjects to rate the similarity of all possible pairs of 13 sentences (shown in Table 21, where each sentence described a common activity that primarily involved one of four types of mental activities:Memory, Comprehension, Attention, Inference. (We included two types of Memory -what we called list memory, and prospective memory.) Subjects were told to judge how similar they felt the activities were based on how they would have to use their mind to do
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each activity. We chose the items based on ratings we had obtained from experts (advanced graduate students in psychology) about the types of mental activities involved in each item.
Table 2 Stimulus sentences with experimenter's elaborations to children shown in brackets List Memory (LM) 1.Making a list at home of all the kids in your new class without missing any. [It is soon after school starts in the year when you do it.] 2. Getting all the things at the store that your mother asked you to get. [Shedidn't give you a list. She just told you, and now you are at the store and you have to get them.] Prospective Memory (PM) 3. Bringing back your permission slip for the field trip. [Nobody tells you. You have to bring it back yourself when you leave to go to school.] 4.Saying Happy Birthday on the right day to your friend who told you her birthday a long time ago. Comprehension (C) 5. Learning a new board game from the instructions on the box. 6. Reading your math book to be able to do the problems at the end of the lesson. 7. Feeling like you know how to get to your friend's house from the directions she is giving you. [You've never been to her house and she's telling you the directions.] A ttention (A) 8. Trying to find the North Star in the sky on a starry night. [The North Star is a special bright star, and you know what it looks like, but there are lots of stars out.] 9. Listening to what your friend is saying to you in a noisy classroom. 10. Picking a yellow flower from a bunch of flowers of different colors. Inference(I) 11.Figuring out what your friend wants when he says, "Boy, that cookie looks good!" 12. Seeing a puddle on the ground and realizing it must have rained last night. [You didn't hear it rain last night. You just see the puddle in the morning.] 13. Knowing that your teacher likes the present you gave him by the look on his face.
We used two techniques to assess conceptual structure: Nonmetric multidimensional scaling, a n d additive similarity trees. We used both of these models in order to highlight different aspects of the data. We used MDS for insight into the underlying dimensions or relations that subjects saw as important among concepts of mental activities. We used additive similarity trees t o see which
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specific items subjects tended to include in the concepts that they formed. The results showed two important developmental changes. The first developmental change involved how mental activities were interrelated. Both 10-year-oldsand adults saw the most important relation among mental activities to be the degree to which they involved memory. There was no evidence that 8year-olds organized mental activities in terms of the amount of memory they involved. The second developmental change involved the specific concepts that were formed. Subjects at all ages had concepts of Memory and Inference. That is, they rated the four Memory activities as having more in common with each other than with other mental activities, and likewise for the Inference activities. This was not the case for Comprehension and Attention. Eight-year-olds did not see the difference between Comprehension and Attention. They seemed to think that they were similar types of mental activities that involved mainly seeing or hearing. Ten-year-olds did see a difference between Comprehension and Attention, but it was only in terms of how much memory they involved. Ten-year-olds still did not recognize unique features for each type of activity. They seemed to think that Comprehension and Memory were similar types of mental activities, and, like 8-year-olds, they thought that Attention only involved seeing or hearing. Finally, adults recognized features that distinguished Comprehension and Attention as unique types of mental activity. We feel that is important that 8- and 10-year-oldshad difficulty forming concepts of Comprehension and Attention, even though they had no trouble forming concepts of Memory and Inference. Our Memory and Inference activities were, in Markman's (1981) terms, constrained by the context so that there was very little room for interpretation, organization and transformation of the information. In contrast, our Comprehension and Attention activities were much less constrained and allowed more room for individual organization and interpretation. We believe that children were insensitive to this difference, and that was why they confused, for example, Comprehension with Memory, and Attention with simply seeing and hearing. To make these distinctions, children would have to understand how it is possible to look at something-such as a figure embedded in a background-but not see it, and to remember something but not understand it. In such cases there is a difference between what is objectively present and what is known. Children's understanding of how such cases are possible may depend on their understanding of the representational nature of mental activity. That is, we felt it was likely that children in our study did not view the mind as able to actively interpret, organize, and transform information to produce subjective experience, and did not understand that psychological processes can impose new structures on information and represent the same information in a variety of ways. Below we elaborate our analysis of categories of mental activities
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vis a vis the representational nature of cognition, and extend this analysis to the categories of Comparison and Planning. We assume that within any category of mental activity-e.g., Memory, Inference, Comprehension, Attention, Comparison, or Planning-particular mental activities can vary along a representational continuum. At one end of the continuum are activities that involve relatively little interpretation, organization, and transformation of information. At the other end of the continuum are activities that involve relatively extensive interpretation, organization, and transformation. Table 3 presents examples of particular activities at each end of the minimally versus highly transformational continuum for six categories of mental activities. Note that any particular mental activity involves some amount of many or even all of these six categories(plus others undoubtedly). In fact, in rating data that we have collected, we found consensus among adults on distinctive “profiles” for different particular activities in terms of the amount of memory, inference, comprehension, etc. they involved. We also found consensus that certain activities involve primarily one category of mental activity. These are the ones we refer to when we talk about “Memory activities“, “Inference activities,” etc.; thus, we do not mean to imply that these activities involved ody memory, inference, etc. Note also that the distinctive features listed (in parentheses) are not meant to be an exhaustive list of features for each mental activity category. The listed features were adapted from the definitions given in The American Heritage Dictionary so as to emphasize the distinctive ways information is handled in each category. We propose that children should be able to understand the distinctive features of Memory, Inference, Comparison, and Planning without understanding the representational nature of mental activity. Further, we propose that understanding the representational nature of mental activity is required in order to understand the distinctive features of Comprehension and Attention. First consider Memory, Inference, Comparison, and Planning. Children’s failure to understand the representational nature of mental activity should be reflected in their failure to distinguish minimally transformational from highly transformational types of activity in each category. Thus, children should fail to see the differencebetween rote memory activities and memory activities that are highly constructive and interpretive, such as autobiographical memory. They should also not differentiate between inferences that are relatively automatic and those that are more worthy of a Sherlock Holmes, where some information could imply several different conclusions and conclusions can be arrived at only through a constructed series of other related inferences. In terms of comparison, they should fail to appreciate the difference between obvious comparisons on which people would be obliged to agree and those that are more amenable to shifting criteria for similarities and differences depending on one’s purposes,
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goals, and values. Finally, they should not see the difference between plans that select an obvious means to achieve a goal, such as using a chair to reach something, and those in which there may be many courses of action available and the criteria for a good solution may be multiple, so that several plans may be optimal from different points of view. In all of these cases, there could be memory load or other differences that children might detect between activities at the two ends of the continuum, but our point is that children should not distinguish the activities on basis of the degree of constructive, interpretative processes they involve. For example, a child might think that it would be more likely to forget what one got for one’s birthday two years ago (autobiographicalmemory) than to forget what one was recently asked to get at the store (rote memory). But we would argue that the child would not think that in the former case as opposed to the latter one’s memory would be more likely to be a plausible construction that might inspire a high degree of confidence, but might nevertheless be untrue. Children should nevertheless be able to understand the distinctive features of Memory, Inference, Comparison, and Planning without understanding the representational nature of mental activity. The differences among those categories are based on features involving the different ways information is handled in each case (i.e., store & retrieve information, draw conclusions, note similarities & differences, and anticipate consequences). Children should be able to appreciate these different ways of handling information without having to be sensitive to the transformational dimension along which mental activities also vary. Second, with regard to Comprehension and Attention, sensitivity to the transformational dimension is necessary in order to appreciate the distinctive features of those activities. The distinctive features of Comprehension include assimilationand accommodation to structured information. As Markman (1981) points out, it doesn’t make sense to talk about understanding unstructured information, such as a phone number. During Comprehension one assimilates information to one’s cognitive structures, and accommodatescognitive structures to the information, and in so doing constructs a representation of the information. This reflects the dictionary sense of comprehend as “to grasp.” Comprehension activities at the highly transformational end of the continuum would involve cases where one has multiple ways of understanding some information or where one accommodates greatly by reorganizing or restructuring one’s prior knowledge in order to understand new information. Comprehension activities toward the minimally transformational end of the continuum would involve information that is highly familiar or otherwise easily and automatically understood. In such cases, as in understanding the question, “How are you?”, comprehension involves mostly assimilation and tends to reduce to primarily acquiring information. That is, we would probably be more likely to say that we heard the above question than to say that we comprehended it. (In fact, the activities that we were able to
Table 3 Six categories of mental activities and examples of activities at each end of the minimally versus highly transformational continuum Memory (store & retrieve information)
Inference (draw conclusions)
Comprehension (assimilate8 accommodate)
Minimally transformational
rote memory
automatic inferences
reduces to rote memory, automatic inference, or seeing/hearing
Highly transformational
autobiographical memory
many inferences appear possible
insight/ restructuring knowledge
Attention (observe carefully)
reduces to seeing/h&ng
selectiveattention: looking/ listening
Comparison (note similarities and differences)
Planning (antidpate consequences)
obvious similarities or differences
simple meansend plans
seeing a new similarity no one else saw
complex Planning situations
3
%
k2 %
8
6R
The older child k theory of mind 125 get consensus on as involving primarily comprehension were activities such as “Reading your math b o o k that would fall somewhere towards the middle of the transformational continuum.) Depending on the context and on what one has to do with the information, Comprehension activities at the minimally transformational end of the continuum could also be seen as primarily involving rote memory (as in responding correctly to the instructions in the following item on the Stanford Binet Form L-M: “Put the pencil on the chair, go open the door, and bring the book to me.”), or as primarily requiring automatic inferences (as in understanding the implications of the question, ‘What are you doing tonight?”). The important point is that if children are insensitive to the transformational dimension of mental activity they should see all comprehension activitiesas cases of acquiring information easily and automatically. That would mean they would confuse Comprehension activities with simply seeing and hearing, or with Memory or Inference activities depending on what else they perceived had to be done with the information. In other words, they would not be able to appreciate that the distinctive features of Comprehension involve constructing a representation or understanding of the information. In contrast, becoming sensitive to the distinctive features of Comprehension should alert a child to the possibility that his or her representation or understanding can be either partially correct, only one of several alternative ways to understand the information, or even fundamentally flawed. This implies that sensitivity to the nature of Comprehension would be important in motivating children to engage in comprehension monitoring. The distinctive features of Attention include careful observation. Attention activities at the highly transformational end of the continuum could include a number of different kinds of transformational activities such as (a) selective aftention, where one has to actively look or listen, and where it is possible for example to look at something-such as a figure embedded in a perceptually similar background-but not see it, (b) intermittent sampling and attention shifting,such as when one systematically compares two complex stimulus arrays, and (c) limited capacityaspects which come into play when one has to maintain a number of pieces of information in mind simultaneously. Children need to know that these capacities are difficult and error-prone and can be carried out in a variety of ways by different people, making them inherently stimulus transformation processes. Attention activities toward the minimally transformational end of the continuum would involve activities in which information is acquired easily and automatically. Those activities would tend to reduce to simply seeing or hearing. Children who are insensitive to the transformational dimension of mental activity should confuse activities that involve these different aspects of attention with seeingand hearing. In Flavell’s (1988)terms they should assume that ” ’perceptible‘ automatically implies ‘perceived.’ For instance, they
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may assume that another person will immediately locate an embedded figure which it just previously took them some time and effort to locate" (p. 257). Several predictions stem from this analysis. First, concepts of Memory, Inference, Comparison, and Planning should be among the easier concepts of mental activities. Second, children should tend to confuse Comprehensionwith either seeing and hearing, or with Memory or Inference, and they should confuse Attention activities with simply seeing and hearing. Third, they should not see differences between minimally transformational and highly transformational types of activities in each of the above categories of mental activity. Finally, developing sensitivity to the transformationaldimension, and to the distinctive features of Comprehension, should be related to children's developing sensitivity to the need for and their increasing use of comprehension monitoring. We tested the first two of these predictions in a follow-up study (Schwanenflugel,Fabricius, & Alexander, in press) using two new items for each of the eight following mental activity categories: Free Recall Memory (which was composed of List Memory and ProspectiveMemory activities),Recognition Memory, Comprehension, Selective Attention, Inference, Comparison, and Planning. In each category, experts had rated one item as primarily visual in character, and the other as primarily auditory. The ages tested and the rating procedure used were similar to the first study. The results showed that as before, subjects at all ages had concepts of Memory and Inference. At age 10, concepts of Comparison and Planning first appeared, while concepts of Comprehension and Selective Attention did not appear until adulthood. Thus,Comprehensionand SelectiveAttention were the most difficult concepts, as predicted, and Comparisonand Planning were easier. Furthermore, the errors that children made with Selective Attention were to confuse it with simply seeing and hearing, and the errors they made with Comprehension were to confuse it with Inference, Memory, or Comparison. In this study, we could see clearly that when children failed to categorize mental activities on the basis of the mental processes involved, they tended to categorize instead on the basis of outcomes of the activities. The conceptual distinctions that 8-year-olds made suggest that on the whole they focused more on the outcomes of mental activities than on the processes involved. Perhaps the clearest example is their concept of Memory. They had a global concept of Memory, in which they grouped together Free Recall and Recognition activities. Eight-year-olds' failure to differentiate the two shows that in their categorization of memory activities they did not weight mental processes very heavily. The important feature of memory activities for them was simply the outcome of the activity-that past information is brought to mind-regardless of whether that occurred via recall or recognition processes. Their failure to form a concept of Free Recall does not seem to be due to unawareness of recall processes, because
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we know from other research (Fabriciusand Cavalier, 1989; Fabricius and Hagen, 1984; Moynahan, 1973) that by 8 years of age most children can talk about associational processes that occur during free recall. There were other cases in which 8-year-oldscategorized on the basis of outcomes rather than mental processes. For example, although one can arrive at a decision using several different kinds of processes, such as Planning or Comparison, what seemed important to 8-year-olds was simply whether the activity required a decision, not the mental processes by which it was achieved. Similarly, they focused on whether activities resulted in acquiring new ideas, following instructions, or answering questions. Ten-year-olds differed from 8-year-oldsbecause they often focused on mental processes. First, they had a concept of Free Recall, which included only the List Memory and Prospective Memory activities, and not the Recognition activities. Second, they distinguishedComparison and Planning on the basis of the processes involved, instead of grouping them together on the basis of outcomes. However, despite their focus on these processes, 10-year-oldsdid not categorize on the basis of the mental processes of Selective Attention, Recognition, or Comprehension. These activities have something in common, in that their distinctive mental processes occur during input of information. SelectiveAttention processes account for how one may look at or listen to external information, such as a figure embedded in a background or several conversations at a party, but not see the figure or hear any one conversation. Recognition involves external information cueing previous experience. And Comprehension involves more extended processes of internal cueing that establish relations and connections with prior knowledge to construct a representation of the external information. In contrast, the mental processes that 10-year-olds did focus on (recalling information, drawing a conclusion, making a comparison, and forming a plan) occur largely after the information has been acquired and represented. This suggests that 10-year-oldsdid not believe that mental processes were important during information acquisition. Instead, they apparently felt that one simply perceived or came to know external information without having to use distinctive types of intervening mental processing such as selectively attending, recognizing, or comprehending. Adults, by contrast, did focus on mental processes that occur during information acquisition. They distinguished features for Selective Attention, Recognition, and Comprehension. In addition, they consistently applied higher level process features involving internal versus external cueing. These process features cut across outcomes, and thus further removed outcomes as important features for adults. That is, adults saw Free Recall and Comprehensionas similar on the basis of internal cueing,and Recognition and Inferenceas similar on the basis of external cueing. This resulted in a different organizationof these four activities compared
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to children, who grouped them only on the basis of outcomes. For example, 8year-olds grouped Recall with Recognitionbecause they have the same outcome of bringing prior knowledge to mind, and 10-year-oldsgrouped Comprehension with Inferencebecause they have the same outcome of coming to know something.
DEVELOPMENT OF A CONSTRUCTIVIST THEORY OF MIND In our first study (Fabricius et al., 1989), we argued that children’s failure to distinguish concepts of Comprehensionand Selective Attention suggested that they did not understand the constructivistnature of mental activity. The present findings allow us to elaborate further. A constructivist theory of mind requires a conception that mental processes necessarily mediate between perception of information and outcomes, such that mental processing can often give rise to different outcomes from the same information. Our findings that 8-year-oldsfrequently categorized mental activities on the basis of either seeingand hearing or outcomes, rather than mental processes, suggests that they did not conceive that mental processes necessarily mediate between information and outcomes. This finding suggests that they have a nonconstructivist theory of mind, in which external information more or less directly leads to outcomes. For example, 8-year-olds seemed to think that alternatives lead to decisions, regardless of whether those decisions were arrived at by planning or comparison. How does this suggestion that 8-year-olds have a nonconstructivist theory of mind fit with our earlier findings that by 6 years of age many children have acquired an Information Processing theory of memory? Children with an Information Processing theory of memory conceive that associational processes form a link in a causal chain from information, to processes, to recall. They assign a causal role to processes in memory, but does this mean that they conceivethat those processes have a constructivist role in that chain, and that their Information Processingtheory of memory is a constructivist one? We think not. We suspect that they think instead that the past external information is directly responsible for the particular associations that are generated during recall, in much the same way that a phone number constrains how one rehearses it. In other words, children may think that because two items-tc-be-remembered are conceptually related, one will cue another during recall, and both will thereforebe remembered, but they might still have no idea that cueing can be constructiveand influenced by other things than the relations presented in the information. In this nonconstructivist view, past information would be as ultimately responsible for the outcomes in free recall, as present information would be in recognition. This would explain why 8-year-oldssaw no important differencebetween recall and recognition, because in both cases external information more or less directly leads
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to the same outcome of bringing past information to mind. Perhaps children’s Information Processing theory of memory is nonconstructivebecause it is a theory of outcomes, specifically, a theory of how recall comes about. In this theory, associational processes are the causal explanations for how recall comes about. But this theory is not a theory about those processes. It does not explain how cueing can be constructive. Ten-year-oldscategorized on processes much more than 8-year-olds, including forming a concept of Free Recall, but by itself this does not mean that they saw recall or other mental processes as constructive. Instead, it is likely that they were fitting these newly discovered processes into a nonconstructivist theory similar to that of 8-year-olds. The reason we are reluctant to grant 10-year-olds a constructivist theory of mind is because they, like younger children, failed to see mental processes as important during acquisition; that is, they categorized information acquisition activities on the basis of seeing and hearing rather than mental processes of selectively attending, recognizing, or comprehending. Mental processes during acquisition may be less conscious than processes that occur after information has been acquired and represented. When children come to see that even acquisition of information is influenced by mental processes, they may be on the verge of their first insight into the constructivist nature of mental processes. This insight may begin when they consider that unconscious processes may influence conscious processes and affect outcomes. This may be how children start to understand how people can seriously disagree even when they receive the same information. While the development of a constructivist theory of mind is apparently not complete even by 10 years of age, it begins early. Even young children know that the same information can give rise to two outcomes. That is, one can have a belief that differs from the actual state of affairs (Wimmer & Perner, 19831, or a perception of something that differs from that of another person (Flavell,Everett, Croft, & Flavell, 1981),or two different beliefs about the same thing (that it looks like one thing but is something else) (Flavell, Green, & Flavell, 1986). The important difference between these early beliefs about the mind and the later constructivist theory of mind may be in children’s understanding of how different outcomes are possible. In the cases that are understood early, stimulus factors, such as outdated information, different vantage points, and different surface appearance are responsible for different beliefs and perceptions. We have argued that it is only much later in development that children come to see that mental processes can also cause different outcomes. This difference between early and later theories of mind suggests that we could find some early sensitivity to the usually difficult processes of comprehension and selective attention, by presenting children with cases in which failures or differences in comprehension and attention could be explained by stimulus
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factors. For example, children might understand that unfamiliar or ambiguous words might be understood differently by different people, or that someone might not understand a foreign word, but nevertheless recall it, or even draw an inference from it (e.g., that the speaker speaks Spanish). Research along these lines by Lovett and Flavell(l990) and Lovett and Pillow (1991) does show early sensitivity to comprehension, but even these tasks are sometimes fairly difficult for 8- to 9-year-olds. Our findings indicate that it is much more difficult for children to see a difference between, for example, understanding teacher’s explanation of an assignment and understanding her simple instruction, or, as in our previous study, understanding a math book and remembering a shopping list. In these cases, the words are all English, the speaker intends to communicate, and the differences have to be understood as due to the differences in comprehension processes for easy-to-understand versus difficult-to-understand information. Similarly, for selective attention, it might be easier for children to understand that one could look at but not see an object that was deliberately camouflaged, than to understand that different perceptions could result from mental processes such as having to divide attention between two clearly presented sources. These examples illustrate that having a constructivist theory of mind depends not on knowing .!%hatthe same thing can be known in different ways, but on understanding how it is possibleby assigning the causal role to mental processes as the explanation for how the same information could be seen, remembered, judged, understood, and used in different ways. What might account for the development of a constructivist theory of mind? We suggested previously (Fabricius et al., 1989) that children’s awareness that memory is part of all mental activities may eventually lead them to the conclusion that it is usually possible to interpret something in a variety of ways. Our current findings show that this awareness begins in 8-year-olds, which is earlier than we previously found. Our current findings also suggest that between 8 and 10 years of age children become aware of an increasing number of distinct processes. This accumulation of evidence that there are many different types of processes may suggest to children that mental processes are pervasive, and occur even during acquisition of information. But understanding the constructivist nature of mental processes would seem to require a more fundamental change in children’s naive theory of mind. Carey (1985) has identified three criteria for determining whether conceptual development involves a change from one naive theory to another. These are that new causal mechanisms are understood in the new theory, new concepts are formed, and the new theory applies to a different domain than the old theory. Future research on the applicability of these criteria to conceptual changes in older children‘s theory of mind should address the following questions: When do children understand that there are unconscious mental processes, and that these unconscious processes can causally affect
The older child k theory of mind 131
conscious mental processes? Is that related to their understanding that mental processes are constructive. Is it also related to their acquisition of new concepts of mental activities during acquisition of information (Selective Attention, Comprehension, Recognition) that are distinct from seeing and hearing? Finally, do children‘s nonconstructivist theory and their later constructivist theory of mind apply to different domains? Perhaps the nonconstructivist theory is really a theory about the outcomes of mental activities, in which case mental processes would be the theory‘s explanatorymechanisms. In contrast, the later constructivist theory may be a theory of the mental processes themselves. In that case, unconscious processes may be posited as the theoretical, explanatory mechanisms for how mental processes can be constructive. Understanding the nature of conceptual change in children’s theories of mind will inform us about children‘s understanding of the mind, and also about the nature of conceptual change more generally. REFERENCES
Astington, J.W., Harris, P.L., & Olson, D.R. (eds.) (1988). Developing theories of mind. New York Cambridge University Press. Carey, S. (1985). Conceptual change in childhood. Cambridge, MA: MIT Press. Fabricius, W.V. & Cavalier, L. (1989). The role of causal theories about memory in young children’s memory strategy choice. Child Development, 60,298-308. Fabricius, W.V. & Hagen, J.W. (1984). The use of causal attributions about recall performance to assess metamemory and predict strategic memory behavior in young children. Developmental Psychology, 20,975-987. Fabricius, W.V., Schwanenflugel,P.J., Kyllonen, P., Barclay, C.R., & Denton, S.M. (1989). Developing theories of the mind: Children’s and adults’ concepts of mental activities. Child Development, 60,1278 - 1290. Fabricius, W.V. & Wellman, H.M. (1983). Children’s understanding of retrieval cue utilization. Developmental Psychology, 19,lS - 21. Fabricius, W.V. & Zwahr, M. (1990, June). Metamemory at age six predicts memory and school performance at age nine. Paper presented at the annual meeting of the American Psychological Society, Dallas, TX. Fabricius, W.V., Zwahr, M., & Roberds, S . (in preparation). If you want to get a strategy, get a theory: The case of memory theories and strategies in young children. Flavell, J.H. (1988). The development of children’s knowledge about the mind: From cognitive connections to mental representations. In J.W. Astington, P.L. Harris, & D.R. Olson (eds.), Developing theories of mind (pp. 244 - 270). New York: Cambridge University Press. Flavell, J.H., Everett, B.A., Croft, K., & Flavell, E.R. (1981). Young children’s
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knowledge about visual perception: Further evidence for the Level 1- Level 2 distinction. Developmental Psychology, 17,99 - 103. Flavell, J.H., Green, F.L., & Flavell, E.R. (1986). Development of knowledge about the appearance-reality distinction. Monographs of the Society for Research in Child Development, 51 (1, Serial No. 212). Frye, D. & Moore, C. (eds.) (1991). Children's theories of mind: Mental states and social understanding. Hillsdale, NJ: Erlbaum. Kassin, S.M. (1981). From laychild to "layman": Developmental causal attribution. In S.S. Brehm, S.M. Kassin, & F.X. Gibbons (eds.), Developmental social psychology (pp. 169 - 190). New York: Oxford University Press. Lovett, S.B. & Flavell, J.H. (1990). Understanding and remembering: Children's knowledge about the differential effects of strategy and task variables on comprehension and memorization. Child Development, 61,1842 - 1858. Lovett, S.B. & Pillow, B.H. (1991). The development of the comprehensionmemory distinction: Evidence from strategy-selection and endstate-evaluation tasks. Paper presented at the biennial meeting of the Society for Research in Child Development, Seattle, WA. Markman, E.M. (1981). Comprehension monitoring. In W.P. Dickson (ed.), Children's oral communication skills (pp. 61-84). New York Academic Press. Moynahan, E. (1973). The development of knowledge concerning the effect of categorization upon free recall. Child Development, 44,238-246. Murphy, G.L. & Medin, D.L. (1985). The role of theories in conceptual coherence. Psychological Review, 92,289-316. Nisbett, R.E. & Wilson, T.D. (1977). Telling more than we can know: Verbal reports on mental processes. Psychological Review, 84,231 - 259. Perner, J. (1991). Understanding the representational mind. Cambridge, MA: MIT Press. Schwanenflugel, P.S., Fabricius, W.V., & Alexander, J. (in press). Developing theories of mind: Understanding categories and relations between mental activities. Child Development. Wellman, H.M. (1985). The child's theory of mind: The development of conceptions of cognition. In S.R. Yussen (ed.), The growth of reflection in children (pp. 169 - 206). New York: Academic Press. Wellman, H.M. (1990). The child's theory of mind. Cambridge, MA: MIT Press. White, P. (1980). Limitations on verbal reports of internal events: A refutation of Nisbett and Wilson and of Bem. Psychological Review, 87,105 - 112. Wimmer, H. & Perner, J. (1983). Beliefs about beliefs: Representations and constraining function of wrong beliefs in young children's understanding of deception. Cognition, 13,103 - 128.
PART I1
Mind and Reasoning
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Intelligence, Mind, and Reasoning: Structure and Development A. Demetriou and A. EMides (Editors) 0 1994 Elsevier Science B.V. All rights reserved.
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Reasoning, Metareasoning, and the Promotion of Rationality* David Moshman University of Nebraska-Lincoln,
USA
Perhaps the most extraordinarily logical individual in modem literature is the title character of Samuel Beckett's (1959)Watt. A servant of the mysterious Mr Knott, Watt spends most of the novel in meticulously systematic analysis of the bizarre events, routines, and circumstances of Mr Knott's household. It is Watt's responsibility, for example, to serve Mr Knott the same precisely prepared meal twice each day, "cold, in a bowl, at twelve o'clock noon sharp and at seven p.m. exactly, all the year round (p. 88)." With respect to the origin of this arrangement, Watt considers twelve possibilities, varying systematically with respect to (a) whether or not Mr Knott was responsible for the arrangement; (b) independent of a, whether Mr Knott knew he was responsible for the arrangement, or knew who (other than he) was responsible, or did not know who was responsible; and (c) formally independent of a and b, whether or not Mr Knott knew that the arrangement existed. To further complicate Watt's responsibilities, and thus his ruminations, Mr Knott does not always finish his meal; whatever is left is to be placed outside to be eaten, between 8 and 10 p.m., by "the dog." But the poor dog cannot count on a good meal, and Watt's combinatorial analysis of the possibilities in this connection is reminiscent of a Piagetian protocol: For though as a general rule Mr Knott ate every atom, both of his lunch and of his dinner, in which case the dog got nothing, yet what was to prevent him from eating every atom of his lunch, but no dinner, or only part of his dinner, in which case the dog got the uneaten dinner, or portion of dinner, or from eating no lunch, or only part of his lunch, and yet every atom of his dinner, in which case the dog got the uneaten lunch, or portion of lunch, or from eating only part of his lunch, and then again only part of his dinner, in which case the dog benefited by the two uneaten portions, or from not touching either his lunch or his dinner, in which case the dog . . . went away with its belly full at last (pp. 92-93). Not content to leave the matter at that, however, Watt feels compelled to consider how arrangements with respect to the dog originally came about. Ever * An earlier version of this chapter was presented at the meeting of the Jean Piaget Society, Montreal, May 1992. I am grateful to Mike Dunkle, Laura Finken, Molly Geil, Patricia Hashima, K. Helmut Reich, and Ellin Scholnick for comments on earlier drafts. Authois address: Department of Educational Psychology, University of Nebraska, Lincoln, NE 68588-0641, USA.
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the formal operational thinker, Watt understands that the actual arrangement is but one of a larger set of possibilities and considers four other potential arrangements, all involving dogs, and the objections to each. He notes two objections to the first alternative solution, three to the second, four to the third, and five to the fourth. A tabulation immediately follows (p. 97) of number of objections as a function of solution, followed by an even more absurd tabulation (p. 98) of cumulative number of objectionsas a function of number of solutionstwo objections to the first solution, a total of five objections to the first two solutions, a total of nine objections to the first three solutions, and, finally, a grand total of fourteen objections to the four alternative solutions. Watt is, here and throughout the novel, impeccably logical but utterly irrational. That is, his reasoning is invariably precise and systematic, never deviating from any applicable logical norm, and yet ultimately pointless, failing to provide any meaningful basis for knowledge or action. What Watt most lacks, I believe, is metacognitionwith respect to his reasoning, or, in a word, metmasoning (Russell & Wefald, 1991; cf. Lehrer, 1990). Rationality requires the purposeful deployment of reasoning,monitoring of progress with respect to the problem at hand, executive control, formulationand coordinationof strategies, reflection on one’s cognitive processes and structures, flexibility of perspective, critical thinking, comprehension of the nature of logic, acknowledgment of the limits of reason, periodic reconstruction of one’s cognitive processes and structures, and so forth. Use of the term metmasoning, however, can mislead us to think of the diverse tendencies and abilities involved as a single entity or process (cf. Alexander, Schallert, & Hare, 1991). The main thesis of this chapter is that metareasoningis usefully construed as encompassing three distinct, though interrelated, aspects, and that all three are critical to human rationality and intelligence. The three aspects of metareasoning are (a) procedural mefareasoning,involving the monitoring and direction of one’s own reasoning; (b) concepfualmefareasonhg, involving declarative knowledge about reasoning, and (c) constructive mefareasoning,involving the developmental reconstruction of one‘s reasoning and metareasoning. I will consider each of these in turn and then conclude with some comments on the relevance of metareasoningto the promotion of rationality.
Procedural Metareasoning Imagine that a year from now you need to locate this book. You know it is either on the top shelf of your officebookcase, where you keep works on cognitive psychology, or on the second shelf, where you keep works on developmental psychology. Not finding it on the top shelf, you immediately begin searching the second shelf. Analysis of your reasoning might suggest you have made the following deductive inference:
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The book is on the top shelf or the second shelf. The book is not on the top shelf. Therefore, the book is on the second shelf. Simple inferences of this sort are routine in all aspects of daily life. Even young children have been shown to make a variety of simple inferences with minimal effort or error (Braine, 1990; Hawkins, Pea, Glick, & Scribner, 1984; Scholnick & Wing, 1992; Smith, this volume). In most cases, such inferences are automatic, unconscious, and virtually instantaneous. Often, in fact, people are unable to distinguish what they have inferred from what they have seen, heard, or read (Jenkins, 1974). Suppose, however, that the book is not on the second shelf either. After another search of the two shelves, you make another deductive inference: The book is not on the top shelf. The book is not on the second shelf. Therefore, the book is not on the top shelf or the second shelf. Having thus rejected the initial premise of your original deductive argument, you now have a problem that probably cannot be solved via some immediate inference. You are likely to consider a variety of possibilities and raise a number of questions: Is there somewhere else I have been keeping books on cognitive or developmental psychology? Could I have classified this book in a different category, such as educational psychology? How would I classify it right now? When did I last see the book? What was I working on at the time? Did I take the book home for some reason? Might I have loaned it to someone? Could it have fallen behind the bookcase? Perhaps I don't own it after all-did I borrow and return it? Addressing these possibilities will likely involve making a large number of immediate inferences. It is possible you will ultimately fail to solve the problem of the missing book because you are unable to make a particular deductive or inductive inference necessary for reaching the correct conclusion about the book's current location. Much more likely, however, is that your success or failure will depend on what strategies you have for addressing problems of this sort and your ability to apply those strategies to the present problem, to monitor their implementation, to coordinate them effectively, and so forth. Many theorists and researchers have distinguished such second-order or executive processes from the immediate inferences that they monitor and control (Alexander et al., 1991; Bransford, Goldman, & Vye, 1991; McGuinness & Nisbet, 1991; Russell & Wefald, 1991; cf. Demetriou, this volume; Efklides, this volume; Langford & Hunting, this volume). Higher-order reasoning-problem solving, decision making, argumentation, etc.-typically takes place over an extended period of time and can be decomposed into numerous subprocesses of reasoning. The coordinating processes in such
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cases may be described as procedures that operate on processes of reasoning, thus as metaprocesses of reasoning or procedural metareasoning. Such processes may be purposely implemented and consciously controlled. With practice, however, they may become automatized strategies that take place rapidly and unconsciously and are themselves subject to coordination by still higher-order processes (Bransford et al., 1991; Pressley, Harris, & Marks, 1992). Evidence from many domains of reasoning suggests that the construction of increasingly sophisticatedand diverse forms of procedural metareasoningbegins very early in childhood and extends through the lifespan (cf. Demetriou, this volume, regarding the Specialized Structural Systems). This is not surprising. As the case of Watt suggests, even the richest and most logically defensible set of inference schemas would be of little value without procedural metareasoning to direct and coordinate their use. The critical importance of procedural metareasoning to rationality and intelligence is clear.
Conceptual Metareasoning
To the extent that a person reasons successfully, we may posit knowledge of how to reason. Such knowledge may simply be implicit in the inferenceschemas and procedural metareasoning of a given individual rather than being an object of explicit awareness. Research indicates, however, that, beginning in early childhood, people come to have explicit, declarative knowledge about the nature and use of reasoning, logic, and rationality (cf. Bransford et al., 1991; Byrnes & Wasik, 1991; Campbell & Bickhard, 1986; Karmiloff-Smith, 1992; Langford & Hunting, this volume). We may refer to such conceptual knowledge about reasoning and related matters as conceptual metareasoning. In the area of deductive reasoning, for example, there is considerable evidence of a systematic increase in metalogical understanding (Moshman, 1990a). Although young children commonly reach logically necessary conclusions from given premises (Braine, 1990; Hawkins et al.,.1984; Scholnick& Wing, 1992; Smith, this Volume), preschoolers typically fail to recognize the logical necessity of those conclusions (Somerville, Hadkinson, & Greenberg, 1979) or even the fundamental conceptual distinction between conclusions and premises (Sodian & Wimmer, 1987). With age, children show increasingly systematic conceptual knowledge about the nature of deductive inference, including an increasingly explicit distinction between cases where a particular conclusion is necessary and cases where two or more conclusionsremain possible (Byrnes& Beilin, 1991;Markovits, Schleifer, & Fortier, 1989). By adolescence, most understand, in abstract terms, the formal distinctionbetween valid and invalid arguments (Moshman & Franks, 1986), suggesting the emergence of declarative knowledge about the nature of the logical domain (Komatsu & Galotti, 1986).
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Similar trends can be adduced with respect to empirical knowledge and inductive reasoning (Moshman & Lukin, 1989). Simple learning, for example, is commonly construed as a matter of refining one’s knowledge by testing hypotheses (Gholson, 1980). Such hypothesis testing can be relatively unconscious, involving elementary inferences under the control of automatized hypothesis testing strategies (procedural metareasoning). There is, however, evidence that, over the course of development, children increasingly distinguish hypotheses from evidence (Sodian, Zaitchik, & Carey, 1991)and that the emergence and refinement of conceptual knowledge about the abstract interrelations of theory and data is an important aspect of development (Kuhn, 1989; Kuhn, Amsel, & OLoughlin, 1988). More generally, people come to have increasingly sophisticatedand explicit understandings regarding the nature and justification of knowledge (Perner & Astington, 1992). These involve self-reflectiveconceptions about the purpose of reasoning and the nature of rationality (Chandler, Boyes, & Ball, 1990; Kitchener & Fischer, 1990). We become increasingly able to state, explain, and justify standards for the evaluation of our own thinking and that of others (Baron, 1991). Conceptual metareasoning may also develop within a variety of domains of content. Thinking, in any domain, involves tacit assumptions, frameworks, methodological norms, and analytical procedures that can become objects of explicit, declarative knowledge. Reasoning about morality, for example, no doubt involves generally applicable patterns of deductive and inductive inference but may also involve inferences and modes of reasoning specific to the moral domain. Progress toward moral rationality may be usefully construed as a matter of increasingly explicit formulation of the rules implicit in one’s moral reasoning and behavior, the principles underlying those rules, the criteria justifying those principles, etc. (Moshman, 1991). Conceptual metareasoning may also involve declarative knowledge about matters specific to one’s own reasoning, including explicit assessment of its strengths and weaknesses (cf. Demetriou, this volume). This may relate importantly to issues of self-concept and to att;.tudinalconsiderationswith respect to reasoning (Alexanderet al., 1991; Baron, 1991; Bransford et al., 1991;Nickerson, 1991). It is important to emphasize the interdependent relation of conceptual and procedural metareasoning (cf. Byrnes & Wasik, 1991; Efklides, this volume). Knowledge about reasoning and executive control of one’s own reasoning are likely to be intricately interconnected. Conceptual knowledge about reasoning in general and about one’s own strengths and weaknesses as a reasoner may be critical to appropriate application of procedural metareasoning (see Demehiou’s discussion of “the hypercognitive system,” this volume). Correspondingly, knowledge implicit in one’s reasoning strategies and procedures may, via reflective abstraction, be a major source-or even the primary basis-of explicit conceptual
140 D. Moshman
knowledge about reasoning (Campbell & Bickhard, 1986; Karmiloff-Smith, 1992; Moshman, 1990a, 1994; Moshman & Lukin, 1989). Specific research on the relation of procedural and conceptual metareasoning is unfortunately sparse (but cf. Byrnes & Wasik, 1991; Demetriou, this volume; Efklides, this volume). Observed age trends, however, are consistent with the proposed interdependent relation (Moshman & Lukin, 1989). With respect to the development of hypothesis testing, for example, the (conceptual)trend toward differentiationand eventual coordination of the concept of theory and the concept of data parallels (procedural) trends toward purposeful testing of hypotheses (Gholson, 1980; Sodian et al., 1991),sophisticated coordination of hypotheses and evidence (Kuhn, 1989; Kuhn et al., 1988)and increasingly systematic application of a falsification strategy for seeking evidence (Overton, 1990a). Conceptual metareasoning is a critical component of rationality. This is not only due to its contributions to the quality of procedural metareasoning. Conceptual metareasoning, in itself, involves explicit knowledge about the nature and purpose of reasoning and thus a self-reflective understanding of the underlying reasons for our beliefs and behavior. Such concern with justifiability and justification-with having and acting on the basis of reasons-is central to what it means to be a rational agent (Moshman, 1990b, 1994; Paul, 1990; Rescher, 1988; Siegel, 1988,1991).
Constructive Metareasoning
To explain an individual's reasoning, then; requires, at the very least, an account of his or her (a) immediate inference schemas, (b) procedural metareasoning, and (c) conceptual metareasoning. Full explanation, however, would also require an account of how these have come to be what they are and how they are changing or could change. One possibility is that immediate inferences are tendencies shaped by learning language, that procedural metareasoning consists of learned strategies, and that conceptual metareasoning is a set of learned facts about reasoning. If the learning in question is simple and direct, involving imitation of or shaping by the environment with little role for active cognitive processing, this would be an empiricist perspective. The standard alternative to empiricist theories is nativism. On this view, whatever inferential and metareasoning tendencies and abilities we have are genetically determined and emerge via an internally-driven epigenetic process in which the environment, though necessary in some general sense for life and development, plays no specific directive role. Various combinations of empiricism and nativism are possible. One might argue,for example, that immediate inference schemas are innate but metareasoning
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is learned (cf. Braine, 1990). A more complex view would suggest a continuing interplay of genetic and environmental influences over the course of development (Gottlieb, 1991; Lickliter & Berry, 1990). Even if certain tendencies or abilities are attributable to heredity, environment, and/or an interaction of the two, however, it does not follow that the development of reasoning and metareasoning can be fully explained in such terms (Moshman & Lukin, 1989). Most modern theorists and researchers take a constructivist view of development in which active construction by the knower is central to developmental change (Lickliter & Berxy, 1990). Some constructivistviews are closer to empiricism than to nativism in their emphasis on interaction with specific environments; they are nonetheless constructivist in stressing, in addition to environmental input, the active role of cognition in determining the course of learning (Bransford et al., 1991; Pressley et al., 1992). Correspondingly, some constructivist views are closer to nativism than to empiricism but are nonetheless constructivist in stressing, in addition to innate knowledge and genetic guidance, the active role of cognition in determining the course of maturation (Gelman, 1991; KarmiloffSmith, 1992). With respect to reasoning, there is much disagreement about the relative importance of hereditary and environmental factors in accounting for various aspects of reasoning and metareasoning and their development. Most psychologists readily acknowledge, however, that the development of reasoning is an ongoing process in which individuals actively think about and reconstruct their own reasoning (Baron & Sternberg, 1987; Bickhard, 1991; Bransford et al., 1991; Gelman, 1991; Karmiloff-Smith, 1992; Kuhn, 1990; McGuinness & Nisbet, 1991; Moshman, 1994; Overton, 1990b; Pressley et al., 1992; Voss, Perkins, & Segal, 1991). I will refer to this constructive process as conshctivernetazeasomhg. Constructive metareasoning is a type of metareasoning in that it involves the operation of cognition on one’s own reasoning. However, although it relates in important ways to procedural and conceptual metareasoning it cannot be reduced to either. Reasoning about reasoning may yield the sort of knowledge about reasoning that I earlier referred to as conceptual metareasoning but it is obviously critical to distinguish the resulting knowledge about reasoning (conceptual metareasoning) from the process that creates it (constructive metareasoning). Given that constructive metareasoning is a process, it is related to procedural metareasoning. It differs, however, in that procedural metareasoning monitors, directs, and coordinates the application of existing cognitive processes and structures whereas constructive metareasoning restructures one’s reasoning to create new inference schemas, strategies, and knowledge. Thus, procedural metareasoning is an aspect of thinking, conceptual metareasoning is a type of knowledge, and constructive metareasoning is the postulated process of learning and development.
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It is useful to distinguish two sorts of constructive metareasoning. One involves reflection on and coordination of inference patterns and strategies presented in the social environment. This corresponds to what is generally called learning and may be central to the emergence of increasingly complex and sophisticated procedural metareasoning. Explaining such changes in terms of constructive metareasoning reminds us that learners are already reasoners and that learning to reason better involves active construction of new reasoning out of old in the course of complex interchangeswith the environment. Even where externally represented patterns and strategies play a central role, learning to reason is not simply a matter of direct internalization (Bransford et al., 1991; Pressley et al., 1992). The other type or aspect of constructive metareasoning, in its pure version, involves reflection on and coordination of the most general and necessary aspects of one's reasoning so as to abstract new understandings about the nature of logic, reasoning, and rationality. This corresponds to the Piagetian concept of reflective abstraction (see Boom, 1991; Campbell & Bickhard, 1986)and may be especially critical with respect to the development of conceptual metareasoning (Moshman, 1990a, 1994; Moshman & Lukin, 1989). Consider, for example, a child who believes in certain moral rules. An encounter with someone who presents and defends an alternative set of rules may lead to an effort by the child to defend his or her own rules and criticize the alternatives. This may require abstraction of general principles underlying the rules in question and, perhaps, coordination and reconstruction of those newly explicit principles. Ultimately, over a period of years, the principles themselves may come into question. This may lead to explicit formulation of, and reflection on, the criteria for evaluating such principles. Thus moral reasoning develops not through accretion of new ideas or rules but through reflective reconstruction of one's moral assumptions and modes of analysis. The environment may play a critical role in this by challenging current moral reasoning, providing possible alternatives, and encouraging genuine reflection. The reflection, however, is an internal metacognitive reconstruction (Moshman, 1991). In sum, procedural and conceptual metareasoning are products of development, whereas constructive metareasoning is the developmental process that creates these products. The interdependent progress of procedural and conceptual metareasoning over the course of development is due to the continuing operation of constructivemetareasoning. In a complexand changing world, no fixed system of reasoning can be totally and forever adequate. Moreover, to be locked by one's genes or indoctrinated by one's culture into patterns, processes, and conceptions of reasoning immune to self-reflective critique and reconstruction would be to lack the ultimate epistemic freedom that lies at the core of rational agency (Lehrer, 1990). Constructive metareasoning, then, is fundamental to rationality and intelligence.
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The Promotion of Rationality Reasoning is a natural process. Even young children engage in reasoning and develop progressively, albeit fitfully and imperfectly, toward increasing rationality (Beilin, 1992; Bickhard, 1991; Moshman, 1990a,b, 1991,1994; Moshman & Lukin, 1989). It does not follow, however, that schools need not concern themselves with promoting reasoning and rationality. Any constructivist perspective, even one with a strongly nativist orientation, will acknowledge that one's environment may greatly hinder or facilitate the development of reasoning. There may even be value in the specific teaching of particular inference patterns and/or reasoning strategies (Baron & Brown, 1991; Baron & Sternberg, 1987; Bransford et al., 1991; Moshman, 1990a; Nisbett, Fong, Lehman, & Cheng, 1987; Pressley et al., 1992). Even if direct teaching of good thinking is possible, however, it is notoriously difficult (Moshman, 1990b). Given that reasoning is a natural process and its development toward greater rationality is a general trend, there is much to be said for a view of education that focuses on facilitating such development. To restate the matter in the terminology of this chapter, I suggest that it is possible to teach specific inference patterns and to improve procedural metareasoning through direct instruction in particular reasoning strategies. Genuine progress toward rationality, however, involves coordination of and reflection on one's procedural metareasoning and the corresponding construction of conceptual metareasoning. Rationality develops, in other words, via constructive metareasoning. The ultimate value of an instructional approach, then, may be a function of the extent to which it facilitates constructive metareasoning. What facilitates constructive metareasoning? I would highlight the encouragement of appropriate self concepts, attitudes, and intentions (Cederblom, 1989; Nickerson, 19911, including "rational passions" for truth, clarity and fairmindedness (Paul, 1990) and what philosophers refer to as a "critical spirit" (Siegel, 1988,1991). Such considerations of will and disposition lie at the interface of cognition with affect, motivation, social relations, and cultural context (Bickhard, 1991; McGuinness & Nisbet, 1991). From this perspective, the specifics of educational practice, including curricular and instructional details, may only be secondary factors in the promotion of rationality and intelligence. What matters most, I suggest, are broad considerations of educational policy, including the core aims and values of a given school and the general atmosphere in which education takes place. Promotion of rationality, in this view, depends on general characteristics of schools, educational systems, and the societies in which they function (Bickhard, 1991). It is critical to recognize that all societies impose substantial restrictions on information and ideas (Chomsky, 1989). Even democratic governments routinely channel public debate via decisions about what information to release to the press, what to withhold, what intellectual and expressiveactivities to fund,
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and so forth. Major media, moreover, are profit-seekingbusinesses and are often owned by large conglomerates with significant military, industrial, and governmental ties. Even in the absence of official censorship, decisions about what to publish or broadcast are inevitably made on the basis of a variety of considerations unrelated-or even antithetical-to the goal of promoting rational discourse. Public expression is, moreover, subject to a variety of social and cultural sanctions (Paul, 1990). Intellectual diversity and open debate may be encouraged, but only within a well-established framework of tacit assumptions and values. Such ideological commitments, moreover, because they are widely shared, may remain invisible, thus fostering the illusion that debate is far more robust and uninhibited than it really is (Chomsky, 1989); Colleges and universities, operating with a tradition of academic freedom, may be somewhat less restrictive in these respects than the communities in which they are located. In elementary and secondary schools, however, constraints on intellectual freedom are generally even greater than in society at large. In the United States, for example, public elementary and secondary schools are under the control of school boards elected by, and answerable to, the communities in which they operate. School administratorsknow that community dissatisfaction can cost them their jobs; teachers know that novel ideas are likely to generate negative reactions. Not surprisingly, then, censorship of textbooks, school library books, and student publications is widespread (Moshman, 1989). Although students have been held to be persons with constitutional rights to express their views (Tinkerv. Des Moines,1969) and not be indoctrinated (West Virginia v. Bamette, 19431, American courts are no longer inclined to enforce such rights. Current legal decisions construe education, at least at the elementary and secondary levels, as a process of inculcatingideas and values. School officials are held to have broad authority to determine what is taught, to select or remove textbooks and library books, and to censor the expression of ideas deemed inconsistent with the school's curriculum and values (Hazelwood v. Kuhlmeier, 1988; Moshman, 1989,1993). Schools vary widely in the degree of diversity permitted in their libraries and cumcula and in the extent to which they restrict, permit, or encourage independent thought. Even where a range of views is presented and active consideration of alternatives is encouraged, however, thought and debate are generally limited by shared frameworks, assumptions, and modes of reasoning that remain largely outside awareness. To the extent that such tacit commitments become conscious at all, they are taken as defining rational analysis and discourse, and thus as beyond legitimate question (Ewert, 1991). Schools may, to be sure, successfully inculcate a variety of useful thinking skills and even teach students how to generalize these to new content. But they
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may simultaneously fail to address-or even acknowledge-the existence of controversial topics and deeply ingrained ideas with respect to which students cannot or will not apply such thinking (Paul, 1990). Devoted to being right, students may selectively use new skills of rhetoric and argumentation to superficially refute disfavored ideas and cIeverly shore up their own positions (Cederblom, 1989; Paul, 1990). Units on problem solving may teach skills applicable to a variety of personal, societal, and academic problems at the same time that the general atmosphere of the school discourages students from identifying and calling attention to disconcerting new problems (Paul, 1990). Instruction in decision making may help students choose wisely within a range of socially acceptable alternatives while other elements of the curriculum reinforce their tendency to reject out of hand a variety of other possibilities (Paul, 1990). To the extent that tacit ideological commitments and socially shared modes of reasoning remain invisible, genuinely radical alternatives to prevailing academic, social, and political orthodoxies remain literally unthinkable. Despite evidence that thinking skills curricula can have detectable positive effects, then, the extent to which they promote rationality and intelligenceis open to serious question. Instruction in thinking may, and often does, take place in schools where books are censored, where student speech and writing are restricted to acceptable views and topics, where discussions are quietly directed away from unorthodox or controversial ideas, and where creativity is, perhaps unwittingly, confined within politically and socially acceptable bounds. It is reasonable to hypothesize that only limited aspects of rationality are fostered in such schools, regardless of what inference patterns or thinking skills are inculcated within the official curriculum. Correspondingly, I would hypothesize that, regardless of curricular and instructional specifics, rationality and intelligence are substantially facilitated to the extent that schools, and the societies in which they function, manifest an atmosphere of genuine intellectual freedom (Moshman, l989,1990b, 1993). In schools fully committed to the promotion of rationality, students would be actively encouraged to think, to question, to explore diverse sources of information, to express their own ideas, and to discuss those ideas with others. Teachers would model genuinely critical thinking, including rigorous critique of cherished assumptions and orthodox modes of analysis. Administrators, politicians, and citizens might join the debate, but would have neither the power nor the inclination to squelch it. Such is the environment in which metareasoning and rationality would flourish.
Summary and Conclusion Rationality is not simply a matter of reasoning in accord with rigorous laws
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of logic. Rather it involves metacognition with respect to reasoning, or metareasoning. Metareasoning, in turn, can be usefully divided into procedural metareasoning, involving control of one‘s inferential processes; conceptual metareasoning,involving knowledge about logic, reasoning, and rationality; and constructive metareasoning, involving developmental reconstruction of one’s reasoning and metareasoning. It is natural to wish we could teach students to process information correctly as easily as one can program a computer to do so. Even if that were possible, however, the resulting student would be no more rational than the resulting computer, or, for that matter, than Beckett‘s Watt. Rationality and intelligence include logical reasoning, of course, but go far beyond it. They encompass coordination and control of one’s reasoning, sophisticated knowledge about reasoning, and, perhaps most critical, reflective reconstruction of one’s reasoning and metareasoning. The direct teaching of thinking may be a valuable part of an educational effort to promote intelligence. The present conception of rationality suggests, however, that the atmosphere within which education takes place may be more critical. It is all too easy to practice one’s logic, as does Watt, as a ritualistic alternative to real thinking, and thus to pass the endless time and relieve the dreadful burden of existence (Robinson, 1969). Social institutions routinely channel people’s minds in socially approved directions and insulate them against the realities of institutionalizedoppression, massive violence, and pervasive suffering (Chomsky, 1989). Educational institutions are no exception and, especially at the elementary and secondary levels, may be even more narrowly and systematically indoctrinative than society at large (Moshman, 1989). Genuine rationality is far more than the instrumental ability to formulate arguments, solve problems, and make decisions within the tacit constraints of the status quo (Ewert, 1991; Paul, 1990). Active encouragement of reasoning and reflection, including radical critique and reconstruction, may be central to preparing students for something more than a lifetime of service in the home of Mr Knott.
REFERENCES Alexander, P.A., Schallert, D.L., & Hare, V.C. (1991). Coming to terms: How researchers in learning and literacy talk about knowledge. Review of Educational Research, 61,315-343. Baron, J. (1991). Beliefs about thinking. In J.F. Voss, D.N. Perkins, & J.W. Segal (eds.),Informal reasoning and education (pp. 169-186). Hillsdale, NJ: Erlbaum. Baron, J. & Brown, R.V. (eds.) (1991). Teaching decision making to adolescents. Hillsdale, NJ: Erlbaum.
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behavior in young children. Child Development, 50,119-131. Tinker v. Des Moines Independent Community School District, 393 U.S. 503 (1969). Voss, J.F., Perkins, D.N., & Segal, J.W. (eds.) (1991). Informal reasoning and education. Hillsdale, NJ: Erlbaum. - West Virginia State Board of Education v. Bamette, 319 U.S. 624 (1943).
Intelligence, Mind, and Reasoning: Structure and Development A. Demetriou and A. Efklides (Editors) 43 1994 Elsevier Science B.V. All rights reserved.
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The structure and development of propositional reasoning ability: Cognitive and metacognitive aspects* Anastasia Efklides, Andreas Demetriou, and Yiota Metallidou Department of Psychology, Aristotelian University of Thessaloniki, Greece For the last thirty years, and under the influenceof Piaget’s work, propositional reasoning has entertained a prominent place in the study of thinking. However, a look at two of the most recent books on reasoning (Johnson-Laird& Byrne, 1991; Overton, 1990b) makes clear that there is still little consensus about the nature and development of propositional reasoning. This is due to the fact that neither the origin of propositional inferences nor their relation with other intellectual abilities has been traced. Furthermore, although propositional reasoning was originally supposed to be an acquisition of adolescence (Inhelder & Piaget, 1958), this proved not to be the case. THE NATURE OF THE REASONING PROCESS With regard to the nature of propositionalability, a distinctionshould be made about logical reasoning in general, which involves inference drawing following logical rules, and propositional reasoning, which refers to inferences from propositions. For Piaget, logical reasoning constitutes intelligence and it takes various forms, depending on the level of intellectualdevelopment. Propositional reasoning is the form assumed by logical reasoning at the stage of formal thinking (Inhelder & Piaget, 1958). However, this claim has been challenged on two grounds. First, intelligence is not a “structure d’ensemble” that obeys the rules of logic (Demetriou & Efklides, 1981,1985). In fact, it is now commonly accepted that many aspects and functions of intelligence cannot be reduced to logic (Case, 1992; Demetriou, Efklides, & Platsidou, 1993; Gardner, 1983; Sternberg & Berg, 1992). Second, although, on the one hand, young children use propositional reasoning schemes efficiently (Greenberg, Marvin, & Mossler, 1977; Hill, 1961; OBrien & Shapiro, 1968), adults, on the other, make mistakes in inference drawing (Wason, 1968). Therefore, Piagetian theory does not suffice to explain either the nature or the development of propositional reasoning. * Author‘saddress: Anastasia Efklides, Department of Psychology, Faculty of Philosophy, University of Thessaloniki,Thessaloniki 540 06, Greece.
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Braine & OBrien (1991) have recently made a similar claim, namely, that mental logic is the means for “going beyond the information as given to draw inferences” (p. 200). In this sense, mental logic is a very general characteristicof the architecture of mind. Mental logic (at least in the case of if) consists of schemas that involve a lexical entry, a propositional logic reasoning program, and a set of pragmatic principles that governs the interpretation of sentences in context. Mental logic develops in childhood. Logical error is due either to pragmatic plausibility factors that override the logically necessary inferences or to failure of the reasoning routines to adapt to new or complex situations. In this case, either nonlogical heuristics or other reasoning procedures are applied, such as probabilistic, narrative, or analogical procedures. Therefore, this theory assumes that besides propositional reasoning there are other thought processes that may be applied in face of specific problems, and these processes cannot be reduced to mental logic. Consequently, although very general in scope, mental logic is still a specialized way of addressing problems. Propositional reasoning is an even more specialized inference-drawingmechanism, involving inferential schemas. It is to be noted, however, that, although Braine and OBrien’s (1991) theory does give a detailed account of propositional reasoning, it does not deal either with its development or with its relation to intelligence. Johnson-Laird (1983,1990;Johnson-Laird & Byme, 1991) has also advanced a general theory of reasoning that includes propositional reasoning. It assumes that reasoning proceeds in three steps: in the first step, the reasoner represents the state of affairs referred to in the proposition(s) into a mental model. In the second step, the reasoner formulates a conclusion on the basis of the relations present in the mental model. In the third step, the reasoner constructs an alternative model of the premises that refutes the initial one. This is a semantic model of reasoning that denies the existence of any sort of mental logic or reasoning schemas. What the person needs is, firstly, linguistic ability that enables the understanding of discourse and the construction of mental models and, secondly, the ability to search for counterexamples (Johnson-Laird, 1990). This theory therefore stands in sharp contrast to the previous theories. Furthermore, although it makes no claims about the nature of intelligence, it does make conjectures about a general mechanism that might underlie the development of both the linguistic and reasoning ability. It is the mechanism for the formation of mental models. A critical aspect of this mechanism is the ability of the mind to form models of its own abilities and even models of this ability itself. This is an in-built machinery that, along with language and reasoning, underlies introspection and metacognition. From this point of view, the architecture of intelligence can be viewed as comprising both specific abilities, such as language and reasoning, and general, in-built machinery, such as the recursive capacity to embed mental models within mental models (Johnson-Laird,1983).
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Our theory about the structure of mind (Demetriou& Efklides, 1988; Demetriou, Efklides, & Platsidou, 1993) postulates that mind presupposes the functioning of three different systems, namely domain-specificSpecialized StructuralSystems (SSSs), a domain-general system which may reflect hardware constraints of the biological substrate of our mind, and a domain-general software system that involves general self-understanding and metacognitive regulation skills. Specifically, the domain-general hardware refers to the constructive features of the cognitive system - such as speed and control of processing, and working memory -which underlie the functioning of all specialized systems of thought. The domain-general software (or hypercognitive system, in our terms) refers to the metacognitive aspects of intelligence which involve both awareness of the functioning of the mind and monitoring of thought processes. The SSSs are broad abilities that are responsible for the processing of domain-specific information. Each SSS is biased towards a specific symbolic system and processing means, and functions in relative autonomy from the others. The theory distinguishes five SSSs, namely the qualitative-analytic, the quantitative-relational,the causalexperimental, the spatial-imaginal, and the verbal-propositional. Propositional reasoning is the processing means of the verbal-propositional SSS. The particular characteristicof this SSS is the processing of semantic relations and the suppression of meaning so that formal relations among entities may be established. Specifically, our theory conjectures that the domain of application of propositional ability is semantic relations and its symbolic vehicle is language. Propositional inference rules (or schemas) constitute the processing means of this SSS. Therefore, Experiential Structuralism differs from the other theories in both the assumptions regarding the nature of intelligence and the nature of propositional reasoning; in the latter case, it lies in between theories that emphasize the semantic character of reasoning (cf. Johnson-Laird)and the mental schemas or mental rules theories (cf. Braine), that emphasize the syntactic aspect of the ability. This position, however, requires that a number of issues are clarified. First, how is semantic content, as conveyed by verbal statements, implemented into formal structures, such as inferential schemas? Second, how do formal structures become the means for the better understanding and enrichment of semantic relations? In other words, how are propositional inference routines acquired and used? Third, how do the concepts of logical necessity and logical validity develop? Logical necessity and validity are the features par excellence of propositional reasoning, that is, the features that render it different from any other inductively led acquisition. Fourth, are there developmental changes in this ability and how can they be explained?
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THE DEVELOPMENT OF THE REASONING PROCESS The answer to the first three issues depend on the study of the development of propositional reasoning. This is so because the formal inferential schemas that are characterized by logical necessity (Piaget, 1986; Piaget &Garcia, 1991; Ricco, 1990; Smith, this volume) and allow validity judgment are nothing but exemplification of the highest level of the functioning of this ability, accomplished in early adulthood (Johansson, 1977; Johansson & Sjoelin, 1975; Moshman & Franks, 1986;Neimark & Slotnick, 1970;Overton, Ward, Noveck, Black, & OBrien, 1987). The assumption is that the study of the developmental course of propositional inferences will provide insight into the mechanism that propels cognitive change in this domain and into the reasons why a significant number of adults fail to reason according to logical rules. Indeed this is the approach adopted here. The evidence regarding the development of propositional reasoning indicates that the use of propositional schemas goes back to 8 to 10 years of age (see Braine & Rumain, 1983) but awareness of the schemas and of the meaning of logical connectivesbegins only after the age of 10 years. Awareness of logical necessity and validity occurs only in late adolescence or early adulthood (Moshman & Franks, 1986). According to Overton (1990a), the major cognitive change that takes place in late adolescenceis that thinking becomes systemic, thereby allowing abstraction and formalization of the relations among sets of propositions. It is this formal or syntacticalorganization which allows the grasp of logical necessity as a property of a deductive system. In fact, Overton suggested that there are two phases of change in logical reasoning: one between 10 - 14 years of age that is marked by the “achievement and consolidation of formal competence”, and one between 14 - 18 years of age when “novel procedures, adequate to the novel competence, are developed’’ (p. 25). However, Overton does not explain in more detail what the ”novel competence” is and the nature of the novel procedures that are being developed. A plausible assumption is that this novel competence acquired during late adolescence is of an epistemic nature. As Kitchener (1983) has pointed out, the particular feature of late adolescent and adult thinking is that of epistemic cognition. Epistemic cognition refers to the ability to reflect on the limits of knowing, the certainty of knowing, and criteria of knowing. Moshman (1990; this volume; Moshman & Franks, 1986)also speaks about metareasoningor metalogical competence that develops in late adolescence and considers awareness of both logical necessity and validity and thinking of logical schemas to be a system which can be contrasted to other systems, such as language. Braine and OBrien (1991)refute the possibility of direct introspective access to inferential schemas, and thus they do not accept metacognitive influences on reasoning. Finally, Johnson-Laird (1990) claims that the development of reasoning presupposes,
Structure and development of reasoning 155
besides a sufficient working memory, a metalinguistic ability that allows the grasp of truth and a metalogical ability that leads to the grasp of validity. Therefore, it is not clear whether the source of change in propositional reasoning is merely cognitive or metacognitive. Of course, the two mechanisms of change need not function independently of each other. In our theory (Demetriou & Efklides 19891, we have suggested that there is a cognition-metacognitionloop, such that development of the one affects the development of the other and vice-versa. In fact, we (Demetriou & Efklides 1985,1987) have initially used the term ‘propositional-reflecting’ability to refer to the verbal-propositional SSS, in order to show the close interaction of these abilities during development. Relating propositional reasoning to metacognition requires, firstly, the definition of the term ‘metacognition’and the specificationof the relation presumed, because metacognition is a very general term often given in a variety of meanings. Experiential Structuralismgives a prominent place to metacognition as a domaingeneral mechanism that serves as the interface between the cognitive system (SSSs) and reality or between the SSSs themselves. Its function is to provide awareness of both the environmental input and mental activity in response to that input for the monitoring of thought activity. On-line awareness may take the form of metacognitive knowledge or metacognitive experiences (Flavell, 1979).Reflection on the contents of awareness offers the building blocks for higher levels of awareness such as epistemic and personal-model awareness (Klatzky, 1984; Efklides & Demetriou, in press). The above distinction of levels of metacognition implies that metalogic, which is epistemic in nature, presupposes not only on-line awareness but also reflection.To put it differently, the assumption is that metacognitive experiences are present even in young children but they do not suffice to lead to metalogical awareness. Metalogic presupposes reflection on the reasoning process, its products and the factors that affect the inferences drawn. Therefore, even if on-line awareness reflects underlying cognitive organizations, this awareness is not readily amenable to the reflection and analysis that allow conscious and deliberate monitoring of the reasoning process (Efklides & Demetriou, 19931,as one would expect if metalogic were the critical factor for the acquisition of higher forms of reasoning, that is, reasoning forms that presuppose consideration of validity. Furthermore, even if metalogic did prove to be the catalyst for the acquisition of higher forms of reasoning performance, one would still have to explain the acquisition of reasoning schemas in early childhood and their transformation to formal schemas in early adolescence. In our view, it is both cognitive and metacognitive factors that propel change, the relative weight of each factor perhaps shifting with advancing age. To test these assumptions the following study was carried out. The aim of the study was to investigate the development of propositional reasoning and the role
156 A. Efklides et al.
of metacognitive experiences and knowledge in the acquisition of the logical validity notion. The data to be reported here are part of a larger project in which the structure of the reasoning process as well as its development were tested (Efklides, Demetriou, & Metallidou, 1991).
METHOD
Subjects Two hundred and sixty one adolescents of 12,13,14,15, and 16 years of age, and 26 university students participated in the experiment. The adolescent subjects represented two socioeconomic levels, high and middle, depending on parental educationalbackground. There were 52, 48,42,68, and 51 subjects in the respective groups. The genders were about equally represented in each group.
Tasks Each of the subjects was tested with a battery of 58 arguments. Each of them was structured in two or more premises and a conclusion. Subjects were asked to decide whether the conclusion given followed from the premises, that is, whether it was right, wrong, or undecidable. The arguments were organized according to content (animals or plants), truth (empirically true, false, or nonsensible), logical rela tion (transitivity, implication, equivalence, conjunction, negajunction, and disjunction),logical connective(only in the case of transitivity and implication, where it is possible to use the connective iLthen or equivalent disjunctive or syllogistic forms), and validity (valid and invalid inferential forms). Table 1 shows some example arguments. The subjects were also required: First, to specify the perceived difficulty of each argument on a 4-point scale ranging from 1:not difficultat all to 4: very difficult.Second, to specify the perceived similarity of pairs of arguments on a . to explain 4-point scale ranging from 1:not similar at all to 4 v e ~ s i m k uThird, their similarity rating. The scoring of the explanations was based on a 5-point scale, ranging from 0: no explanation at all or non-sensical to 4 stating at least three ofthefactorsthat underlied the construction of the items (namely content, truth, logical connective, logical relation, validity), one of them being necessarily validity. These were the metacognitive measures used in the study; the first two measures represented metacognitive experiences whereas the explanation of similarity judgements represented metacognitive knowledge based on reflection, comparison, and analytical processes.
Structure and development of reasoning 157
Table 1 Examples of items used per logical relation, truth condition and validity TRANSITIVITY
If lemons are sourer than oranges and oranges are sourer than mandarins Then lemons are sourer than mandarins
CONJUNCTION
Grass is a plant. Trees are plants. Therefore grass and trees are plants
NEGAJUNCTION
It is not possible for a shark to be both a fish and a bird. The shark is a fish. Therefore the shark is not a bird
DISJUNCTION
The fox is either brown or white. The Canadian fox is not brown. Therefore the Canadian fox is white
IMPLICATION
1.If a plant is grown in a flower-pot,then it requires fertilizer. The tomato is grown in a flower-pot. Therefore it requires fertilizer
2. Either the rose is not wild or it has a few petals. The rose is wild. Therefore it has a few petals 3. All pigeons are birds. Squirrels are not birds. Therefore squirrels are not pigeons
EQUIVALENCE
If and only if an animal has wings, then it is bird. Hens have wings Therefore hens are birds
RESULTS AND DISCUSSION In order to delimit the relations between reasoning, metacognitive experiences, and metalogic, the results were analysed in two levels: a structural level, aiming to reveal the organizational constructs governing the reasoning process at both the cognitive and metacognitive level, and a group comparison level, aiming to trace developmental effects on performance and metacognition.
158 A. Efklides etal.
The structure of propositional reasoning ability
Performance. In order to test the plausibility of various alternative models regarding the organization of propositional reasoning, a series of confirmatory
H-y-& Fg==
2(45)=59.130, p=..O8..C f 1s.981
Figure 1.The general-reasoning-factormodel best fitting to the structure of mean performance scores attained on items when pulled around logical relation. The symbols trans, impl, nj, cj, di, equ,mtg, n-cntg and g stand for transitivity, implication, negajunction, conjunction, disjunction, equivalence, contingent, non-contingent, and general factor, respectively.
factor analyses were applied on the data. The EQS statistical program (Bentler, 1989) was used for this purpose. The first model tested assumed, followingBraine and OBrien (19911, that logical reasoning involves only inferential schemas that are triggered by logical connectives; in other words, logical relation is the basic organizational principle of reasoning performance regardless of the semantic
Structure and development of reasoning 159
(truth) or logical (validity) status of the arguments. In order to test this model, each of the various logical relations were represented by two half-scores. Each of these half-scores involved raw scores from all task categories (i.e., categories organized according to truth, validity, etc.). However, this simplistic model did not fit the data. The model that did fit the data best is given in Figure 1. The model presented in Figure 1 shows that logical relations do function as powerful organizational pivots of propositional reasoning. It also shows that the first-order factors are accounted for two second-order factors; the first factor accounts for the logical relations that involve affirmatively related propositions - that is, propositions that are contingent and can be jointly asserted; the second factor accounts for the logical relations that involve negatively related propositions, that is, non-contingent ones. The first factor is loaded by conjunction, implication, transitivity, and equivalence, and the second by negajunction and disjunction. Finally, the contingency and non-contingency factors are explained by a thirdorder factor, that is take to stand for general reasoning. This model essentially suggests that besides logical relations, that might function as inferential schemas, propositional reasoning also taps a critical element of reality, namely the possible contingency between the asserted facts or events, and, consequently, the possibility of their co-assertion. The various logical relations serve the coding of the possible variations of this contingency relationship. However, the above model does not show if truth and validity also affect the reasoning process. In order to test this assumption, performance scores were reorganized so that each of the logical relations of transitivity, implication, and disjunction was represented by four mean scores: The first mean score represented True Valid items, the second True Invalid items, the third False Valid items, and the fourth False Invalid items. Conjunction and negajunction were each represented by two mean scores, namely a True Valid and a True Invalid score. Equivalence was also represented by two mean scores, one representing True Valid items and one representing False Valid items. The model that fit the data best is given in Table 2. This model assumes that there is a general factor related to all items, two factors that explain the True and False items respectively, two factors that explain the Valid and Invalid items respectively, and five specific factors, each of them corresponding to one of the logical relations except conjunction. Conjunction could not be explained by a specific factor. This model implies that propositional reasoning involves on the one hand semantic factors, related to the empirical truth of the propositions, and on the other logical and syntactic factors, that is, factors related to validity and logical form specific to each of the logical relations. It is also worth noting that there is a strong general factor, which is difficult to identify and which probably taps the inferential character of the reasoning process.
160 A. EMdes et al.
Table 2 The EQS statistical model involving a general factor, truth and falsity factors, validity and invalidity factors, and factors tapping the various logical relations that fit performance data Variable F1 ~~
~
~
TRTV .371' ITV ,682' .168' NJTV CW .081 DTV .531' EQTV .367' TRTN .467' -.587' lTlV DTN -.523'
NJnV -.219'
cnv
TRFV IFV
DFV EQFV
TRFN IFlV DFlV
.022 .487' ,697' .739' ,586' .092 -.452' -.708'
F2
F3
F4
F5
F6 ~
~~~~
,722' ,144 ,348' ,118 .165 -.028 -.093 -.092 -.112 -.095 -.035
,202' .538' ,168' .162' ,336' ,327'
,139
F8
F7 _
~
_
F9
F10
E
~
.530 .420 -.617' .665 .974 .072 .009 .760 .316' ,811 .721 .517 ,255' .444 ,717 .490' .786 ,902 .495 .288 -.541' .138' .534 ,764' ,209 ,621 .652 .308' -.216' .555
-.221'
,374' .338' ,561' .040 .292* ,089 .420' ,389'
.460' ,392' ,368' -.051' .382' ,068 ,122 .122 ,401' -.396' ,472' -.232' -.376' -.055
,536'
NokThe symbolsTR, I, NJ,C, D, EQ stand for transitivity, implication, negajunction, conjunction, disjunction and equivalence respectively. The symbols T, F, V, IV denote true, false, valid and invalid respectively. Factor 1is the general factor, F2 is the Truth factor, F3 is the Falsity factor, F4 is the Validity factor, F5 the Invalidity factor, F6 is the Transitivity factor, F7is the Implication factor, F8 is the Negajunction factor, F9 is the Disjunction factor and F10 is the Equivalence factor. The symbol E stands for Residuals. The model also involved the correlation of IFV with ETV (r=.640) and IFIV with ETV (r=-.262). The * denotes significant loadings.
Difficultyestimation. The models found to fit performance scores were also tested on the difficulty estimation scores. The aim was to find out whether the feelings of difficulty experienced during the processing of the items can be explained by the same factors - namely logical relation and contingency - that accounted for reasoning performance. The model tested involved first-order factors tapping each logical relation, second-order factors explaining all the firstorder factors and one third-order factor explaining the second-order ones. This model did fit well the data. The second model, involving the truth/falsity and validity/invalidity factors was also confirmed, although with a number of modifications which imply that feelings of difficulty are affected by the negation involved in the non-contingent relations, namely negajunction and disjunction. Therefore, it seems that logical relations function as response organizers at
Structure and development of reasoning 161 both cognitive and metacognitive level. At the same time, contingency considerations are also present. It is important to note here that the coexistence of logical relations with contingency relations in the same model seems contradictory, in the sense that the logical relations factors imply a reasoning ability that consists of the coordination of reasoning schemas that correspond to logical relations, whereas the contingency factors imply that reasoning is a semantically driven process that depicts real-life situations. This issue needs further clarification. Similarity estimation and explanation.Another source of evidence that might shed light on the nature of the reasoning process comes from the other metacognitive indices used in this study, namely similarity estimation and explanations of these similarity estimations. As mentioned above, similarity ratings involved pairs of arguments. The various pairs were constructed so that the compared arguments differed in one, two, three, four or all of their characteristics, namely content, logical relation, logical connective, truth, and validity. For technical reasons, the scores for the 29 pairs involved were reduced to 12, each one being the mean of the scores for pairs that reflected the same similarity relationship. The same procedure was applied to the similarity explanations, so that each similarity score was matched by an equivalent explanation score. The 12 similarity scores are given in Table 3. Table 3 The 12 similarity estimation and explanation score groups organized according to content, truth, validity, logical connective and logical relation of the pairs of arguments depicted Pair
Content
1 2
Different Similar Similar Similar Similar Similar Different Different Similar Different Similar Similar
3 4
5 6
7 8 9 10
11 12
Truth Similar(T,T) Similar(T,T) Different(T,F) Similar(T,T) Similar(T,T) Similar(F,F) Different(T,F) Different(T,F) Similar(F,F) Similar Different(T,F) Similar(T,T)
Validity Similar(V,V) Similar(V,V) Similar(V,V) Different(V,Inv) Similar(V,V)
Different(V,Inv) Different(V,Inv) Similar(Inv,Inv) Similar(Inv,Inv) Similar(Inv,Inv) Different(V,Inv) Different(V,Inv)
Logical Connective Similar Different Similar Similar Similar Similar Different Different Different Similar Similar Different
Logical Relation Similar Similar Similar Similar Different Similar Different Similar Different Different Similar Different
In order to find out the basis for subjects’ similarity judgement, a number of models were tested depending on the number of factors that were supposed to
162 A. Efkldes et al.
be taken into considerationby the subjects.The model found to have an excellent fit to the data was one that involved two factors, one loading all pairs that shared the same logical connective, and one loading all the pairs that differed in this characteristic.The “different” factor was further regressed on the “similaf factor.
X2(30)=26.087.
p=.67l. CFI=l.OOO
Figure 2. The model best fitting to the structure of mean similarity estimation scores. Note: The symbols siml ... sim12,sml, diff, cont, conn, inv stand for similarity group 1 to 12, similar, different, content, connective, and invalid, respectively.
Structure and development ofreasoning 163
However, semantic factors also played a role; that is, similarity of content and similarity of truth explained part of the variance, too. Finally, similarity in validity affectedjudgement in a number of cases. Logical relation did not come out as an independent factor (see Figure 2). Therefore, logical connectives, as logical relation markers, and not logical relation per se, play the major role in the perception of similarity of propositional arguments. This finding is not in full agreement with the evidence provided by the structural analyses of performance and difficulty scores, where logical relation appeared to be the organizer of responses. This was due to the fact that logical relations were confounded with logical connectives and, therefore, it was not possible to make this differentiation. Similarityjudgment was also sensitive, as mentioned above, to other features of propositions, namely semantic content and truth. Validity, in the sense of necessarily correct or incorrect conclusion as derived from the premises, also affected the perception of similarity. Therefore, both logical and non-logical factors seem to be taken into account when dealing with propositional reasoning problems. The model tested with the similarity estimation scores was also tested with explanations scores and had a good fit to the data. It can be concluded, then, that both similarity estimation and explanations are sensitive to semantic and logical aspects of the arguments. Yet subjectsbase their judgement mainly on surface characteristics, such as logical connective, content, and truth, and less on analysis or perception of the underlying logical relation. Validity, although affecting subjects’ judgement, is not explicitly stated in their explanations until college years, as it will be shown below. The development of propositional reasoning abilities
Performance,A series of MANOVAs, were performed on the data in order to uncover the development of the various aspects of reasoning ability as well as the effects of age and sex on this development. Only the main effect of age was found significant. Specifically,with regard to true valid arguments, performance is generally high and does not show significant changes over the age span from 12 to 16 years of age, except in the cases of transitivity, disjunction, and equivalence. Performance on false valid arguments is lower than that on true valid items and it shows a steady improvement from the age of 13 up to 16 in the case of transitivity, implication, disjunction, and equivalence. After 16 years it reaches the level of performance on true valid arguments for transitivity and disjunction but not for implication or equivalence. Performance on invalid arguments lags well behind performance on valid ones; improvement with advancing age comes for transitivity, particularly after the age of 15, and implication and disjunction after the age of 16.
164 A. Efkldes et al.
Therefore it can be concluded that propositional reasoning does change during adolescence.The changes regard, first, the abstraction of the reasoning schemas so that they can be applied without the support of semantic relations and general knowledge background. This process starts at about 13 or 14 years of age. After approximately two years, a second significant change occurs, and this regards invalid arguments. Performance improves after the age of 15but even at college age it does not reach the level of performance on valid arguments. Furthermore, invalidity is not uniformly understood either in all logical relations or for true and false items alike. Difficulty estimation. The most interesting finding with regard to difficulty estimation, is that difficulty ratings tend to decrease in the age span from 14 to 16 years and increaseat the age of 20. A series of MANOVAs, were also performed on the data; they showed a significant age effect for all true valid cases except True Valid Negajunction.Significant differences were also found for Transitivity and Equivalence False Valid items and Transitivity False Invalid items. Taken into account that from 13 to 16 years of age, significant improvement occurs in performance on both true and false valid arguments, it is evident that this increased facility with the form of reasoning arguments influences difficulty ratings, causing them to decrease. The same does not hold for 20-year olds. A test of the differencesbetween 16 and 20-year-old subjects did indicate a significant age effect, but this time college students gave higher difficulty estimations than 16-year-old adolescents. 20-year-olds exhibited a more accurate perception of the differences between true/false and valid/invalid arguments, rating false and invalid items as more difficult than true and valid ones. The only exception found was in the case of false invalid transitivity arguments, which were rated as the easiest of all other transitivity cases. This might be due to the fact that invalidity in the case of transitivity is marked by the form of the reasoning schema, whereas in the other logical relations it is not. Thus, it is easily perceived and differentiated from the valid case, and this awareness decreases difficulty ratings, regardless of the truth status of premises. In general, increases in perceived difficulty at college years are parallel to improved performance with all arguments and particularly the invalid ones. Therefore, it could be assumed that students follow a different strategy, a more reflective and analytic approach, to reasoning tasks. This metacognitively guided problem-solving approach elevates difficulty awareness and comes in contrast to either automatic use of reasoning schemas at early adolescence or reasoning based only on argument form in midadolescence, which causes low levels of perceived difficulty. Similarity estimation. Mean similarity ratings per argument group and age are given in Table 4. The MANOVAs performed showed a significant age effect.
Structure and development of reasoning 165
Table 4 Mean similarity estimation scores per age Age/
1
2
2.289 2.338 2.381 2.705 2.666 2.854
2.294 2.231 1.892 2.356 2.248 2.259
Simil. 12 13 14 15 16 20
3
4
5
6
7
8
9
2.645 2.628 2.938 2.972 2.869 2.671
2.464 2.610 2.698 2.963 2.967 3.126
2.896 2.856 2.963 2.998 3.098 3.186
1.628 1.977 2.165 2.043 2.168 1.730
1.576 1.695 1.898 1.990 1.893 1.776
2.091 2.123 2.227 1.998 2.216 1.757
10
11
12
2.915 2.924 3.056 3.104 3.302 3.074
1.506 2.491 2.384 1.488 1.692 1.816 1.723 1.215
2.771 3.121 2.939 2.893 3.000
2.274 2.311 2.188 2.175 1.829
The picture emerging from the analyses is the following: Content and truth affected similarity ratings up to the age of 15 years; after that, subjects did not consider them significant factors for the reasoning process and shifted their attention to more formal aspects of arguments, such as logical connectives. This shift of interest, however, was not consolidated, and thus, although 14 to &yearold subjects tended to underestimate the effect of content and truth, they did not consistently take into account the effect of connective, logical relation or validity. As a result, they underestimated their effect, too. It was only the college age subjects who based their similarity judgement on logical relation. Explanations of similarity.The change of criteria noted above with regard to similarityjudgement, however, did not come to consciousnessand did not become an object of reflection and analysis even at college age. Thus, no significant age effect for explanation scores for all age groups was found. Even the 16 vs. 20year-old age main effect was non-significant, although the univariate F-tests for a number of explanation groups -namely, explanation groups 1,2,3,4,5,6,9,10 and 11-were significant. Inspection of Table 6 shows that the differences found reflected a more accurate perception of the importance of the critical factors for reasoning, such as logical relation, logical connective and validity. Still, considering that the maximum score in explanations was 4 and mean performance did not exceed 1.610 in the best case, it is obvious that explanations of similarity estimation lagged well behind either reasoning performance or feelings of similarity. It can be concluded then that feelings of difficulty tend to reflect performance variations but not match them, because they are affected by automaticity in the reasoning process. Similarity estimations tend to reveal changes in the perception of factors affecting reasoning but it is only in college years that they become accurate enough to reflect the really critical factors. Explanations of the feelings of similarity are even less sensitive to these factors, although they begin to change at 20 years of age for university students.This finding implies that cognitive
166 A. Efklideset a1
Table 5 Mean similarity explanation scores per age Age/ Expl.l 12 .665 13 .702 14 380 15 .808 16 .839 20 1.303
2
3
.651 .795 .682 1.006 .771 .861 .754 .932 .781 1.lo8 1.169 1.610
4
5
6
7
.711 .633 .747 .554 .777 .786 .751 .523 .918 .782 268 .627 380 393 269 .680 .935 .893 .961 .781 1.190 1.346 1.409 1.145
8
9
.576 .727 .524 .635 .605 .700 .747 .732 .757 331 1.019 1.266
10
11
12
.546 .543 -553 .685 .788 1.166
.687 .784 .907 .822 .870 1.357
.711 .611 .914 .749 .776 .943
changes are triggered by different factors and not by metalogic. Metalogic essentially follows performance changes and lags well behind them. GENERAL DISCUSSION
This study aimed to investigate the structureand development of propositional reasoning at both the cognitive and metacognitive level, so that questions pertaining to its nature and mechanism of change might be answered. The basic findings were as follows: First, the fundamental feature of propositional reasoning is the organization of propositional representations in terms of logical relations. At the core of this organization, however, there is a contingency/non-contingency consideration between objects of representation or propositions.The contingency relation allows, on the one hand, the joint iteration of the c.ontingent entities with and, and, on the other, the implication relation between them with &then (Braine, 1990). The non-contingency relation leads either to joint iteration of incompatibles (negajunction)or to iteration of alternatives (disjunction).It is no wonder that the meaning of or for children is always exclusive disjunction and only in late adolescence does it become inclusive (Neimark, 1970; Neimark & Slotnick, 1970). This basic structure of propositional reasoning is also detected at the metacognitive level, i.e., in difficulty estimation. Second,similarity judgement of propositional arguments is basically organized around logical relations, and, particularly, logical connectives as markers (Falmagne, 1990) of the specific relation involved each time. This criterion, however, does not reach awarenessbefore middle adolescence.Younger subjects are influenced by meaning relations (content, truth) rather than formal ones, such as logical relations. Validity considerations appear very late in adolescence or in early adulthood for educated persons.
Structure and deveIopmentof reasoning 167
Third, the development of propositional reasoning during the age span from 12 to 20 years leads thought from meaning to form, and from form to analytic consideration of alternative inferences, so that the validity of the various logical forms and the inferences they lead to can be determined. The implications of these findings with respect to the origin, nature, and development of logical thinking are the following: Origin and nature. As stated in the introduction, the Verbal-Propositional ability is a Specialized Structural System. Although this study did not involve other SSSs, so that its specialized character in comparison to the others would be demonstrated, it did reveal that the various inferential schemas become coordinated and form one higher-order system, the Propositional.The origin of inferential schemas, however, is not clear. The findings of this investigation indicate that contingency might be the pool out of which they grow. Contingency,as Braine (1990)and Rachlin (1976) suggested, is the foundation of learning and thinking, the building block of meaning relations. Contingencies are represented in thought and refined through accumulated experience, so that they form systems in which the joint presence, absence, or presence of one and absence of the second event are coordinated. Mental models might be formed in this way. However, what our analyses have shown is that there are two basic models or types of contingencies that are important for propositional reasoning: joint iteration of compatibles or joint iteration of incompatibles. Negation is the marker in the second case. Thus, the basic contingencies (i.e., p.q, p.-q, -p.q, -p.q) become formed. Language, through lexical markers, i.e., the logical C O M ~ C ~ ~ V ~ S , codifies the fundamental relations between entities. Language and pragmatic factors enrich and differentiate the meaning of connectives. Thus, a joint iteration contingency becomes, through the use of the corresponding marker, either a coexistence situation or an expectation (or implication) situation. Reasoning that started as a purely semantic process becomes part of the linguistic system, which allows for both semantic and syntactic as well as pragmatic considerations. In this way, inference schemas, which are syntactic in nature, are formed (Braine, 1978; Braine & Rumain, 1983) and cued by language connectives. Development. Inference schemas are formed in childhood and they involve valid inferences. They start becoming autonomous from around 8 years of age. However, even in puberty they serve only relatively simple and familiar situations, where truth can be checked and verified by recourse to one’s experience, and where meaning relations support the inferences drawn. Systematization, refining, and correct application of the various schemas is a long process that extends throughout adolescence. In adolescence another important change takes place. The nature of propositional ability changes and the established inferential schemas are abstracted from the particular concrete situations in which they have been used in the past;
168 A. Efilides et al.
they obtain a syntactic autonomy. This accomplishment allows adolescents to draw inferences in absence of meaningful situations. Empirical truth, in the sense of accurate representation of the world, at this point becomes a non-necessary condition for thought exercises. Thus, inferences can be drawn and possible worlds can be created without the limitations imposed by the stringent "reality principle". Furthermore, the various inferential forms become systematized around logical connectives, and the reasoner may draw alternative conclusions from the initial input. At the same time, the person progressively becomes aware of the necessary character of syntactic inferential rules and the organizational importance of logical connectives. Yet being able to function at the level of possibility rather than at the empirical level may distort the individual's perception of the world and have a cost for one's adaptability. Thus, a resurgence of interest in meaning relations occurs during late adolescence and adulthood. This time, however, meaning is enriched, in the sense of multiple contingency models of particular situations, and the inferences drawn through purely syntactic or formal means are tested against existing or created models. In this way, valid reasoning forms are differentiated from the invalid, the latter being the ones that cannot be used in all possible situations unreservedly. As a consequence, invalid inferential modes become the ones that require the conscious monitoring of the reasoning process. It should be made clear, however, that at this point validity differentiation is based on the individual's previous experience of the situation depicted in the argument each time; it does not have the form of a rule or explicit criteria that dictate the use of the various inferential means. It is only when the experience of invalid cases becomes the object of reflection and analysis that it becomes explicit. This seems to be the reason why performance and similarity estimation, which are products of implicit processes, imply the existence of validity considerations but explanations, which require the use of explicit criteria, do not. The above presentation suggests that propositional reasoning undergoes a number of transformations during its development and no single account of these transformations suffices. The role of metacognition in this developmental process needs some further comment. The relationship ofpropositional ability with metacognition. First of all, it should be stressed that metacognition is a different processing system than any specialized structural system. Metacognition is a general system, whose domain of application is the various SSSs and whose goal is cognitive self-sensing and monitoring (Demetriou & Efklides, 1989). Self-sensing is mediated by metacognitive experiences which do not rely on reflection; monitoring may be guided by metacognitive experiencesor by reflection and analysis of metacognitive experiences and knowledge. The evidence provided in this investigation is that metacognitive experiences, such as difficulty estimation and similarityjudgement,
Structure and development of reasoning 169
are to a large extent reliable indicatorsof underlying cognitive processes. However, they do not lend themselves to analysis; therefore, the efforts made by the subjects to explain the basis of their experienceof similarity, for instance, essentially failed to reveal the details of the criteria that led to the experience reported. This lag has been documented before (Campbell & Bickhard, 1986; Efklides & Demetriou, in press). Therefore, the mismatch between cognition and explanation of either cognition or metacognitive experiences shows that until at least college years, changes in reasoning performance are not due to explicit, reflective monitoring but to changes in cognitive functioning and monitoring based on metacognitive experiences only. Metareasoning, in the sense of explicit, conscious awareness of the reasoning process, then should not be conceived as the sole source of reasoning development in adolescence. Analysis and explanation of cognitive endeavours can be achieved after a state of cognition has been established and reflected upon, after it has become an object of knowledge itself. Thus, although validity becomes an object of concern for young adults, its presence as such is not yet perceived or conceptualized. This may be achieved later and perhaps under the guidance, and with the suggestions, of experts. Educational implications. The issue above is directly relevant to educational practice and the possibility of cognitive intervention. Should there be intervention for the acceleration of reasoning performance, and if yes, when and how should instruction about inferences take place? The evidence provided by this study implies that inference drawing is a highly automated process already at the age of 12.The changes that occur during adolescenceare not product of direct teaching. Nevertheless, if one is to accelerate the rate of acquisition of logical reasoning, one should try to build on the individual's current awareness of the factors that are critical for it. The course of development of this awareness follows the pattern outlined above, namely from content knowledge to truth, to logical connectives, and from these to inference schemas and their necessity regardless of content. These are accomplishments that may be achieved in late adolescence. Yet intervention should not stop at this point; there is one more step to be taken, at later ages. This involves the transition from the necessity of inferential schemas to the differentiation between logical connectives and logical relations. This will lead to a grasp of the exact pattern of contingency cases each logical relation taps, even if the logical connective does not mark it. This differentiation will also consolidate the search for validity, that is the necessity of the inference in all possible worlds. This form of instruction should probably take place in young adulthood, when persons are sensitive to the multiplicity of factors that might affect the situation denoted by a proposition. Instruction at this point should pass from formal notation to actual and possible worlds, so that the exact relation can be determined each time. In this way, the struggle of the propositional system for the best and most accurate representation of semantic relations will
170 A. Efklides et al.
be fulfilled at the highest possible level. REFERENCES
Bentler, P.M. (1989). EQS: Structural equations program manual. Los Angeles, CA: BMDP Statistical Software. Braine, M.D.S. (1978).On the relation between the natural logic of reasoning and standard logic. Psychological Review, 85,l-21. Braine, M.D.S. (1990).The "natural logic" approach to reasoning. In W.F. Overton (ed.), Reasoning, necessity, and logic: Developmental perspectives (pp. 133157). Hillsdale, NJ: Erlbaum. Braine, M.D.S. & O'Brien, D.P. (1991).A theory of ik A lexical entry, reasoning program, and pragmatic principles. Psychological Review, 98,182 - 203. Braine, M.D.S. & Rumain, B. (1983). Logical reasoning. In J.H. Flavell & E.M. Markman (eds.),Handbook of child psychology.Vol. 111.Cognitive development (pp. 263-340).New York: Wiley. Campbell, R.L. & Bickhard, M.H. (1986). Knowing levels and developmental stages. Basel: Karger. Case, R. (ed.) (1992).The mind's staircase. Hillsdale, NJ: Erlbaum. Demetriou, A. & Efklides, A (1981).The structure of formal operations: The ideal of the whole and the reality of the parts. In J.A. Meacham & N.R. Santilli (eds.), Social development in youth: Structure and content (pp. 20 - 46). Base1 Karger. Demetriou, A. & Efklides, A. (1985). Structure and sequence of formal and postformal thought: General patterns and individual differences. Child Development, 56,1062-1091. Demetriou, A. & Efklides, A. (1987).Towards a determination of the dimensions and domains of individual differences in cognitive development.In E. de Corte, H. Lodewijks, R. Parmentier, & I?. Span (eds.), Learning and Instruction: European Research in an international context, Vol. 1 (pp. 41-52). Oxford: Leuven University Press and Pergamon Press. Demetriou, A. & Efklides, A. (1988). ExperientialStructuralismand neo-Piagetian theories: Toward an integrated model. In A. Demetriou (ed.),The neepiagetian theories of cognitive development: Toward an integration (pp. 173-222). Amsterdam: North-Holland. Demetriou, A. & Efklides, A. (1989).The person's conception of the structures of developing intellect: Early adolescence to middle age. Genetic, Social, and General Psychology Monographs, 115,371-423. Demetriou, A., Efklides, A., & Platsidou, M. (1993).The architecture and dynamics of developing mind. Monographs of the Society for Research in Child Development, 58 (Serial No. 234). Efklides, A. & Demetriou, A. (in press). Image of cognitive self, task-knowledge,
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and cognitive performance. In S. McDonald & M.L. Commons (eds.), Adult Development: Postformal Stages, 3. New York: Praeger. Efklides, A. & Demetriou, A. (1993, August). Levels of awareness and cognitive performance: The complex web of cognition-metacognition interactions. 5th EARLI Conference: Aix-en-Provence, France. Efklides, A., Demetriou, A., & Metallidou, Y. (1991, August). The structure and development of propositional reasoning ability: Cognitive and metacognitive aspects. 4th EARLI Conference, Turku, Finland. Falmagne, R.J. (1990). Language and the acquisition of logical knowledge. In W.F. Overton (ed.), Reasoning, necessity, and logic: Developmental perspectives (pp. 111-131). Hillsdale, NJ: Erlbaum. Flavell, J.H. (1979). Metacognition and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychologist, 34,906-91 1. Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. New York Basic Books. Greenberg, M., Marvin, R., & Mossler, D. (1977). The development of conditional reasoning skills. Developmental Psychology, 13,527-528. Hill, S.A. (1961). A study of the logical abilities of children. Doctoral dissertation, Stanford University. Ann Arbor, Michigan: University microfilms, no 61-1229. Inhelder, B. & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York Basic Books. Johansson, B.S. (1977). Levels of mastery of the coordinators and and or and logical test performance. British Journal of Psychology, 68,311-320. Johansson, B.S. & Sjoelin, B. (1975). Preschool children’s understanding of the coordinates “and” and ”or”. Journal of Experimental Child Psychology, 19, 233-240. Johnson-Laird, P.N. (1983). Mental models: Towards a cognitive science of language, inference, and consciousness. Cambridge: Cambridge University Press. Johnson-Laird, P.N. (1990). The development of reasoning ability. In G. Butterworth & P. Bryant (eds.), Causes of development (pp. 85 - 110). New York Harvester Wheat heat. Johnson-Laird, P.N. & Byme, R.M.J. (1991). Deduction. Hove, UK Erlbaum. Kitchener, K.S. (1983). Cognition, metacognition, and epistemic cognition: A three-level model of cognitive processing. Human development, 26,222-232. Klatzky, R.K. (1984). Memory and awareness: An information processing perspective. New York: Freeman. Moshman, D. (1990). The development of metalogical understanding. In W. Overton (ed.), Reasoning, necessity, and logic: Developmental perspectives (pp. 205-225). Hillsdale, NJ: Erlbaum. Moshman, D. & Franks, B.A. (1986). Development of the concept of inferential
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validity. Child Development, 57,153-165. Neimark, E. (1970). Development of comprehension of logical connectives: Understanding of “or”. Psychonomic Science, 21,217-219. Neimark, E. & Slotnick, N. (1970). Development of understanding of logical connectives. Journal of Educational Psychology, 61,451-460. OBrien, T. & Shapiro, B.J. (1968). The development of logical thinking in children. American Educational Research Journal, 5,531-542. Overton, W.F. (1990a). Competence and procedures: Constraints on the development of logical reasoning. In W.F. Overton (ed.), Reasoning, necessity, and logic: Developmental perspectives (pp. 1-32). Hillsdale, NJ:Erlbaum. Overton, W.F. (ed.) (1990b). Reasoning, necessity, and logic: Developmental perspectives. Hillsdale, NJ: Erlbaum. Overton, W.F., Ward, S.L., Noveck, I., Black, J., & O’Brien, D.P. (1987).Form and content in the development of deductive reasoning. DevelopmentalPsychology, 23,22-30. Piaget, J. (1986). Essay on necessity. Human Development, 29,301-314. Piaget, J. & Garcia, R. (1991). Towards a logic of meanings. Hillsdale, NJ:Erlbaum. Rachlin, H. (1976).Behavior and learning. San Francisco: Freeman. Ricco, R. (1990).Necessity and the logic of entailment. In W.F. Overton (ed.), Reasoning, necessity, and logic: Developmental perspectives (pp. 45 - 65). Hillsdale, NJ: Erlbaum. Sternberg, R.J. & Berg, C.A. (eds.) (1992). Intellectual development. Cambridge, UK: Cambridge University Press. Wason, P. (1968). Reasoning about a rule. Quarterly Journal of Experimental Psychology, 23,273 - 281.
Intelligence, Mind, and Reasoning: Structure and Development A. Demetriou and A. Emides (Editors) Q 1994 Elsevier Science B.V. All rights reserved.
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Reasoning Models And Intellectual Development* Leslie Smith Department of Educational Research Lancaster University, UK There are many accounts of the mind and their systematic survey would require a grand odyssey. In one category are those accounts due to empirical investigation, some of which are noticed by Sternberg (this volume). His messenger should do well writing brochures about holidays where you can travel where you want, going to Epistemologia or avoiding it completely as you prefer. Caveat emptor! There is another category, comprising accounts due to rational investigation which have their basis in philosophy. The point is that these rational accounts identify normative issues which are constitutive of the explanatory domain of empirical accounts. These issues cannot be avoided. What would you think of a travel brochure, stating that you could travel terrestrially from the North to South Poles without crossing the equator? What would you think of an account of the mind which failed to address the modal properties of coherence and necessity in human thinking? Modal properties are an essential characteristic of rationality and so have to be reckoned with. It will be said: very well, but why do we need the empirical accounts at all? Behind this challenge is the assumption that rationality is fully present or completely absent. Following Cohen (1986), the rationality of human reasoning could not be comprehensively impugned on empirical grounds. Even so, there can be degrees of rationality (Cherniak, 1986).Empirical investigation is needed to identify the extent to which minimal rationality is instantiated in some population. It is this complaint which is central to Piaget’s claim that philosophical accounts identify some epistemic mechanism by which knowledge should be acquired. ”Though careful to characterise the properties which they attribute to this instrument (these accounts)have omitted to verify that it was actually at the subject‘s disposal. Here, whether we like it or not, is a question of fact” (Piaget, 1977, p. 5; my translation). What is evidently required is an account of the mind * I wish to thank Trevor Bond, Wolfe Mays and Henry Markovits for their welcome and stimulatingcommentary on an earlier version of this paper. Author‘saddress: Leslie Smith, Departmentof Educational Research,Lancaster University, Lancaster LA1 4TY,UK, E-MAIL
[email protected]
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which does justice to both empirical and normative issues. It is well known, of course, that this dual focus is central to cognitive science (Hunt, 1989) -almost as well known as Piaget‘s (1923,1979) long-standing commitment. One reason why coherence and necessity are important runs thus. “We consider it as self-evident as anything in philosophy that one cannot do justice to actual human experience without a conceptual system that includespsibilia” (Hintikka & Hintikka, 1989, p. 73). The point is that possibilia, and so coherence and necessity, are pervasively present in epistemic acquisition and use (cf. Smith, 1993; Langford 8.1 Hunting, this volume). Consider epistemic acquisition. Some knowledge must be possessed as a prior condition of the acquisition of new knowledge (Aristotle, nd/1975, 51.1). Coherence is required to exclude cases where a new epistemic acquisition contradicts available knowledge. Suppose Jean already knows (1) Today is 23 June 1992 and then states today (2) Tomorrow is a Tuesday. Since (1)and (2) are contradictory, something must be changed. Notice that this choice is symmetrical, since Jean can drop either (1)or (2). In trivial cases, the choice is easy, for example by checking a calendar. Difficulties arise when it is unclear which one of a pair of seemingly acceptable contradictories is the one to reject, and unclear what its successor should be. Russell’s (1919) paradox was designed to show that early versions of set theory were antinomic and so that an existing body of knowledge was incoherent (cf. Wittgenstein, 1978, p. 370). Faced with this type of contradiction, novel epistemic growth is required. If this is difficult for the best intellects, it can be expected to be similarly so for the developing minds of children. Some account of mental organisation and growth is thus required. Piaget has offered several accounts of mental organisation (Montangero, 1985). One of them concerns the development of modal understanding (Piaget, 1921; 1923; 1980a, 1987a,b). In this account, mental organisation is characterised in terms of the conservation of epistemic systems through their hierarchical transformation. This re-organisational,or metacognitive, element in intellectual development is regarded by Piaget (1931; 1986)as a general characteristic of all epistemic systems in which invariable functioning (some form or other of modal understanding is always present) has variable structural manifestations (some specified form of modal understanding is present). An epistemic system is selfsustaining and self-enhancing through successive transformation of its available elements into their better successors. There is some dispute among developmentalists about the extent to which Piaget‘s account does lay down general features of a mechanism responsible for intellectual change (Chapman, 1988; Buttenvorth & Bryant, 1990;Smith, 1992a).Evidently this dispute is set to continue
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(Demetriou, this volume; Moshman, this volume). A simple case is provided in conceptual change. A concept has a set of defining properties which are logically necessary and which lay down how that concept is applied to cases. These properties are distinct from the empirical properties, which are never logically necessary in the same sense and which happen to be associated with many of the cases to which that concept is applied (Murray, 1978). Difficultiesarise when this distinction is not drawn at all, or drawn only partially in epistemic growth. Some degree of modal understanding is required in the use of concepts in two respects. First, the defining criteria for that concept should be respected, conferring some understanding of necessity. Second, the concept should be applicable not merely to its actual instances in the real world but also to its possible instances across 'possible worlds'. Both points are implicated in the claim made by Hintikka & Hintikka (1989).Both points are central to Piaget's (1985, p. 13; cf. Smith, 1987a)account in which intellectual development is the search for coherence through a process of constructive necessity. According to Piaget, the successive terms of this process are marked by structuralist models based on extensional logic (Piaget, 1972). These models embody two assumptions which are commonly accepted by other developmentalists(cf. Demetriou, this volume; Efklides, this volume). One assumption is that mental organisation is logical, the other that this logic is extensional. Recently, however, both assumptionshave been challenged, the former in research on mental models which are non-logical and the latter in research on modal models based on entailment logic. Attention is now given to each challenge. REASONING WITHOUT LOGIC Logic can be used in empirical investigationsin two different ways, as a model of the mind or for purposes of proof. In work on mental models, logic is used in the second sense only, in that logical systems set the standard by reference to which descriptions of thinking can be tested. But logic is not used in the former sense in this research, since logic is not part of the proposed description and so is not a model of human thinking. This claim is remarkable claim because of its express applicationto logical reasoning. "There is no need to explain how formal rules of inference are acquired by children, because the theory (of mental models) has no recourse to them in accounting for the ability to reason" (Johnson-Laird, 1990, p. 97). Rather, the proposal requires the individual to construct a logic-free model for use in inferential reasoning. Several considerationsmake this position attractive. First, its stock of problems is evidently both logical and inferential (Wason & Johnson-Laird,1972; JohnsonLaird & Bara, 1984; Johnson-Laird, Byme, & Tabossi, 1989).Second, the stance is resolutely empirical with explicit requirements of testability (Johnson-laird,
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1983).Third, the position avoids the special pleading which is characteristic of its rivals. Logic is constituted by an infinite number of logical systems. A privileged status is given to no logical system as a model of thought (Johnson-Laird, 1980). Fourth, logical models are taken not to capture psychological processes in that ”such formal models bear only a remote relation to the menfalrepresentation of meaning” (Johnson-Laird, 1978, p. 17). Fifth, even if mental logic is rejected, mental models of how deductive ability develops are stated to be at hand uohnsonLaird, 1990, p. 86). Indeed, the general availability of this approach as an instrument for the analysis of experimental findings is its primary value. Developmentalists have noted the difficulty in gaining acceptable evidence for the use of Piaget’s logical models (Markovits, 1984,1992). Finally, research on mental models and the selection task has led to a negative evaluation of Genevan account of formal operations (Johnson-Laird & Wason, 1977). Three steps are involved in using this approach. The individual, firstly, forms a mental model of the formal properties of the task; then extracts a novel conclusion (if any) which is true of that model even though not stated in it; and finally attempts to construct a counter-example, which is a different model of the same premises but without the novel conclusion. Inferential reasoning, which is deductively valid, is stated to be the outcome of this psychological process which is outside logic (Johnson-Laird, 1980, p. 121; 1990, p. 97). Three objections to this approach are now reviewed. One objection is that model-building depends on creative search (JohnsonLaird, 1980, p. 122). But this search is inductive, as is evident at step three. The individual forms a model, extracts a conclusion and tests this in another model. There are two outcomes here and both are inductive in character. Suppose the creative search is successful and a counter-example is found. The only conclusion which the model-building individual is entitled to draw is that one of the models is discrepant with the other. But this conclusion is an inadequate basis for the judgment that at least one of the models musfbe changed. What is the origin of this necessity? Notice, firstly, that someone who understands the premises of a deductively valid argument does not thereby have to draw the conclusions implied by them (Stroud, 1979).The point is that even if the modelbuilder‘s judgments are correct, this is never due to the understanding of necessity qua logical notion. Notice, secondly, that the naturalistic fallacy is committed if a normative conclusion, which is necessary, is derived from premises which are solely empirical, and not necessary (cf. Smith, 1991; van Haften, 1990; Langford & Hunting, this volume). If a mental model specifies the sole abilities which are used in deduction, when these abilities are psychological, then this fallacy is committed by any model-builder whose inferences embody necessity. Yet necessity is one of the normative properties which constitute deductive implication and so which should be captured in the epistemic conditions of inference.
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Suppose now that the creative search is unsuccessful and no counter-example is found. The failure to construct a counter-example is too weak since an argument "is valid only if it couldn't have, not just doesn't have, true premises and false conclusion" (Haack, 1978, p. 22). The aim in creative search is to test the validity of an argument which, in turn, requires the individual to understand that the conclusion (step 2) could not be other than it is -could not be represented by the model at step 3- given that the model of the premises at step 1.The construction of any finite number of further models is sufficient to show that no counterbeen found.But such a conclusion is too weak when questions example has, so fs, about logical validity arise: it needs to be shown that no counter-example could be found. Thus whatever the outcome, creative search is reliant upon an inductive process as the grounds for drawing deductive conclusions. In short, this approach leads to an unwarrantable empiricism. Secondly, covert use of logic is made in a mental model account. This objection has been stated by Braine (1990) who contends that truth-table analysis and inference schemata are built into model construction. This objection can be extended, since logical notions are explicitly invoked in the description of model construction. These standard logical notions could have a logical meaning, in which case the account does embody logic. Alternatively, a stipulative definition which assigns them a new meaning could be given, in which case model construction remains unexplained until this stipulation is carried through. JohnsonLaird rejects the former but does not carry through the latter option. To see why, the individual who constructs a mental model faces the problem: "how can an individual know that the conclusions of an argument are or are not contradictory with the premises, if there are no longer any rules to govern the deduction, if the deduction is replaced by a 'construction' whose outcome cannot be foreseen in advance?" (Piaget, 1923, p. 59). If the "rules" which Piaget has in mind are the rules of a mental logic, the "conitruction" applies to the construction of mental models. Illogical reasoning is one expression of construction which disregards logic. The evidence is to hand. The studies of self-contradiction or pathological reasoning reported by Wason & Johnson-Laird (1972) are relevant here. Other examples are not hard to find, including adolescents' self-contradiction in psychometric tests of transitive reasoning (Piaget, 1921). The subject, aged nearly fourteen years, is presented with the premises that Edith is both darker than Lily and lighter than Susan. His train of reasoning from these premises can be represented thus: First Reading: check on coding of premises:
(3) (4)
Edith is lighter than Susan Edith is darker than Lily
(premise) (premise)
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Second Reading: check on derived conclusions: (5) (6) (7) Therefore (8) (9) Therefore (10)
Lily is the darkest Susan is the lightest Edith is lighter than Susan
Edith is more blond than Susan (derived premise) Edith is darker than Lily (premise)
Edith is the darkest Edith is average Susan is light Susan is darker than Edith Lily is dark Lily is lighter than Edith (15) Therefore Both Lily is the darkest (16) And Susan is the lightest (17) (11) (12) (13) (14)
(conclusion) (conclusion) (premise)
(conclusion) (conclusion) (conclusion) (conclusion) (conclusion) (derived premise) (conclusion) (conclusion)
Clearly, the subject has coded the premises correctly (3,4)and can even correctly invoke them (7,9). But although some correct conclusions are drawn from these premises (8,11,13), most are not (5,6,10,12,14,16,17). The key question is how a subject, who is presumed not to use logical notions, can come to recognise that this train of reasoning embodies counter-examples. The natural answer at this point is to say that the subject could realise that some of the conclusions contradict others, for example (8,lO). But contradiction is a logical notion. A different answer would be that the subject could realise that some beliefs (10, 16) are not implications of other beliefs (9,15 respectively) but, once again, implication is a logical notion. Again, the subject could notice that some conclusionsare compatible (7,8,13).But consistencyis a logical notion. Finally, the subject could notice that some conclusions are not all true (6,8).But negation is, of course, a logical notion. In short, the objection is that mental construction makes covert use of logical notions. A covert use of logic is, of course, still a use of logic. A third objection concerns the celebrated selection task (Wason & JohnsonLaird, 1972).Although it was not initially designed as a test of formal operational thinking (cf. Wason, 19661, it has subsequently been taken to pose problems for its interpretation (Wason, 1977) and even to be incompatible with the Genevan account (Johnson-Laird & Wason, 1977).Several points can be noticed. First, Piaget’s (1954, p. 247; cf. 1986, p. 301) interests lay in the evolution of ”the formal operations which bear on the possible and bring about directly the synthesis of the possible and the necessary”. This is an interest less in the
Reasoning models and inteffectualdevelopment 179 comprehension of the logic of truth-tables as in the development of reasoning abilities. Thus Piaget (1966, p. 180) stated that extensional logic was used in his models through its convenient availablity. Further, such qualifications are lost in the standard translation, which is used by critics (Wason & Johnson-Laird, 1972).Consider the key claim that “reasoning is nothing more than the calculus embodied in the propositional operations” (Inhelder & Piaget, 1958, p. 305; my translation). The claim is not - as the standard text implies - that reasoning is an instantiation of the propositional calculus whereby formal operations become propositional operators. Rather, the claim is that reasoning is an instantiationof the calculus of propositional operations (cf. Smith, 1987b, p. 344). The (mistranslated)claim would be open to disconfirmation through research using the selection task since intelligent adults do not reason in accordance with extensional logic. The quoted claim would be open to such disconfirmation,only if the selection task was designed in a manner congruent with the account of which it is a potential falsifier. But this condition has not been met. It is simply assumed that propositional reasoning abilities are already at the disposal of individuals used in research with the selection task (Johnson-Laird & Wason, 1977).In fact, analogues of the selection task were devised in Genevan research during the 1950s, i.e., before Wason‘s (1966) initial report. It was specifically noted, however, that the design of such tasks is different from that of formal operational tasks (Morf, 1957, p. 174; Matalon, 1962/1990, p. 108). Further, what needs to be shown is how conditional reasoning develops with special attention to its modal characteristics. The Genevan account does at least address this question and, as such, is better than no answer at all. (Thisissue is further discussed in Smith, 1993, ch. 7.) Second, a requirement for the assessment of formal operations is not just that an individual has formal operational ability but rather that the individual’s concrete operational abilities have been activated in performing the task. Formal operations are operations on concrete operations (Inhelder & Piaget, 1958, pp. 254, 297). Mays (1992) demonstrates the logical basis of this position. The requirement is met when the selection task is presented with realistic content. In the sealed letter version, the universe is the class fetterwhich has two subordinate classes, namely sealed fetterand 5d stamped fetter.Successful performance on this task is possible by means of concrete operations. By contrast, with the abstract version dealing with letters and numbers, there is no permissible superordinate class to subsume vowel and even number. This is because any superordinate such as the class object breaks one of the conditions of concrete operational classification which is restricted to adjacent inclusions in a hierarchicalsequence (Piaget & Inhelder, 1969, p. 132). The class object is not adjacent to the classes vowel and number in this sense. It is for this reason that certain versions are at concrete, and other versions at post-formal, operational levels (cf. Smith, 1986).
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Third, almost all of the research based on the selection task has failed to include any control of formal operational abilities. Although such research typically makes use of adult students, who are assumed to have such abilities, it is notorious that formal operations are not universal (Shayer & Adey, 1981).In a recent study, adolescents, aged fifteen years, were presented with formal operational tasks and the abstract version of the selection task. The results showed that success on the former was in fact a necessary, but not sufficient, condition of success on the latter (Bond & Shayer, 1991). In short, there are doubts as to whether the inductive character of a mental models approach ever could present an acceptable account of deductive reasoning (cf. Langford & Hunting, this volume). Its notable defect is an in-built deus ex machina. The user of the model ultimately has to take on trust that a logical judgment is the outcome of a non-logical process. The explicandum of a mental model is logical reasoning; yet the model itself is stated to be devoid of logic. It is as if an individual can successfullydo arithmetical problems without knowing any arithmetic. This is not to say that this approach is itself open to objection. To the contrary, the argument has been merely that interpretations and findings associated with assessment tasks should not be too hastily generalised beyond their own domain in the provision of under-determining evidence for developmental account which is beyond their scope. REASONING WITH NON-STANDARD LOGIC
The distinction between standard and non-standard logic is discussed by Haack (1978). Most empirical studies of reasoning invoke standard systems of propositional and predicate logic (cf. Efklides, this volume). Systems of modal logic, which subsume these systems, are also standard. However, the entailment logic of Anderson & Belnap (1975) is a non-standard logic, in which certain logical principles, including the disjunctivesyllogism, are specifically excluded. Some logicians regard this exclusion as a sufficient reason for rejecting the Anderson & Belnap system (Hughes & Cresswell, 1972, p. 338). However, entailment logic has recently been used in developmental studies (Piaget & Garcia, 1991; Overton, 1990; Ricco, 1990; Bymes, 1992). Entailment logic is designed to be a logic of entailment, which is the converse relation of deducibility. Entailment is neither material nor strict implication, if the well-known paradoxes are to be avoided (von Wright, 1957; Pieraut-Le Bonniec, 1980). The system outlined by Anderson & Belnap (1975, p. 106) is intended to avoid these paradoxes and their aim is captured in the principle of 'no funny business'. Their proposal is that a set of premises (A) entails (->I a conclusion (B) just in case the relation A -> B, where A is relevant to B, is, if true, necessarily true. Thus entailment logic embodies the dual criteria of relevance
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and necessity. Anderson & Belnap (1975, p. 262ff)deny that entailment logic is the logic of strict implication with restrictions due to relevance. They also deny that propositional logic is subsumed by entailment logic (pp. 258-61). There is an exegetical question surrounding Piaget's interest in entailment logic. Under one interpretation, his interest is late, confined to one recent study (Piaget & Garcia, 1991), and probably due to his collaborator. Piaget (1949, pp. 40, 256) was aware of the paradoxes of (material, strict) implication in his elaboration of operational logic. Further, Inhelder & Piaget (1958, p. 305) issue the clear denial of any concern with entailment due to pre-occupation with (operational)implication.Paradoxical implicationswere investigated in Matalon's (1962/1990) Experiment 3 and Piaget (1963, pp. 31-21 was well aware of this study. Finally, bare interest was expressed by Grize & Matalon (1962, p. 19) -and by implication Piaget also- in the system of "strenge Implikation" formulated by Ackermann, which Anderson & Belnap (1962)acknowledge to be inspirational. There is an alternative interpretation to consider, that Piaget's interest in alternative logical systems was long-standingbut restricted by their availability. In particular, sympathy with a relevance-criterion can be traced to a comment by Grize (1962, p. 97) who, at a Genevan symposium, noted that "p -> q only if p and q have something in common and, in normal case, somethingmore than truth-value". The suggestion is that common variables are required for operational thinking to be manifest. It is short step from this claim to the replacement of extensional by intensional logical systems, in which "p implies q if, and only if, a meaning of q is incorporated in that of p and if this meaning is transitive" (Piaget, 1980b, p. 5). Further, Piaget's interest in a necessity-criterion is longstanding, evident in his early (Piaget, 1921)and recent (Piaget, 1987b, pp. 137-8) studies. The twin features of entailment logic are relevance and necessity. Each leads to problems in their application to empirical studies of reasoning. Problems with the relevance-criterion Firstly, the proposals made by Anderson & Belnap are directed upon formal proofs in logic where full specificationof premises is required. Less clear is how this requirement can be satisfied in empirical studies of natural reasoning since conscious inspection by a subject is not a condition of even mature thinking. Formal thinking is not always formalisable. "We agree with Bernays that only mathematical thought in its most developed forms permits of a formalization that modern theories of axiomatic logic would recognise as adequate. A fortiori the thought of the adult or young child is unformalizable" (Piaget, 1953, p. 24). In turn, there are methodological issues to confront, namely that intensive use of Piaget's (1947) methode critique will be necessary for full exposure of an
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individual’s train of thought. Yet this method is conspicuouslyabsent from most studies of reasoning (see Smith, 1992b for a supporting discussion of this issue.) If the precedent set by Gou’s protocol is a guide, reasoning analysis will not be easy (Bond &Jackson, 1991). Secondly, relevance is a variable, not a constant. To understand an utterance (proposition), a context must be available. Yet a context “consists of the assumptions expressed and implicated by preceding utterances, plus the encyclopaedicentries attached to any concept used in any of these assumptions, plus the encyclopaedicentries attached to any concept used in the new utterance” (Sperber & Wilson, 1986, p. 135).Without context-specific knowledge, which is an individual construction, it is impossible to infer from (a) Peter: I’m tired (18) (b) Mary: The dessert is ready. I’ll make the speciality of the Capri restaurant what Mary will make. Possible responses could include an aperitif, an hors d’oeuvre, or a fish dish, but without context-specific knowledge the correct response -an osso-bucco- will not be forth-coming. The point to notice is that there are developmental differences in the understanding of relevance. Such differences are an explanandum,to be explained, rather than an explanans,an explanation in its own right. Interest in entailment logic -at least for Piaget & Garcia- centres primarily on its capacity to explain developmental differences other than by invoking that which is to be explained. The incipient circle in this position requires attention. Thirdly, the disjunctive syllogism is a standard argument form: (p v q) & -p -> q or, colloquially, from a disjunction of propositions and the falsity of one disjunct, the remaining disjunct can be inferred. In extensional logic, this argument form is valid (Haack, 1978) and is accorded a key place in empirical studies of reasoning (Braine & OBrien, 1991).In Piaget’s studies, some version of this form is attributed to children and adolescents. In a study of inferential necessity, children were presented with a hidden figure parts of which could be serially exposed by removing up to twenty (1-20) covers. The task was to decide which one of an available twelve (coded A-L) templates matched the hidden figure. The correct template was G (Piaget, 1987b, ch. 8). The findings in a parallel study (Dionnet, 1987, p. 139) revealed one child, aged 10 years, who removed four covers (12,18,15,5) as follows yielding the templates as follows: 12 G, E, D, K, H, L; 18 D,G,E, I; 15 E, G, I, not-D; 5 G, so not-E, not-I. The child is proposing alternatives which are severally rejected on the basis of the observed information. Again, in the magnet task Gou, aged 14 years,
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hypothesised that either content or weight could be responsible for the behaviour of the needle; discounted the latter; hypothesised that content or distance could be responsible; discounted distance; and concluded that the effect is due to content. His argument is a disjunctive syllogism (Inhelder & Piaget, 1958, p. 102). Yet in the entailment logic of Anderson & Belnap (1975, pp. 259,296-300), the validity of this form of argument is specifically denied. Indeed, it has to be denied since Anderson & Belnap have to show that their system is not open to the paradoxes of strict implication. Their position is that this form of argument is invalid but consistent, not that it is contradictory. Using this position in accordancewith the recommendationof Piaget & Garcia (19911, there is a problem. The case of the child with the hidden figure involves relevant variables: one of the twelve templates is correct and so the successive elimination of eleven of them leads to certainty. So it is plausible to use entailment logic in such (developmentally primitive) cases. But the disjunction is truthfunctional in the case of Gou, whose task it is to ascertain, and then to justify, both which variables could be and which ones actually are influential in the magnet task. Of course, Gou's case is not unique since the subjects are placed in exactly this situation in many of the formal operational tasks, especially where a ceterisparibusclause is involved. So in these (developmentallyadvanced) cases, entailment logic is not similarly applicable: Yet, according to Braine & Rumain (1983, p. 3191, the use of a strategy for isolating variables in an organized problemspace is "an interesting and important aspect of intellectual development". The use of this strategy could not be explained through entailment logic. In this respect, standard logic provides a better model of mental organisation. Problems with the necessity-criterion First, it is evident that there is considerable complexity, and so disagreement, surrounding modal notions. Firstly, a variety of defining criteria -analyticity, unrevisability, self-evidence, apriority- have been suggested by philosophers. But none of these is adequate (Haack, 1978). Secondly, the Leibnizean notion of "possibleworlds" continues to be the subject of major philosophical disagreements (Kripke, 1980; Lewis, 1986).Discussions of the empirical consequences of these positions are virtually absent. Finally, Piaget's (1986, pp. 301-2; 1987b, p. 136) own definition of necessity replaces the standard definition (a necessary proposition is one whose negation is impossible) by a non-standard definition, due to Leibniz, whereby a necessary proposition is one whose negation entails contradictions. One advantage of the latter definition is that the denial of necessity entails a contradiction which, in turn, entails any proposition. Modal errors in reasoning lead to any conclusion and illustrations in children's reasoning are easy to find. But this preference sits uneasily with a commitment to the entailment
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logic of Anderson & Belnap (1975, p. 164)where there is a specific denial that a contradiction entails any proposition. Second, Braine (1979) has argued that systems of modal logic, such as strict implication, are inapplicable to conditionals which are contingent, or causal or instantiatedby arbitrary content. Reasoning on formal operational tasks is similar in this respect. In none of these cases are the conditional propositions logically necessary. By parity of argument, Braine’s objection rules out the applicability of entailment logic. Yet modal reasoning is a fact. The major theoretical problem is, in part, to decide which one of the infinitely many modal systems to use in the description of modal reasoning (cf.Johnson-Laird,1978) and, in part, to show how reasoning in its polymorphous forms (propositional, modal) develops (Braine & Rumain, 1983). A third problem follows from this. The suggestion might be that entailment logic is expected to be explanatory not of the individual’s understanding of specific propositions -which are often not necessary- but rather of the progress from non-necessary to necessary understanding. In a Piagetian approach, understanding becomesnecessary (cf. Piaget 1987b, p. 115)and it is this transition which entailment logic is supposed to explain. But it is precisely this aspect of Piaget’s constructivism -the passage from extensional generality to deductive justification (Piaget, 1987b, pp. 138-9) or the temporal construction of atemporal necessity (Piaget & Garcia, 1989, p. 15)- which entailmentlogic could not explain. Yet the intellectualdevelopmentis the conversion of psychological understanding into its epistemological successor (Smith,1993). Consider a paradigm case which is the transition from stage I1 to stage I11 in concrete operations. A defining chamcteristicof a stage I1 response is its empirical, and so non-necessary, chamcter in contrast to the necessity which is constitutive of a stage I11 response (Smith, 1992b). But this is a transition from a contingency to a necessity and so the underlying relation could not be entailment (cf.Anderson & Belnap, 1975, p. 14). A contingency can always be false. Even if a contingency is true, an entailment should not depend upon the accidents of individual psychology. Thus there are problems to confront in this approach as well. The aim of this discussion has not been to assign priorities in favour of model based on standard rather than non-standard logic or conversely but rather to identify questions which merit more attention.
CONCLUSION The primary aim of this discussion has been to review alternatives, not with the aim of selecting one model rather than another but rather to examine issues which should be confronted in any adequate model of the mind. Competing evaluations of Piagetian theory abound (Demetriou & Eflclides, 1988; Halford,
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1989).Alternative accounts have been proposed by way of compensation. These accounts are welcome as alternatives for comparative analysis. One attraction is the promise of new insights into developmental sequences and explanations. But there are risks as well. One is proliferation through re-description. Another is the premature dismissal of viable accounts. Two conclusions can be drawn from the discussion, one negative and the other positive. The negative conclusion is based on Reichenbach’s (1938/1961, pp. 67) claim that there is logic of justification but no logic of discovery. The positive conclusion draws upon Piaget’s concern with the construction of necessary knowledge. The negative conclusion is that the mental models approach is too weak and that the entailment model is too strong. According to the former, human reasoning occurs without the individual’s use of logic. This approach is compatible with Reichenbach’s claim that there is no logic of discovery, since mental organisation is never logical. The effect is to open up the possibilities by allowing human reasoning to occur in an unlimited number of individual ways. But in that prodigality lies the weakness. If formal criteria and rules are not part of this creative process, individuals are in no position to place their own fertile ideas in a closed system of thought. This weakness becomes especially acute when the creative individual is the author of a formal system. If Euclid’s own thinking was based on his use of a logic-free model, how did Euclid come to realise that the formal system which bears his name has logical properties (cf. Piaget, 1980c)? According to the entailment model, human reasoning has the twin properties of necessity and relevance. But this system is too strong in the sense that it lays down criteria and rules which are too restrictive. Such a system does focus on important aspects of thinking, including the modality of the connection between different ideas which occur within an individual’s mind. But it does so by excluding from official consideration other equally important aspects of the deductive process. Using the other part of Reichenbach‘s distinction, this model pays so much attention to the logic of justification, through entailment, that other types of valid justification are passed over. In short, the argument has been that neither approach is comprehensive enough to present a complete account of human reasoning. The positive conclusion is to regard these two alternatives as complementary. The task ahead would be to show both the respects in and the extent to which the elements in any one model can be combined with those of the others to produce a minimally adequate model of reasoning. There is a psychological component in human reasoning, which the mental models approach attempts to capture. But there is a logical element as well, which is the concern of the entailment model. If epistemic growth is a process leading from the former to the latter, the joint use of such approaches is indispensable to the provision of an account which
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does justice to the normative criteria of coherence and necessity. In this regard, Piagetian ideas cannot seriously be regarded as having merely historical interest (cf. Johnson-Laird, 1983, p. 6). Whilst there are historical questions to ask about Piaget’s own position (Ducret, 1990), his ideas continue to have contemporary relevance (Smith, 1992a, 1993).
REFERENCES Anderson, A.R. & Belnap, N. (1962).The pure calculus of entailment. Journal of Symbolic Logic, 27/19-52. Anderson, A.R. & Belnap, N. (1975). Entailment: The logic of relevance and necessity. Princeton, NJ:Princeton University Press. Aristotle (nd/1975). Posterior analytics. Oxford: Oxford University Press. Bond, T. &Jackson,I. (1991).The Gou protocol revisited. Archives de Psychologie, 59,31-54. Bond, T. & Shayer, M. (1991). Piaget‘s logical model of formal operations and the selection task. Unpublished paper. Braine, M. (1979). If-then and strict implication: A response to Grandy’s note. Psychological Review, 86,154-6. Braine, M. (1990).The “natural logic” approach to reasoning. In W. Overton (ed.), Reasoning, necessity and logic: Developmental perspectives. Hillsdale, NJ: Erlbaum. Braine, M. & OBrien, D. (1991).A theory of if A lexical entry, reasoning program, and pragmatic principles. Psychological Review, 98,182-203. Braine, M. & Rumain, B. (1983).Logical reasoning. In P. Mussen (ed.),Handbook of child psychology. Vol. 111. New York: Wiley. Butterworth, G. &Bryant, P. (1990). Causes of development. New York: Harvester Wheatsheaf. Byrnes, J. (1992). Meaningful logic: Developmental perspectives. In H. Beilin & P. Pufall (eds.), Piaget’s theory: Prospects and possibilities. Hillsdale, NJ: Erlbaum. Chapman, M. (1988).Constructive evolution. Cambridge: Cambridge University Press. Cherniak, C. (1986). Minimal rationality. Cambridge, MA: MIT Press. Cohen, L.J. (1986).The dialogue of reason. Oxford: Oxford University Press. Demetriou, A. & Efklides, A. (1988). The neo-piagetian theories of cognitive development: Toward an integration. Amsterdam: North-Holland. Dionnet, S. (1987).Aspects developpementaux des processus de reconnaissance dans une tache d’identification de forme. These Doctorale, Universite de Genhe. Ducret, J-J. (1990).Jean Piaget. Lausanne: Delachaux et Niestlk.
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Grize, J-B. (1962).Note sur 1'EtudeGenetique de Hmplication" de B. Matalon. In E. Bell, J-B. Grize, R. Martin, B. Matalon, A. Naess, J. Piaget. Implication, formalisation et logique naturelle. Paris: Presses Universitaires de France. Grize, J-B. & Matalon, B. (1962). Raisonnement naturel. In E. Bell, J-B. Grize, R. Martin, B. Matalon, A. Naess, J. Piaget. Implication, formalisation et logique naturelle. Paris: Presses Universitaires de France. Haack, S. (1978).Philosophy of logics. Cambridge:Cambridge University Press. van Haften, W. (1990). The justification of conceptual development claims. Journal of Philosophy of Education, 24/51-69. Halford, G. (1989).Reflections on 25 years of Piagetian cognitive-developmental psychology, 1963-1988.Human Development, 32,325-57. Hintikka, J. & Hintikka, M. (1989).The logic of epistemology and the epistemology of logic. Dordrecht: Kluwer. Hughes, G. & Cresswell, M. (1972).An introductionto modal logic. 2nd Edition. London: Methuen. Hunt, E. (1989). Cognitive science: Definition, status, and questions. Annual Review of Psychology, 40,603-30. Inhelder, B. & Piaget, J. (1958).The growth of logical thinking. London: Routledge & Kegan Paul. Johnson-Laird, P.N. (1978). The meaning of modality. Cognitive Science, 2,1726. Johnson-Laird,P.N. (1980).Mental models in cognitive science. CognitiveScience, 4,71-115. Johnson-Laird, P.N. (1983). Mental models. Cambridge: Cambridge University Press. Johnson-Laird, P.N. (1990). The development of reasoning ability. In G. Butterworth & P. Bryant (eds.), Causes of development. New York Harvester Wheatsheaf. Johnson-Laird, P.N. & Bara, B.G. (1984). Syllogistic inference. Cognition, 16,l61. Johnson-Laird, P.N., Byme, R., & Tabossi, P. (1989). Reasoning by model The case of multiple quantification. PsychologicalReview, 96,658-73. Johnson-Laird, P.N. & Wason, P.C. (1977).Thinking: Readings in cognitivescience. Cambridge: Cambridge University Press. Kripke, S. (1980). Naming and necessity. Oxford: Blackwell. Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell. Markovits, H. (1984).Awareness of the "possible"as a mediator of formal thinking in conditional reasoning problems. British Journal of Psychology, 75,367-76. Markovits, H. (1992). The development of conditional reasoning: A Piagetian reformulation of mental models theory. Merrill-Palmer Quarterly (in press). Matalon, B. (1962/1990). A genetic study of implication. W. Overton (ed.),
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Reasoning, necessity and logic: Developmental perspectives. Hillsdale, NJ: Erlbaum. Mays, W. (1992) Piaget's logic. Archives de Psychologie, 60,45-70. Montangero, J. (1985).Genetic epistemology: Yesterday and today. New York CUNY, Graduate School & University Center. Morf, A. (1957). Les relations entre la logique et le langage lors du passage du raisonnement concr&tau raisonnement formel. In L. Apostel, B. Mandelbrot, A. Morf (eds.), Logique, langage, et theorie de l'information. Paris: Presses Universitaires de France. Murray, F. (1978).Teaching strategies and conservation training. In A. Lesgold, J. Pellegrino,S. Fokkema, R. Glaser (eds.),Cognitivepsychology and instruction. New York: Plenum Press. Overton, W. (1990).Reasoning, necessity and logic: Developmentalperspectives. Hillsdale, NJ: Erlbaum. Piaget, J. (1921). Une forme verbale de la comparaison chez l'enfant. Archives de Psychologie, 18,141-72. Piaget, J. (1923). La psychologie et les valeurs religieuses. Sainte-Croix 1922. Association ChrCtienne d'Etudiants de la Suisse Romande. Lausanne: La Concorde. Piaget, J. (1931). Le developpement intellectuel chez les jeunes enfants. Mind, 40,137-60. Piaget, J. (1949).Trait6 de logique. Paris: Colin. Piaget, J. (1947). Avant-Propos de la Troisieme Edition. Le jugement et le raisonnement chez l'enfant. Neuchatel: Delachaux et NiestlC. Piaget, J. (1953).Logic and psychology.Manchester:Manchester University Press. Piaget, J. (1954). La pCriode des operations formelles et le passage de la logique de l'enfant 21 celle de l'adolescent. Bulletin de Psychologie, 7,247-53. Piaget, J. (1963).Travaux de l'annk 1959-60. In P. Grko, B. Inhelder, B. Matalon, J. Piaget. La formation des raisonnements recurrentiels. Paris: Presses Universitaires de France. Piaget, J. (1966).Part 11. In E. Beth & J. Piaget, Mathematical epistemology and psychology. Dordrecht: Reidel. Piaget, J. (1972). Essai de logique operatoire. Pans: Dunod. Piaget, J. (1977). Psychology and epistemology. Harmondsworth: Penguin. Piaget, J. (1979). Relationsbetween psychology and other sciences.Annual Review of Psychology, 30,l-8. Piaget, J. (1980a).Experiments in contradiction. Chicago: University of Chicago Press. Piaget, J. (1980b).Recent studies in genetic epistemology.Cahiers de la Fondation Archives Jean Piaget. No.1. Geneva. Piaget, J. (1980~). The psycho-genesis of knowledge and its epistemological
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significance. M. Piattelli-Palmarini (ed.), Language and learning. London: Routledge & Kegan Paul. Piaget, J. (1985). Equilibration of cognitive structures. Chicago: University of Chicago Press. Piaget, J. (1986). Essay on necessity. Human Development, 29,301-14. Piaget, J. (1987a). Possibility and necessity. Vol. 1. Minneapolis: University of Minnesota Press. Piaget, J. (198%). Possibility and necessity. Vol. 2. Minneapolis: University of Minnesota Press. Piaget, J. & Garcia, R. (1989). Psycho-genesis and the history of science. New York: Columbia University Press. Piaget, J. &Garcia, R. (1991).Towardsa logic of meanings. Hillsdale, NJ: Erlbaum. Piaget, J. & Inhelder, B. (1969).The psychology of the child. London: Routledge & Kegan Paul. Pieraut-Le Bonniec, G. (1980).The development of modal reasoning. New York Academic Press. Reichenbach, H. (1938/1961).Experience and prediction. New York: Dover. Ricco, R. (1990). Necessity and the logic 6f entailment. In W. Overton (ed.), Reasoning, necessity and logic: Developmental perspectives. Hillsdale, NJ: Erlbaum. Russell, B. (1919).Introduction to mathematical philosophy. London: George Allen & Unwin. Shayer, M. & Adey, P. (1981). Towards a science of science teaching. London: Heinemann. Smith, L. (1986). General transferable ability: An interpretation of formal operational thinking. British Journal of Developmental Psychology, 4,377-87. Smith, L. (1987a). On Piaget on necessity. In J. Russell (ed.), Philosophical perspectives on developmental psychology. Oxford: Blackwell. Smith, L. (198%). A constructivist interpretation of formal operations. Human Development, 30,341-54. Smith, L. (1991). Age, ability and intellectual development in Piagetian theory. In M. Chandler & M. Chapman (eds.), Criteria for competence. Hillsdale, NJ: Erlbaum. Smith, L. (1992a).Jean Piaget: Critical assessments. 4 Vols. London: Routledge. Smith, L. (199213).Judgments and justifications as criteria for the attribution of children's knowledge. British Journal of Developmental Psychology, 10,l-23. Smith, L. (1993).Necessary knowledge: Piagetian perspectives on constructivism. London: Erlbaum Ltd (in press). Sperber, D. &Wilson, D. (1986).Relevance. Oxford: Blackwell. Stroud, B. (1979).Inference, belief and understanding. Mind, 88,179-96. Wason, P.C. (1966). Reasoning. In B. Foss (ed.), New horizons in Psychology.
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Harmondsworth, UK Penguin Books. Wason, P.C. & Johnson-Laird,P.N. (1972).Psychology of reasoning. London: Batsford. Wittgenstein, L. (1978).Remarks on the foundations of mathematics. Third edition. Oxford: Blackwell. van Haften, W. (1990).The justification of conceptual development claims.Journal of Philosophy of Education, 24/51-69. von Wright, G.H. (1957).Logical studies. London: Routledge & Kegan Paul.
Intelligence, Mind, and Reasoning: Structure and Development A. Demetriou and A. Efklides (Editors) Q 1994 Elsevier Science B.V. All rights reserved.
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A Representational CommunicationApproach to the Development of Inductive and Deductive Logic' Peter E. Langford and Robert Hunting, School of Education, L a Trobe University We call our view a "representational communication" approach because, unlike orthodox Piagetian theory, it views one of the primary sources of qualitative and quantitative differences between different domains of reasoning as emanating from the ways in which meanings and ways of forming representations are transmitted from other people to the developing child and adolescent. One way in which such socially-constructed habits of representation influence cognitive development involves the distinction between external and internal representations. The first author has drawn attention to the serious conceptual confusion that has arisen in the study of children's solution of arithmetical word problems from a failure to draw this distinction (Langford, 1986,1988). It is often claimed that children show an ability to manipulate mental representations for concrete objects in such problems when in fact they are manipulating the objects themselves. Another example of this difficulty occurs in the literature on some of the logical tasks reported by Inhelder and Piaget (1964), in which children are asked to sort external coloured shapes and it is held this shows manipulation of internal representations. The kinds of problems for which external representations are used and the way they are used are culturally specific and in contemporary Western cultures are quite different for, for instance, arithmetical and logical problems. Socialisation also influences other aspects of representations and their use. In our culture, children receive systematic analytic training in arithmetic from an early age, but only very patchy training in logic, most of their understanding of logic being learned in informal conversationalexchanges that do not offer precise definitions of terms. Thus, children develop abilities in arithmetic earlier and more rigorously than in logic (Langford, 1981,1992). Most of this chapter will be taken up with presentation of some detailed work on deductive reasoning with syllogisms. This will be followed by a brief digest of work we have reported elsewhere on inductive reasoning using conditionals * Author's address: Peter E. Langford, School of Education, La Trobe University,Bundoora, Victoria, Australia 3083.
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and other logical expressions. In the concluding discussion we consider other approaches to the development of logic and the question of mental abilities.
DEDUCTIVE REASONING WITH SYLLOGISMS Our approach to the deductive logic of syllogisms arose from a number of sources: the philosophy of mathematics and logic contained in the later writings of Wittgenstein; discontent about the way psychologists have construed the learning of mathematical concepts by mathematics educators, especially Freudenthal(1974,1978,1983); and our own previous work on the existence and origin of learning hierarchies, again especially in mathematics learning. These sources suggest some initial bearings for approaching the learning of logic: 1. We need to draw a clear distinction between mathematics and logic as conceived by most mathematicians and logicians and performance in the deductive reasoning tasks used to study deductive reasoning by psychologists. The way this distinction will be drawn here will be partisan, being largely based on the interpretation of Wittgenstein’s later philosophy of mathematics contained in Shanker (1987).Thus it will be asserted that to be a proposition in pure mathematics or logic a proposition must have a perspicuous and surveyable proof. This will be contrasted with “production systems” in mathematical and logical reasoning, that involve the application of mechanical techniques to produce answers to problems. A surveyable step in a proof is one in which we know exactly what to do with all the relevant variables over all the relevant ranges and in exactly what circumstances the step can be taken. 2. It is one of the distinctive features of Wittgenstein’s later approach to the philosophy of mathematics and logic that he claimed the certainty of proofs in these fields derives from our norms of representation,rather than from the world, from our ideas, or from relations between our representations and the world. 3. Conceptually, pure mathematics and pure logic comprisea motley of proof techniques that intersect with one another. Examples of such techniques are: those using geometrical intuition or insight; those that list all possibilities in a surveyable way (this may be using a diagram, table or annotations to the possibilities); mathematical induction; reducfio ad absurdurn. Conceptually, production systems also comprise a motley of techniques. Psychologically, most users of mathematics are well known to employ a mixture of proofs and mechanical techniques when solving problems or arriving at new results. 4. The official definitionsof logical terms are poorly understood by adolescents and adults untrained in logic. This is likely to be connected to their tendency to commit logical fallacies. When we turn to the psychological literature on deductive reasoning in adults and children, we find that the picture just painted is rather contentious. There
A represenfational c o r n unica tion approach to logic 193
has been a tradition of theories that deny that untrained adults possess natural logical rationality (e.g. Erickson, 1974; Revlis, 1975; Evans, 1977,1989). On the other hand, perhaps a preponderance of current opinion favours the idea of natural logical rationality. We will be particularly concerned with two issues: a) what do adolescentsand adults usually know about the certainty of logic; b) how reliable are their logical procedures? a) m a t do adolescents and adults know about the certainty oflogic?I’iaget and his followers have always been interested in the topic of logical certainty or necessity, at least since the publication of Piaget’s magnum opus on genetic epistemology in 1945. He repeatedly said that he wanted to explain how adults come to have such notions (Inhelder & Piaget, 1956; Piaget, 1986; 1987a,b).This is in clear contrast to the work of Johnson-Lairdand to work on deduction flying the flags of “informationprocessing theory” and “cognitivescience” in general. Such theorists are generally only interested in production systems and not in any actual or potential knowledge of certainty or necessity. In saying this, it is important to emphasise that Johnson-Laird’s approach in particular aims to develop a competence model of such a production system that also explains some but not all aspects of performance. In our view it is essential to distinguish a competence model of a production system, that provides an idealised account of the knowledge of the reasoner used in the production of conclusions,from knowledge of certainty. A person may have a completely adequate knowledge of the principles involved in the production of logical inferences and a perfect ability to apply this knowlege, without having any inkling that deductive logic is any more certain than inductive reasoning. There is nowhere in Piaget’s writings, that we can detect, any direct empirical study of adolescents’ knowledge of logical certainty, as distinct from their ability to operate correct procedures. It is asserted both that there is an extensive underlying competence in logic that emerges in many individuals in late adolescence and that this competence is somehow indicative of knowledge of necessity, but this latter claim is established entirely by assertion. As some evidence for what might otherwise appear a surprising claim, we cite the following sentence by one of the leading exponents of Piagetian thinking on this topic: ”This system (i.e. the deductive competence system), representing a developmental transformationof the earlier systems, permits the kind of logical understandings that involve genuine implication, entailment, logical truth, and validity that are evident in traditional deductive reasoning problems” (Overton, 1990). We simply deny that traditional deductive reasoning problems offer any information about logical necessity or logical truth. Such problems typically ask the subject to inspect a sequence of premises and a conclusion for validity, to choose a valid conclusion for an argument from confusers or to produce a conclusion given premises. They do not ask the subject how certain their conclusion
194 P.E. Langford and R. Hunting
was. We are going to argue later that, contrary to what is sometimes thought, correct performance in such tasks is no guarantee that correct logical procedures were used, for the simple reason that subjects may reach the right answer for wrong reasons. Thus we regard correct performance on “traditional deductive reasoning tasks” as at two removes from knowledge of logical certainty. One study that did undertake direct assessment of logical certainty was that of Byrnes and Overton (1986).However, we interpret their results very differently from the way they do. This will be discussed after presentation of our model. b) Do adolescentsand add&have reliable logicalpmcedures?Everyone can at least agree that some logical fallacies are common in the kind of ”traditional deductive reasoning problems” discussed in the previous section. Various possible reasons for such fallacies are given in the literature. One of the most frequently canvassed is that adolescents and adults who are not trained in logic may interpret the language used in premises, particularly conditional expressions like “if X is A, then X is B” and ”all As are Bs”, in ways that are not those of the logician. Overton and his associates have undertaken a number of training studies to try to show that adolescents have access to an adequate underlying competence in understanding the meanings of conditionals and biconditionals (see Overton, 1990).The term “competence“ here is evidently being used in the conventional sense “that the individual in some sense ‘has’ the rules” (Overton, 1990, p. 6). In view of this, it is hard to escape the objection that an individual who can be trained in a rule acquired it as a result of training and did not “have” it at all prior to training. Although this argument might be considered as delivering a knock-out blow to Overton‘s thesis taken in a literal sense, it is not entirely clear that it is meant in this sense. A broader view of his claim would apply it to deductive procedures. Our own model suggests that, given only training in the meaning of premises rather than in procedures of deduction that permit passage from premises to conclusions, untrained adolescents would acquire a fairly adequate ability to perform deductions. They might, prior to training, have had competence in these rules and procedures without competence in the interpretation of premises. We return to this issue later. There are three main methods that have been used to indicate interpretations of logical premises: Euler circles, Venn diagrams and inference from deductive reasoning tasks. A number of inadequacies in these methods have been pointed out by Johnson-Laird and Bara (19841, Newstead (1989) and Langford (1992), most importantly that they constrain subjects to a narrower range of interpretations than they may conceivably have. To overcome these limitations, we devised a new task. This gives subjects a premise like ”All the As are Bs” and asks which of the four possible combinations of “A true” or “A false” with “B true” or “B false” musfexist given that this is true and which may exist.
A representational communication approach to logic 195
Method Forty undergraduate students in the age range 18-29 years at L a Trobe University were given the following interviews, half receiving the questions in the order shown and half in reverse order, 18 being male and 22 female. Subjects were given a sheet from which to read the questions as well as being read the initial part of each question. The first interview ran: 1. There is a group of people in a room, who may be artists or beekeepers or both or neither. Assume that all the artists are beekeepers. Which of the following kinds of people have to be in the room: a) People who are artists and beekeepers; b) People who are artists and not beekeepers; c) People who are beekeepers and not artists; d) People who are neither artists nor beekeepers? "Which of the following kinds of people may there be in the room?" The same list of possibilities then followed. Questions 2-4 asked the same questions about the assumptions "if a person is a mathematician then they are a birdwatcher", "some of the musicians are inventors" and "no teachers are joggers". Subjects were asked to tick their chosen replies. Twenty subjects received this interview and 20 the same interview with different professions and hobbies mentioned in the questions. Results and Discussion The request to distinguish those things that may exist from those that must proved the most difficult aspect of the task. Many subjects said they were not sure which to choose for a given kind of information and some picked both may and must for the same item of information. A conditional reply to the first two questions was defined as picking "must exist" for a), not picking b), "may exist" or "must exist" or both for c) and "may exist" for d). A biconditionalreply was the same where c) was not chosen at all. A reduced conditional was as for a conditional where d ) was not chosen. A positive only reply was picking "must exist" for a) and not picking anything else. A some reply at the third question was as for a conditional with a "may exist" or "must exist" reply for b) and d). A no reply was picking "may" or "must exist" for b), c)and d )and a reduced no reply was "may" or "must exist" for b) and c).The distribution of these replies is shown in Table 1. While 18 subjects chose the same type of reply from the above list for "all" and "if" expressions, 20 chose different replies from the above list or one from the above list and an unclassified reply, while 2 chose identical unclassified replies. One significant aspect of the above findings is that there is more confusion about, and greater individual differences in, undergraduate beliefs about what must
196 RE. Lan&ord and R. Hunting
and what may exist given the assumptions suggested than has been generally assumed. Table 1 Types of choice made for four kinds of expression Type of Expression
Conditional Biconditional Reduced Conditional Positive Only
All
If
7 8 7
8 7
13
11
Some
4
Some No
12 27 21 10
Reduced No Total
No
35
30
39
31
A revised approach to syllogistic reasoning by undergraduates
Our first assumption in developing a revised model of syllogistic reasoning was that undergraduates’ models of premises can be inferred from the assessment task just described. In making this claim we were mindful of the finding of Newstead (1989) that Venn diagram assessment of premise meaning was a poor predictor of the errors of an individual in a deductive reasoning task. Informal studies of our own also showed that if a subject is given two consecutive assessments of the same form of wording, such as “All the artists are beekeepers‘’ and “All the bankers are joggers”, they often give different meanings for the two statements. Thus we assume that the way premises are modelled by subjects fluctuates from one occasion to the next. Our approach also differs from the related approach of Johnson-Laird and Bara (1984), in that they only aimed to predict the probability of a correct reply and certain kinds of response bias. We wanted to go beyond this to predict which replies subjects will produce when presented with a pair of syllogistic premises and how probable each kind of reply is. Johnson-Laird and Byrne (1991) have somewhat altered the earlier view of how premises are modelled, this more recent
A representationalcommunica tion approach to logic 197
view is quite similar in many respects to our own approach. One critical difference, however, is that we assume that premises are very often modelled in ways that are quite alien to the logician and that, in addition, fluctuate from occasion to occasion. Johnson-Laird and Byrne (1991, pp. 189-190)also offer a suggestion about the order in which specific types of conclusion are tested against a joint model of the premises in syllogistic reasoning. This represents an attempt to make their model more specific in its predictions, but no discussion is given of how predictions from their suggested order of testing measure up against what human subjects actually do in syllogistic production tasks.Even cursory examination of what their order of testing would predict in relation to Johnson-Laird‘s and Bara’s (1984)production data shows that their assumptions are highly questionable. For this reason we have proposed a different set of principles governing the order in which conclusionsare tested against a model of the premises, outlined below. Before embarking on the model, we pause to review the general scope of syllogistic reasoning problems. There are four kinds of premise used in syllogisms, traditionally denoted by the following letters: “All -s are -s” (A); ”Some -s are s” (I); ”No -s are 4’(E); “Some -s are not -s” (0). Syllogismsare also divided into four figures, each figure containing sixteen premise pairs. In each figure all combinations of the four kinds of premise just outlined taken as first premise and the same four kinds of premise taken as second premise are considered. In the first figure the order of variables is A - B, B - C. Thus the combination of A as first premise and A as second (AA) in the first figure is “All the As are Bs, All the Bs are Cs.” The combination EO in the first figure is “No As are Bs, Some Bs are not Cs.” In the second figure the order of variables is B - A, C - B. Thus in this figure the (AA) combination of premises becomes “All the Bs are As, All the Cs are Bs.” In the third figure the order of variables is A - B, C - B; in the fourth it is B - A, B
- c.
Like Johnson-Lairdand Bara (19841, we assume that production of a conclusion from syllogistic premises proceeds in three parts, which are outlined below. 1. Initial modelling ofpremises. One premise is modelled first. This model may or may not need to be reversed before the second premise is modelled. This may or may not need to be reversed before the two models can be integrated into a joint model of the premises. Thus for ”All the Bs are Cs, All the Bs are As” the second premise may be modelled first in the form of the combination B, A. Such a model encodes the information that there is at least one individual who possesses quality B and quality A. It is assumed that information exists in the model in an ordered form that must be taken into account in thinking about how processing occurs. The order of representation in the model of the second premise may then be reversed to form the model A,B. The first premise may then be modelled by the combination B,C and the two models combined into the “path” A,B,C. The
198 RE. Langford and R. Hunting
object of this process of reordering and reversing premises is to be able to reason through the middle term B by constructing a joint model of the premises that consists of paths connecting the extreme terms A and C through the middle term B. This joint model may contain several paths, but in the example just discussed it contains only one path. Although Johnson-Laird and Byrne (1991)assume that the models for these premises are more complex than those just given, our initial study suggests that reasoners who adopt a "positive only" model of premises having the form "All Xs are Ys" will only model the combinationsjust mentioned. Our model assumes that in trying to reach syllogistic conclusions subjects operate under performance constraints that require them to ignore some things they know about the premises to reduce processing load. This causes them to abandon attempts to tag combinations of qualities as having necessary or possible existence. Instead, anything they think has at least possible existence is modelled, untagged. In addition, they only draw up rudimentary models of the first premise to be modelled, reserving full modelling for the second premise. Further, only those parts of the model of the second premise that can actually be attached to the first premise are introduced into the joint model. Any model of a syllogistic premise with two variables contains a maximum of four paths. If A is mentioned before B in the premise, these are: A,B; not A,B; A,not B; not A,not B. We will now list the detailed rules for modelling particular kinds of premises. The premise "All the As are Bs" will be modelled just as A,B if modelled first. If modelled second, it will be interpreted according to one of the common interpretations suggested by our study of premise meaning, though only those paths that can be attached to the first premise will be introduced into the joint model. Possible interpretations are: 1. Full conditional - A,B; not A,B; not A,not B; 2. Biconditional - A,B; not A,not B; 3. Reduced conditional - A,B; not A,B; 4. Positive only - A,B. If the premise "Some As are Bs" is modelled first it will also be modelled by the single path A,B. If modelled second, available paths are: 1. Positive only A,B; 2. Some interpretation - A,B; not A,B; A,not B; not A,not B. Premises of the form "Some As are not Bs" are modelled in the same way with "not B" replacing " B in the above formulation. If the premise "No As are Bs" is modelled first it will be modelled by the two paths not A,B; A,not B. If it is modelled second, possible interpretations are: 1. A "no" interpretation - not A,B; A,not B; not A,not B; 2. A "reduced no" interpretation - not A,B; A,not B. 2. Combinafionofpremises. The combination of premises into a combined model follows closely the rules for combining premises suggested by JohnsonLaird and Bara (1984, pp. 32-3). First the middle term is identified. If the figure of the premises is A - B, B - C (as in "All the As are Bs, All the Bs are Cs") then the second model is attached to the end of the first by attaching every example
A representationalcommmica tion approach to logic 199
of B in the first premise to every example in the second and every example of not B in the first to every example in the second. This results in a series of search paths through the model. For B - A, C - B premises (as in "All the Bs are As, All the Cs are Bs"), the second is modelled first and then the model of the first renewed as a continuation of it; for the figure A - B, C - B either the first premise is modelled, the second modelled, switched round so the combinations begin with B and then integrated with the first, or the second is modelled and the first modelled, switched round and then integrated; for B - A, B - C either the first premise is modelled and then switched round before the second is modelled and integrated or the second modelled and switched and the first integrated. 3. Deri'ving conclusions.Having modelled the combination of premises, subjects now search these models for paths linking A or not A with C or not C. The conclusion "All As are Cs" is verified if at least one path from a representation of A to one of C exists and there is no path from a representation of A to one of not C. A and C may either or both be replaced by "not A" and "not C in both the conclusion and the search rule. The conclusion "Some As are Cs" is verified if there is at least one path from a representation of A to one of C. Replacement of A and C by either or both "not A and "not C is again possible. The conclusion "No A is a C" is verified if there is no path from a representation of A to one of C. Substitution with "not A" and "not C is again possible. To clarify terminology, an "all", "no" or "some" premise or conclusion says "All/no/some Xs are Ys"; a "some-not" premise or conclusion says "Some Xs are not Ys." In production tasks undergraduates first search for a "no" conclusion if there is at least one "no" premise; they first search for a "some" or "some-not" conclusion, if there is at least one "some" or "some-not" premise and no "no" premise; they first search for an "all" conclusion if there are two "all" premises. If a "some" search fails, then a "some-not" conclusion will be announced for the variables searched. If a "some-not" search fails, then a "some" conclusion will be announced for the variables searched. If an "all" search or a "no" search fails, subjects will proceed to a "some" search on the same variables. If no paths can be constructed while searching for a "no" or "some-not" conclusion, these conclusions will be announced as valid. If no paths can be constructed while searching for "all" or "some" conclusions the search is considered to fail. When a variable, such as A, appears in a premise it may have a positive modality, as in "All As are Bs", or a negative modality, as in "Some Bs are not As." The first conclusions sought are those connecting the modality mentioned in the premises of the variable that appears first in the model with the mentioned modality of the variable that appears last in the model. Plausible explanations for most of these search procedures can be given. Conclusions are announced when key common elements in the most frequent
200 P.E. Langford and R. Hunting
meanings given to the conclusion are identified (the search rule for an "all" conclusion is a partial exception here, discussed later). Second searches tend to look for conclusionsrequiring less demanding criteria than first searches.Subjects probably prefer to search for conclusions involving the mentioned modalities of A and C first because their mention implies, under Grice's (1975) discourse maxims, that the speaker or author has mentioned these modalities because they are the ones of interest. Subjects are reluctant to search for "all" conclusions as these involve high processing load. It is currently much less clear why subjects are so eager to search for "no" conclusions as these also incur high processing load. It may be that mention of a "no" premise is considered an unusual or marked linguistic form that again triggers the discourse presupposition that this would not have been used were it not relevant. Predictions about syllogistic production. Johnson-Laird and Bara (1984) provide extensive data on spontaneous syllogistic deductionsfrom premise pairs when under no time constraint. We now proceed to predictions about this data. Inspection indicates that subjects are unlikely to announce conclusions from their third or subsequent searches. Adopting this principle, we can make two sorts of prediction. We will call any reply other than "no conclusion" a positive conclusion. Our first sort of prediction is that a given-set of positive conclusions may be reached for a particular premise pair and that few other positive conclusions will be reached. The model also provides a set of parameters attached to each predicted positive conclusion that can be used to predict its likelihood. This is the second sort of prediction. The first sort of prediction would be of little interest if the model predicted that a large number of conclusions could be reached for each premise pair. However, in fact the model only predicts between one and four replies for any premise pair and the observed range of types of reply is generally also between one and four. A premises-conclusion(PC) prediction is the predicted occurrence of a particular positive conclusion after a given premise pair. Of one hundred and thirty three PC predictions by the model, 80 were observed to occur. In addition, eighty three per cent of positive replies were PC predictions. All the 53 replies that were predicted to occur, but did not, have parameter values attached to them that make their occurrence relatively unlikely. That is to say, they involve some difficulties in the construction of a joint model of the premises and/or in searching this for a conclusion that are likely to lead to difficulties in reaching a positive conclusion. It is of interest to look at those premise pairs that generated the greatest proportions of unpredicted conclusions. Many of these seem to have arisen because of inaccuracies in checkingfor paths while searchingfor a "no" conclusion. Subjects sometimes announce "no" conclusions when the search should have failed. On other occasions they appear to have rejected "no" conclusions that
A representational communication approach to logic 201
should have been verified on the initial search and then to have moved on to a second search. One of the most distinctive features of our model is that it considerably reduces the number of paths to be searched. That subjects still run into trouble in searching the remaining paths supports our contention that such reduction is essential if subjects are to grapple with the task at all. The tendency for searches for "no" conclusions to produce substantial numbers of search errors appears to arise from the eagerness with which subjects attempt to establish such conclusions combined with the high processing load involved in doing so. We now turn to the influence of parameters on deductions. The model provides five parameters (numbered 1-5):proportion; number of paths; number of searches; number of representations of premises; number of representations of models. Proportion refers to the proportion of subjects who are predicted to run through a particular search process. To simplify our approach here we made two assumptions. First of all, it is assumed that subjects use the same interpretations of premises on all searches. This is probably inaccurate, but the influence of such variability on the kind of data we are seeking to predict is likely to be minimal. Secondly, we assume that subjects adopt the following interpretations in the following proportions, which are based on those found in our study of premise interpretation. For "all" premises, full conditional, biconditional, reduced conditional and positive only interpretations occur in the proportions 1:1:1:2.For "some" and "some-not" premises, positive only and some interpretations occur in the proportions 1:2. For "no" premises, no and reduced no interpretations occur in the proportions 2:l. These two assumptions taken together permit prediction of the proportion of subjects that will adopt a particular search process. A "search process" is defined in this context as a set of search types that occur for a given premise pair, produce a single positive reply and have a common set of parameters 2-5 attached to them. Each search process involves a certain number of paths on the successful search that leads to announcing a conclusion. This number is assumed to always be 1for announcement of a "some" or "some-not" conclusion, because although other paths may have been searched before that traversed immediately prior to the conclusion, the results of these previous searches do not have to be held in memory and thus do not incur memory load. For "all" and "no" searches all available paths must be evaluated and the results held in memory until a final evaluation is made. Thus for such searches the number of paths parameter is taken to be the total number of paths in the joint model. As already explained, it appears that third searches are unlikely to succeed and thus the number of searches undertaken is either 1 or 2. The number of representations of premises refers to the total number of times premises are represented during the process of reordering premises. This parameter will assume the value 1 if the order of premises does not have to be reversed and 2
202 P.E. Langford and R.Hunting
if it does. The fifth parameter refers to the number of representations that must be made of the models representing premises during the process of reversing the order in which variables are listed during problem solution. Thus, if neither model is reversed, this assumes the value 1, if the model of one premise is reversed before construction of a joint model, this assumes the value 2, and if the models of both premises are reversed, it assumes the value 3. The influence of proportion is predictable directly from the model without the need for estimation of the effects of this parameter, as the probability of reaching a given conclusion should vaty directly with proportion. Table 2 shows the mean proportion of observed replies for predicted conclusions categorised according to numbers of paths, searches and representations of premises and models. In cases where the proportion parameter attached to the prediction was less than 1 the observed proportion of that reply was divided by the proportion parameter to give an estimate of the likelihood of the kind of search in question being successfully completed. Table 2 also shows the standard deviations of proportions of observed replies calculated in this way.
Table 2 Summary statistics and predicted means for corrected proportion of observed replies per search process classified by four parameters ~
~~~~~~~~~
N
Paths Schs Reps Prems Reps Mods Obs. Mean Pred. Mean Std Dev'n ~
1
1
1 1 1
1
1 1 1 1
1 2 2 2 2 2 1
1 1
2 2 2 2 2 3 3 3 3
1 1
1
1 1
1 1 1 1 1
1 1 1 2 2 1 1 1 2 2 1 1 1 2 2 1 1 1 2
1 2 3 1 2 1 2 3 1 2 1 2 3 1 2
1 2 3 2
~
.64 .43 .06 .54 .36
.28 .46
.23 .18 .05 .26
.26 .04
.24
.19
.21
.44
.68 .44 .07 .61
.27
.83 .84 .05 .52 .68 .55 .90 .05 .80
.10
.23 .31
.09
15 22 10 13
10 2 13 7 5 13 3 5 2 3 5
1 1 2 1
A representational communication approach to logic 203
Inspection of this table suggests that as the number of paths increases from 1 to 2 the paths parameter has little influence on the likelihood of successfully reaching a conclusion. This is not suprising as searching two paths is unlikely to impose substantial memory load. Only five search processes yield conclusions from searching three paths. Although the numbers of predictions here are too small to yield reliable results, initial indications from these five search processes are that even with three paths to check this parameter still has little impact on the probability of announcing a conclusion. For present purposes it will thus be assumed that the paths parameter has no influence on the probabilitity of reaching a conclusion. The final step in the analysis was to find equations that would predict the observed mean proportions shown in Table 2 from parameters 3-5. Only cells with N > 7 were used for this analysis. If we call these parameters respectively x, y and z, then two equations of about equal complexity can be found to provide adequate predictions of the stated means: P = a(b - x2)(c - y2)(d - 22) with the constants estimated from the data as .00052,8.54,19.45and 9.88 respectively; and P = abxcu(d - 22) with the constants estimated as .19, .61, .76 and 9.67 respectively. Distributions of the observed proportions of replies for each row of Table 2 were examined and, despite the transformation exercised on the data involved in correcting the observed proportions by dividing by the proportion parameter, these appeared approximately normal. Accordingly observed mean proportions were tested against predicted cell means using the formula for deriving the standard deviation of the mean of a normally distributed variable from the standard deviation of the variable. All predicted cell means were within two standard deviations of observed cell means for all cells with N 2 7 for both equations (see Table 2 for the predictions from the first equation).Although both these equations predict the cell means adequately, the second has the drawback that it predicts appreciable numbers of searches will be successful when the search parameter is raised to 3, which as already mentioned does not occur. The first equation successfully predicts that with three searches the probability of success is about zero and so is to be preferred. General Discussion The approach to syllogistic reasoning already outlined can be expanded to provide a developmental model of such reasoning. Langford (1993b)reported a developmental study using the method described earlier for assessing premise interpretations. This shows, as suggested by Venn diagram studies, that in early adolescence “positive only” (conjunctive-like) interpretations of conditional premises are even more common than among undergraduates. At the same time, there are considerably fewer hlly conditional interpretations of ”all” and other
204 RE. Langhord and R. Hunting
conditional premises. We would also expect that the impact of number of searches and numbers of representations of premises and models would be more severe on younger subjects.Johnson-Laird, Oakhill and Bull (1986) have already shown that the figure of syllogistic premises has a considerable impact on syllogistic reasoning by 9-12-year-old subjects, with performance declining progressively from the first to the fourth figure, which according to the present approach reflects the influence of numbers of representations of premises and models. However, when we compare their data with comparable results obtained on undergraduates by Johnson-Lairdand Steedman (1978)) we find that figures for the younger and older age groups are quite similar, with little evidence that numbers of representations of premises and models have any greater influence on younger subjects. While Johnson-Laird et al. (1986) used a group selected for high ability, it is likely that if the representations parameters have a greater influence on younger subjects, we must look earlier than nine years to detect it. We now turn to consider the topic of natural human rationality. By this we will, for present purposes, understand the doctrine that by their late teens or early twenties most undergraduates in our society have acquired adequate logical procedures. A key point here is the interpretation we give to the phrase "adequate logical procedures". At one extreme we could say a person's reasoning is adequate if it is self-consistent. Thus we could argue that the severely reduced meanings that subjects give to premises in our model are the meanings they choose to give to these things under these circumstances. However, this leaves out of account subjects' failure to sustain a consistent interpretation of premises, which shows they are not, in reality, even self-consistent in their use of logical terms. At the other extreme, we could say a person's logical procedures are adequate if they agree with some system of formal logic. In general this seems an excessively stringent demand. Thus our main aim in claiming that the great majority of undergraduates lack deductive rationality in syllogistic reasoning is not to stress that they fail to agree with some system of formal logic, but that they are neither self-consistent nor able to adopt a consistent socially accepted criterion for the meaning of logical terms. Without these two things any claim that they have adequate logical procedures must be extremely hollow. Our model raises a further problem, which is that it claims that the procedures adopted by subjects often get the right answer according to formal logic, although the means by which the answer was reached are not such as to provide an adequate justification for it. In short, they often get the right answer for the wrong reasons. Once again, this is not what we normally think of as human rationality. A possible line of defence against our conclusions has already been mentioned in the introduction. This is that if it were to turn out that subjects trained in the correct interpretation of premises and conclusions could, without being trained in anything else, then achieve a high rate of success in syllogistic deduction, this
A representational communicationapproach to logic 205
would indicate that certain aspects of the ability to construct and evaluate models are acquired without special instruction. Although we do not at present have any conclusive information on this topic, our approach suggests that, although some weaknesses in logical procedures would remain, these would mainly be due to the tendency to simplify the first premise to reduce processing load, which can properly be described as produced by performance constraints. Thus we are inclined to agree with Overton (1990) that some kind of underlying competence could be revealed by training in the meaning of premises. Nonetheless, we must still protest against callingthis ”logicalcompetence”, as without publicly verifiable consistency in the understanding of premises no one can reason logically. In addition, we have deliberately adopted a search rule for “all” conclusionsin our model that is closer to that suggested by standard logic than to the meanings for ”all” expressions given on the meaning assessment task, as this simplified model proved adequate. Further work may favour several search rules for such conclusions, some closer to the biconditional and positive only interpretations of “all” expressions and, thus, less indicative of adequate competence in logical procedures. Training in standard meanings might or might not rapidly generalise to such search rules. Finally, we return to our initial puzzle over the untrained individual’s knowledge of logical certainty. As mentioned earlier, Byrnes and Overton (1986) showed that many adolescents realise there is a differencebetween the certainty of some simple kinds of logical deduction and probable inferences. However, viewed in the context of our procedural model, such certainty must be viewed in a very different light from that in which Byrnes and Overton (1986)and Overton (1990) view it. One obvious problem with calling this ”logical certainty” is that such subjects are, according to us, often reaching the right conclusions for wrong reasons, that is reasons not accepted by others, and then saying they are certain about what they have deduced. We object to the idea that such a person possesses a true understanding of logical certainty, as logic is a common socially accepted way of reasoning. In addition, that some logical deductions are thought more certain than some probable inferences may just indicate that, say, the subjective probability of the inference is ninety rather than 80 per cent. Logical certainty is one hundred per cent certain.
INDUCTIVE REASONING Langford (1992,1993a, 1993b)and Langford and Hunting (1992) have described a model of inductive reasoning with conditional hypotheses and other logical expressions. This suggests that when adolescent subjects are asked to evaluate such hypotheses using items of informationbearing upon them, they first interpret the hypotheses in the way indicated by the model of deductive reasoning just
206 P.E. Langhord and R. Hunting
described. They then operate in one of two ways. If the task suggests the hypothesis be evaluated without reference to an alternative, they use the strategy: "If an example necessarily occurs under the hypothesis, it supports it; if it possibly occurs under the hypothesis, then it either supports it or tells you nothing; if it cannot occur under the hypothesis, then it disproves it." If the task suggests the hypothesis be evaluated against an alternative hypothesis they use the strategy: "If an example can occur under both hypotheses it tells you nothing; if it can occur under one hypothesis and not the other, then it supports the hypothesis that makes it possible and disproves the other." This model is able to explain performance in such inductive reasoning tasks in a way that rival models, such as those of Johnson-Laird (1986), Johnson-Laird and Byrne (1991) and Overton (1990) do not. Part of the improved predictions of this model again originate from taking account of the varied and fluctuating interpretations of logical expressions among adolescents and adults, which are responsible for the varied and fluctuating responses we find in inductive reasoning tasks. The developmental trends in interpretations of conditionals outlined above can also be used to explain developmental trends in inductive reasoning responses. CONCLUDING DISCUSSION The most notable developmental trends in the interpretation of logical expressions during adolescence occur for conditionals. Insofar as adolescents and adults are able to give anything like a correct interpretation of conditionals, this tends to resemble the biconditional interpretation "X is B if and only if X is A". One explanation for such conversion relies on discourse presuppositions. However, attempts to remove the discourse implication that saying or writing "If X is A, then X is B implies that, if there were another possible antecedent of B, then this would have been mentioned, have been largely unsuccessful in reducing conversion to the biconditional (Langford,1992,1993a).The best available alternative explanation is a modified version of Inhelder's and Piaget's (1956) view that biconditional interpretations arise from an attempt to avoid the complexities involved in considering the eight combinations of events that can occur when another antecedent C is considered (combinations of A or not A with B or not B with C or not C). According to them, it is only through such consideration that a conditional interpretation can arise, as children and adolescents focus on positive causal connections between antecedents and consequents and thus the combination "not A,B" can only arise if it is thought that C is causing B, resulting in the combination "not A,B,C". The positive only or conjunctive-like interpretations of conditionals common among younger adolescents could reflect an even more radical effort to avoid combinatorial complexity. However, the relative success that younger adolecents have in coping with combinatorial
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complexity equivalent to that found in biconditionals, when dealing with arithmetical concepts, suggests that lack of detailed explanation of the meanings of conditionals during everyday conversational exchanges is a more important factor here (Langford, 1992). Next, some comments about the other qualitative approaches to the development of logical reasoning contained in this book. Our views differ in at least four ways: the extent to which they assume untrained adults possess adequate logical procedures and knowledge of certainty; our analyses of the origins and nature of logical certainty; the model or models in formal logic thought most useful for psychological purposes; whether or not a sharp distinction is drawn between inductive and deductive reasoning. The chapters by Efklides, Moshman and Smith are all relatively more Piagetian than we are. We have already explained our differences with Piaget and Overton in regard to the first issue. However, many Piagetians would accept the argument of Shayer (1980) that full formal operations reasoning is considerably less common in late adolescencethan Piaget claimed in his earlier work. Although none of the other contributors to this volume are very specific on this point, they generally seem to share Shayer's position, reducing the differences between themselves and us. The differences between Piagetians and ourselves on the nature of logical certainty are also quite subtle, as they too see logical certainty as constructed rather than, as do Platonists, originating from insight into a super-human realm of ideas. They do not, however, tend to emphasise the diversity of logical and mathematical methods of proof in the way that Wittgensteinians do (see Baker and Hacker, 1986; Shanker, 1987). Our differencesabout the most useful models in formal logic are perhaps rather greater. We advocate the use of fully quantified predicate logic, while others favour propositional logic, with Smith also raising the possibility of using entailment logic. Our differences over the inductive-deductive distinction are also substantial, with other contributors following Piaget in minimising it, while we emphasise it. The main reasons we would give to justify our positions on these last two issues are conceptual rather than empirical. We agree with the long-standing complaints of logicians that Piaget's use of propositional logic is conceptually incorrect (see Parsons, 1960; Seltman & Seltman, 1985).Finally, brief comments on the structure of abilities. It is likely, as Demetriou says in his chapter, that "Mental units ... tend to get organized in broad complexes which make coactivation possible for the sake of particular mental goals." Although we define the broad structural system involved in logical reasoning through predicate logic rather than propositional logic, the prediction that there will be a general ability in this area is common to our view and that of Demetriou and Efklides. In practice, our predictions here differ surprisingly little, as they tend to describe the same set of tasks as involving propositional logic that we think involves predicate logic. A difference in our views of abilities at the next level of specificity is that we think
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inductive and deductive tasks are likely to tap fairly distinct sub-abilities, while they have not emphasised this prediction. REFERENCES
Baker, G.P. & Hacker, P.M.S. (1986).Wittgenstein: Rules, grammar and necessity. Oxford: Basil Blackwell. Byrnes, J.P. & Overton, W.F. (1986). Reasoning about certainty and uncertainty in concrete, causal and propositional contexts. Developmental Psychology, 22, 793-799. Erickson, J.R. (1974). A set analysis theory of behavior in formal syllogistic reasoning tasks. In R. Solso (ed.), Loyola symposium on cognition, Vol. 2. Hillsdale: Erlbaum. Evans, J.St.B.T. (1977). Linguistic factors in reasoning. Quarterly Journal of Experimental Psychology, 29,297-306. Evans, J.St.B.T. (1989).Bias in human reasoning: Causes and consequences. Hove: Erlbaum. Freudenthal, H. (1974). Mathematics as an educational task. Dordrecht: Reidel. Freudenthal, H. (1978). Weeding and sowing. Dordrecht: Reidel. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel. Grice, H.P. (1975).Logic and conversation. In P. Cole & J.L. Morgan (eds.), Syntax and semantics. Vol. 3: Speech Acts. New York: Seminar Press. Inhelder, B. & Piaget, J. (1956).The growth of logical thinking from childhood to adolescence. New York: Wiley. Inhelder, B. & Piaget, J. (1964). The early growth of logic in the child. London: Routledge. Johnson-Laird, P.N. (1986). Conditionals and mental models. In E.C. Traugott (ed.), On conditionals. Cambridge: Cambridge University Press. Johnson-Laird, P.N. & Bara, B.G. (1984). Syllogistic inference. Cognition, 16,l61. Johnson-Laird, P.N. & Byrne, R.M.J. (1991). Deduction. Hove: Erlbaum. Johnson-Laird, P.N. Oakhill, J., & Bull, D. (1986).Children's syllogistic reasoning. The Quarterly Journal of Experimental Psychology, 38A, 35-58. Johnson-Laird, P.N. & Steedman, M.J. (1978). The psychology of syllogisms. Cognitive Psychology, 10,64-99. Langford, P.E. (1981). A longitudinal study of the development of logical laws in arithmetic and Boolean algebra. Educational Psychology, 1,121-142. Langford, P.E. (1986).Arithmetical word problems: Thinking in the head versus thinking on the table. Educational Studies in Mathematics, 17,193-199. Langford, P.E. (1988).Arithmetical word problems: Evidence for thinking on the
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table. Research in Mathematics Education in Australia, 4(2), 1-7. Langford, P.E. (1992).Evaluation strategies for some nonstandard conditionals during adolescence. Psychological Reports, 70,643-664. Langford, P.E. (1993a).Evaluation of conditional and biconditional hypotheses in information-use tasks during adolescence.Journal of Genetic Psychology, 154,111-126. Langford, P.E. (1993b).A test of a twustage model of the evaluation of conditional hypotheses. The Psychological Record, 43,255-269. Langford, P.E. & Hunting, R. (1992). A test of a two-stage model of the evaluation of hypotheses from quantified first-order predicate logic in information-use tasks. Psychological Reports, 71,1091-1104. Newstead, S.E. (1989).Interpretational errors in syllogistic reasoning. Journal of Memory and Language, 28,78-91. Overton, W.F. (1990). Competence and procedures: Constraints on the development of logical reasoning. In W.F. Overton (ed.), Reasoning, necessity and logic. Hillsdale: Erlbaum. Parsons, C. (1960). Inhelder and Piaget's The Growth of Logical Thinking I1 A Logician's viewpoint. British Journal of Psychology, 51,75-84. Piaget, J. (1986). Essay on necessity. Human Development, 29,301-314. Piaget, J. (1987a).Possibility and necessity. Vol. 1:The role of possibility in cognitive development. Minneapolis: iniversity of Minnesota Press. Piaget, J. (198%). Possibility and necessity. Vo1.2 The role of necessity in cognitive development. Minneapolis: University of Minnesota Press. Revlis, R. (1975).Two models of syllogistic reasoning: Feature selection and conversion. Journal of Verbal Learning and Verbal Behavior, 14,180-195. Seltman, M. & Seltman, P. (1985).Piaget's Logic. London: Allen & Unwin. Shanker, S.G. (1987).Wittgenstein and the turning-point in the Philosophy of Mathematics. Albany: State University of New York Press. Shayer, M. (1980).A Piagetian approach to sciense education. In S. & C. Modgil (eds.), Towards a theory of psychological development. Slough: National Foundation for Educational Research.
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Intelligence, Mind, and Reasoning: Structure and Development A. Demetriou and A. Etklides (Editors) Q 1994 Elsevier Science B.V. All rights reserved.
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Gulliver Ravel's Travels: An Excursion to the Theoretical Islands of Intelligence* Robert J. Sternberg Yale University, New Haven, USA Completely bereft of ideas for this chapter, I decided to take a walk on a beach, hoping that this would bring me inspiration. I took in the Ocean and its waves, the sandy beaches, and the wind of sea and surf. All was perfect, with the possible exception of the beach having been washed in Oil DExxon. Unfortunately, despite the lovely setting, my mind remained barren. But then suddenly I noticed a floating bottle with sheaves of paper carefully sealed within. I picked up the bottle (once, apparently, the home of a forgettable Bulgarian beer) and plied it open. Inside was an account, written on yellowed yet still preserved paper, of a voyage by one Gulliver Ravel, a traveler. I enter here verbatim the text of the account as I found it, translated carefully from the original Serbo-Croatian. "My name is Gulliver T. Ravel, and I hope that this message washes ashore so that my story can be told. One day in the year of our Lord 1992, I awoke in my bedroom in Crimesville, U.S.A., a city notorious for the highest crime rate in the nation. Perhaps the name of the town encouraged criminals. Who can say? To my horror, I discovered that I had been robbed. All my material possessions were intact, however; no, something of even greater importance had been stolenmy intelligence. What I had spent years developing into a finely honed, delicately crafted instrument that could pierce through any problem was gonestolen. In order to keep it safe I had stored it in a hermetically sealed black box, but the box was nowhere to be found. You may ask, why a hermetically sealed black box? It seemed like a safe place for my intelligence, for the box could not be opened. It never occurred to me that someone would steal the box along with its contents. I brought my rather dilapidated yet serviceableboat, the HMS Metaphor, out from storage in the back yard and immediately set sail in search of my intelligence. I embarked from the raging waters where Crimesvilleand the Pacific Ocean meet. Given that Crimesvilleis in the heartland of the U.S.A. and not along its shores, this intersection had never previously been found. Indeed, there was not a soul
* Author's address: Robert J. Sternberg, Department of Psychology, Yale University. Box 11A Yale Station, New Haven, CT 06520-7447, USA
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on the beach, much less a shoe, when I departed. I decided to search for the villain who had stolen my box of intelligence and to recover it in the process. I did not know where this villain had gone, but my perseverance was great, even if my intelligence no longer was, and I was determined to find him (or her, as the case may be). I would sail from island to island until the job was done.
Factorlandia After sailing for several weeks and plugging God knows how many leaks, I found an immense island. On its sands was a sign proclaiming Welcome to Factorlandia,’ but the island seemed at first not to contain a living soul, just a litter of dead bodies and a foul smell. After searching the national archives in the capital city, Psychometrica, I pieced together the following sad story while holding my nose.
The Spear Men This island had once been the home of a fierce and proud race, the Spear Men. They had been ruled by a dictator imported from South America, named only General Factor. The general insisted that he reign supreme and that everyone else be subordinate to him. In order to guarantee their submission, he had ensured that each inhabitant be able to perform just one specific task. His subjects were called ‘specific factors,’ in order to emphasize how little they could do. From the start, things had not gone as well as they might have with a more efficient form of government. The specific factors were just too limited; for example, one specific factor only dotted i’s, and another only crossed t’s. They were practically useless. People talked about the dictator, General Factor, as though he alone were the whole functional population of the island. At the same time, the number of specific factors kept multiplying, but their ability to do anything did not increase. Moreover, so suppressed were they that there was no way they could work together. They were static, rigid, uncooperative. Eventually, the dictator found himself in the uncomfortable position of having to do everything important that needed to be done on the island. That was a great burden for any one entity, even one as powerful as General Factor. To the untrained eye, General Factor appeared omnipotent. This, however, was not so; the general couldn’t possibly do everything on the island. Furthermore, he certainly couldn’t do everything equally well, which soon became transparently obvious. The general was always running into trouble because he knew everyone’s name on the island, but he could never locate anyone. Indeed,
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he even had trouble finding his own palace! But those who had sworn obedience and obeisance to General Factor also swore that the problem was not that he couldn’t do everything equally well, but rather that his performance on each task was not always assessed equally well. It was not his skill, but the evaluation of it that was faulty, claimed his mental slaves. In time, General Factor grew old, and an argument ensued over the succession. The most conservative on the island wanted the post to be an entirely hereditary one. They argued that General Factor’s intellectual abilities were at least one hundred percent heritable, and given his skill in ruling the island, his heir should take over his position. Others argued that one’s upbringing might better equip one for intelligent leadership, and therefore the succession should not be based strictly on heredity. Still others argued that both heredity and upbringing, or environment, should be taken into account in considering the most able and intelligent candidates. These arguments got nowhere, despite many ingenious efforts to prove one point of view or another. Part of the problem seemed to be that it was very hard to separate heredity from environment. Which truly endowed one with intelligence? Was the general’s daughter a good successor because of her genes, or because of her exposure ever since childhood to power and politics? Various clever experiments were devised, but none of them conclusively settled the issue, and arguments over the succession continued. The Thurs Before his successor could be named, the General was overthrown by an invading race. The spears of the Spear Men were no match for the Thur-stones, mighty boulders hurtled from the tops of high cliffs. Although the Thurs gained control over the island, an underground resistance evolved. Civil war between the Spear Men and the Thurs continued for a number of years, each side claiming that it could better run the island. The Thur invasion was historically important because with it came the overthrow of the dictatorship. The Thurs believed more in egalitarianism, and they wanted no part of a government that put all significant power in one entity. But factions on the island would always remain that longed for the simplicity of the old dictator. The government of the Thurs was quite different from that of the Spear Men, at least on the surface. An oligarchy of seven rulers controlled the island. Each was assigned to oversee a different kind of task: One ruler read correspondence, another wrote letters, another remembered the laws, and so forth. Their tasks overlapped somewhat, resulting in correlation between what they did, but this
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apparently caused little problem. At times the Thur rulers’ division of power seemed too coordinated, and some suspected that underlying the government was a single, hidden power that controlled the seven, much the way General Factor had done. The Thur rulers denied being pawns, but the suspicion remained. The Guils
The Thur oligarchy ruled for a number of years, but this era was a difficult period for the island, at best. Not only was there a secret conspiracy on the part of the Spear Men, but other groups were trying to gain supremacy as well. One such group was the Guils. The Guils mounted a full-scale invasion of the island with large ships on which were stored automobiles, a11of the same manufacture. The Guils tried to overrun their enemies, appropriately enough,by running them over with their mighty automobiles, called Guil-Fords, on which the Thur-stones could at best only make dents. The Guil-Fords themselves eventually ran out of gas, however, because of inadequacies in their form of government. The Guils’ system comprised 120 rebel leaders, and as is the case with so many rebel groups, the leaders couldn’t work together. Indeed, they couldn‘t even communicate. Some leaders accepted only verbal input, others only symbolic input, others only behavioral input, and so on. Worse, their forms of outputthe products of their work-differed as well. In addition, each was fiercely independent and guarded closely his small allotment of turf, while also coveting jealously the others’ equally small plots of land. The problem was that the division of responsibility, not to mention turf, among the 120 leaders was quite arbitrary, and consultants hired by enemies showed that the division didn‘t make any real sense at all. In fact, a stinging attack by a consultant named Horn-et showed that even a randomly chosen set of izo functions would provide as good a government as was being obtained with those actually in control. Indeed, it was very difficult to figure out what some of the rebel leaders really did. Eventually, the rebel movement imploded, overcome by its own weight and unwieldiness.
The Vernons Despite surviving the Guil threat, the Thur government did not last forever. Its end was not a violent overthrow, but rather an absorption of sorts. In time, the seven Thur leaders delegated tasks to subordinates, who eventually needed their own subordinates, and thus multiple levels of government gradually emerged. Moreover, in order to resolve their disputes, the Thur leaders sought a small ruling council, which then sought a supreme iudge who became a sort of less powerful General Factor. What had started out as an oligarchy became
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a hierarchy, and a fairly successful one. The political system altered so much that the government officially changed the name of the people from the Thurs to the Vernons, after the leader who had first successfully and cleverly inserted the principle of hierarchy into the government. But no government lasts forever, and the Vernons’ hierarchical one was no exception. Like those preceding, it was rather static. The processes of government were never well specified, and as citizens became more concerned not only with the results of government, but with how they were attained, people started emigratingfrom the island. Others died off, and the island became all but deserted. I searched the area thoroughly, still holding my nose, and found pockets of inhabitants here and there. All of them claimed, despite obvious evidence to the contrary, that nothing had really changed and the island was as thriving and as powerful as it had ever been. But then I came, at long last, to a remote part of the island, which was new and shiny and inhabited with people who seemed to be not only alive, but in good health.
T h e Undhafssons These people proved to be Undhafssons. Their appearancewas vaguely Nordic, although I couldn’t say for sure. Their story was an interesting one. Recognizing that the collapse of the old regime was imminent, they had migrated to a remote and, at the time, uninhabited portion of the island. Although they saw value in the old systems, they recognized that the internecine fighting among various ideologies was suicidal. They decided to build on some of the old forms of government, but used very sophisticated mathematical models to determine the ideal form of government. In general, their claims to truth were not as strong as those of their predecessors. And as a result, here they were flourishing on an otherwise desolate island. But I found no sign of any intelligence here, and so decided to sail away.
COGNITIA It did not take me long to arrive at Cognitia. This island had a new, fresh appearance; it obviously had been settled more recently than Factorlandia. Cognitia was divided into different regions, each competing for control of turf. What an ideal place for a thief to hide! I decided to search each nook and cranny for the villain, and more importantly, my box of intelligence. I just had to hope that the thief had not pried open the box and then spent it all or spilled it somewhere. I decided to start looking in the town I first came to, one of grand proportions.
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The Jensens The Jensens were a curious bunch, if ever I saw one. They seemed to be grouped into two distinct clusters, those with naturally green hair and those with naturally purple hair. People with green hair were doing menial jobs, whereas those with purple hair held higher level and higher paying positions. Without meaning to seem rude, I asked a purple-haired individual about this division. He willingly explained that the people with green hair were genetically inferior, and hence consigned to inferior jobs. Then I asked him the obvious question-how he knew. Again, he willingly explained. All Jensens were given a test that determined their life course, placing them either in menial or meaningful jobs. I must admit to having been impressed; our own measurement of abilities had come nowhere close to developing such a powerful test. The Jensens were obviously far more advanced than we. It occurred to me that I might be able to bring this knowledge to my own people, and so I asked the Jensen with whom I was talking for a description of the test. He was more than happy to oblige. Each young Jensen was placed at an impressive computer console that was very precise in its measurements. On the computer screen were a series of locations, each corresponding to an enemy tribe. In this test, or game, as it seemed to me, the illumination of a location corresponded to an attack by that enemy tribe. As soon as the screen lit up, the Jensen was to press a button indicating counterattack. The faster the counterattack-that is, the more quickly the correct button was pressed in response to the flash of light-the more able the Jensen was judged to be. I must admit to having been surprised by this test. After all, not every job in the town was a defensejob, and even the defense jobs seemed likely to be at least slightly more complicated than pressing a button in response to an attack. But the Jensen assured me that the ability to initiate a rapid counterattack was fundamental to all other abilities-indeed, it was hard-wired into the neurons. And what could be more important for adaptation, and even survival, than the ability to thwart an enemy advance? The Jensen showed me several other tests that had been used from time to time for job placement. All of them seemed rather game-like and remote from the complex tasks of many work situations. But again the Jensen emphasized that on each test, people with purple hair performed better than people with green hair, thus justifying the difference in societal status and jobs. I asked the Jensenwhether his comrades had shown that performance on these games or tests-whatever they wereactually predicted performance on the job. He claimed that after correction for attenuation, extenuation, insinuation, disindividuation, and extermination, the level of prediction was actually quite high, often as high as .1 or .2 on a proportional scale of variation accounted for. I must admit that these numbers seemed low to me, but I assumed that the Jensens
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must work in base 3 or some such in order to interpret the numbers as so high. Later, I spoke with some green-haired people, and found them to be utterly dispirited by this oppressive system. Their living conditions were poor, their incomes were low, their educational resources practically nonexistent. They reacted in varying ways to their hardships. Some gave up. Indeed, they scarcely tried when they took the test, believing it wouldn’t matter how they did because the suppression would continue regardless. Others actively rebelled. These rebels were often carted off to jail, charged with antisocial behavior, and kept behind bars to rethink their challenge to the status quo. Still others tried to work within the system, facing the challenges confronting them head-on, with mixed results. The purple-haired people claimed that green-hairs were given full opportunities. What’s more, a few slots for good jobs were always set aside for green-hairs, though when the green-hairs took these slots, they were treated as though they had been given gifts. Purple-hairs were constantly reminding green-hairs of how much was being done for them. It seemed to me that there were many unhealthy aspects of the Jensen society which, fortunately, do not characterize our own. Not only are we fortunate enough not to have people with green and purple hair, we also realize that choice reaction time is not all there is to ability-there are many other kinds of reaction times as well! But in any case, I was rather disgusted with the whole business, and after convincing myself that such a stupid society could not possibly have given birth to someone clever enough to steal my intelligence, I left.
T h e Hunters The next town was larger than the last. It was obvious this town would not employ the same class division as the Jensensused, for here everyone was almost completely bald. They were also armed to the teeth, and I quickly found out that this was because these people were hunters of whatever they could track down. The Hunters, as they rather creatively called themselves, had some unusual abilities, although not likely ones stolen from me. They could rapidly tell me whether two objects were the same physically, or in name only. If I showed them identical twins, they would notice a small mole hardly visible under the neckline of one, and respond that the twins were physically different. Yet if I showed them two mustard seeds with different shapes, they could easily recognize that both were mustard seeds. Indeed, their only error was to state that a person with the strange habit of calling himself Tweedledum under normal circumstances, but Tweedledee when he looked in the mirror, was two different people. Most hunted among the Hunters seemed to be individual differences. They were likewise very concerned with how people varied in their ability to recognize
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differences, as well as similarities. These people would not have made the error of a hunter in the state of Maine, U.S.A., who shot a person because he mistook her for a deer. A Hunter who was poor at recognizing distinctions was himself viewed as different by his society, although he might not recognize himself as different. But that in itself was further proof, the Hunter majority would say, of his inability to recognize differences. By this time, as my reader might imagine, if there is any reader, I was rather tired of simplistic accounts of how people vary. These people could not possibly have my intelligence. I wasn't even sure they had their own. I moved on to the next town, where I was told that everything would be much more complicated. Little did I know what that meant.
The Complex Simons This village made the previous one seem positively normal, because there were no people in the next village at all. To my amazement, it was populated by machines calling themselves Complex Simons in reaction to an overthrown idiot monarch of long ago, Simple Simon. The Complex Simons were a varied lot. Some of them looked like mice, others looked like fruit, perhaps an apple, and still others looked rather bucolic; one referred to himself as the Farmer in the Dell. The Complex Simons apparently had once been regular people, like me and probably like you, but then they evolved into a master race of sorts. Originally, they had decided that they wanted to understand themselves and particularly their abilities better, so they started off studying the human race. Later, they decided they could better understand people by studying computers as well as people. After a while, they discovered that computers were easier to understand than humans, so they spent most of their time trying to understand computers. They still pretended, though, that these were attempts to understand people. Eventually, the charade ended. No one talked much about people, and soon they just studied computers for their own sake, And finally they decided-what the hell? If they were going to study computers, they might as well be computers! But once they had evolved into machines, some of them returned to studying humans and suggested that maybe they should become people again. Such computers were considered dangerously revolutionary, however, and if caught, had their circuits chopped quite unceremoniously. The Complex Simons could do many things well. When I received a bill for lunch which the waiter had neglected to add up, my companion, a Complex Simon, computed the addition in a matter of microseconds. Indeed, he finished the addition before I had even encoded the first number. These computers were also adept in other ways. They could solve almost any well-structured problem
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rapidly, as long as someone told them how to do it. The problem, of course, was that there was no one to explain how to solve the problem, since people had long ago deserted the town. This left the computers in something of a bind. Nevertheless, they got by on old programs written years ago when there had been people around. I do not want to imply that the Complex Simons were not creative. They could come up with an idea as well as the next computer, so long as a human had had the idea first. They could then reproduce the idea, though only if they were programmed to structure and solve the problem exactly the way the original discoverer had. They could also understand language, although sometimes less than perfectly. Once when I said I was dead from exhaustion after all the searching I had been doing, they immediately brought me to a hospital and started massive artificial resuscitation. They were rather literal, I must say. It seemed to me extremely unlikely that one of the Complex Simons had stolen my intelligence, because their computer frames made these beings rather immobile. Furthermore, some programmer from long ago would have had to plan to rob me in order for the thought to have occurred to the Complex Simons years laternot too probable. Thus, fascinating though I found their society to be, I decided to depart. On I traveled to the next, and what appeared to be the last, town on the island.
The Chi-selers The last town on Cognitia was a popular one indeed, occupied as it was by assorted groups with different names but a common belief structure. I entered a barrio in the southwest portion of the town, inhabited by a group called the Chi-selers. I could not be sure, but their appellation suggested the possibility of a chiseler who might have stolen my intelligence. The Chi-selers proved an agreeable people indeed. They went out of their way to be hospitable, and indicated complete willingness to help me find the thief who had stolen my intelligence. It became apparent to me, though, that their desire to help was not totally altruistic. In this society, one’s intelligence, and hence status, was determined directly by the extent of one’s knowledge. Therefore if someone knew who the robber was, he would be more highly valued simply by virtue of possessing this knowledge. This was obviously a partly valid basis for assessing intelligence. But I must admit to being bothered by the discovery that Chi-selers would fill their heads with empty, meaningless facts simply to know more than either their fellow Chiselers or themselves in earlier days. They were great memorizers, associating number of facts known with greater intelligence. One Chi-seler had memorized the entire Chi-selannica Encyclopedia, and was thus universally considered
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virtually all-knowing. It seemed to me odd that this Chi-seler, who knew the full name of every past leader of the Chiseler society and what each had accomplished, nonetheless had no well-formed opinions about whether they had been effective or even what made a good leader in the first place. This information was not in the encyclopedia, so ultimately, who cared? I could see their point. At first, I thought it a shame that people knew so much and understood so little, but after looking up understanding in the encyclopedia, I grasped that the important thing to a Chiseler was not to actually understand anything, but merely to be able to define the term. I might have hung around to memorize at least a few volumes of the Chiselannica, but I didn’t have time. I needed my intelligence back, perhaps to be able to do the memorization in the first place. There were no more towns to visit, and no thief to be had here, so I decided to leave the island. I launched my boat once again, though I was having trouble remembering what I had been robbed of, which was a bad sign, because it suggested that I had been robbed in part of the ability to remember of what I had been robbed. It was clear that I would need to find the thief with no further delay.
EPISTEMOLOGIA After a long journey, I finally caught sight of land up ahead. I maneuvered my boat toward it and saw a small sign that said ‘Epistemologia.’ Logically, I concluded that was the name of the island. Indeed, from the moment I set foot upon the island, I found myself thinking much more logically than I ever had before, even before I had lost my intelligence. Perhaps it was logical that I should become so logical, because everything about the island was so damned logical, from the design of the buildings to the layout of the offices to the people themselves.
The Piagetians After landing, I walked toward what appeared to be the largest city on Epistemologia. It was an old, but nevertheless elegant, city. It was, however, mysteriously empty, showing signs of recent depopulation. Empty apartments and houses, once occupied, stood vacant. Perhaps there had been a migration. I introduced myself to a townsperson who described herself as a Piagetian. She had white hair, thick glasses, and a strong accent, as did everyone else I saw. Was everyone here actually born this way? Most of the people I saw were older, so it was difficult to say for sure.
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The Piagetian stared at me a bit longer than was comfortable, sizing me up. I explained my problem to her, and she told me she would help me with my problem if I helped her with her own. Her husband had acted illogically that morning, and she was wondering whether it was something in her own behavior that had brought it on. She was therefore trying all possible combinations of behaviors that she had exhibited in the past in the hope of discriminating those that caused his illogical behavior. Could I help her find all possible combinations? I had the uneasy feeling that she was testing me, but I attempted to rise to the challenge. Apparently, I didn’t rise high enough. Obviously dissatisfied with my answer, she offered me no help with my problem, merely suggesting that I make sure I cover all possible places in the world where the thief might be hiding. Then she strolled away. I walked and walked for a long time. Thirsty, I bent down at a fresh-flowing river. Fortunately, I had brought my supplies with me, and was thereby able to fill my glass to my heart’s content. As I was drinking, a disheveled, unwholesome fellow approached and asked if he too could share in my bounty. Why not, I figured? He seemed in bad physical condition, so rather than force him to bend down to help himself, I leaned over to fill my glass and then poured all the water from my long thin glass into his short fat one. ‘Hey,’ he said, ’Holding out on me, are you?’ I stared at him with astonishment. I had poured all the water from my tall tumbler into his stubby cup, but for some strange reason, he believed that I was keeping most of the water for myself despite the fact that I had emptied my glass and filled his. I decided to leave without further confrontation. As he was in no shape to keep pace with me, I soon left him well behind. Other Piagetians were more agreeable and far more logical, unlike the poor soul I had met at the river. They were also more balanced: They equilibrated, assimilating and accommodating as the situation demanded or didn‘t demand. Because of this, my attempts to start conversations often proved frustrating. One time I tried breaking the ice by discussing literature, but they only wanted to discuss whether the literaturewas coherent and made structural sense. Discussions of art got me no further. This upset me, but they pointed out to that I had no logical reason for feeling that way. At this point, my inquiries had convinced me that no one here was likely to have stolen my intelligence, because everyone seemed to have so much of it. I decided it was time to move on, and so move on I did. The Pascualians The next hamlet I visited was quite a bit smaller than the last, but it made up for lack of land area with high population density. The inhabitants called
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themselves Pascualians. The residents were divided into two groups, the Old Pascualians and the New Pascualians. The Old Pascualians were generally more elderly, and each sect had its own particular preoccupations. The Old Pascualians were a curious lot. Whenever I spoke to them, they would repeat my sentences backward, as though I would somehow be impressed by this. I didn‘t quite see the point, but it seemed rude to say so, especially as I was soliciting their help. They also seemed rather spacey, as we might say, but apparently in their culture, being spacey was well-regarded.Different Pascualians were spacey in different ways, and the most highly-regarded was called ‘MSpacey.’ The New Pascualians were a different breed entirely, and even spoke a different dialect which they called, simply enough, aialectic.’ I approached one of these New Pascualians in the hope of obtaining advice about where I might look for the thief of my intelligence. After describing various possibilities, she suggested that my whole thesis might be wrong. Perhaps the antithesis was true-namely, that a thief hadn’t stolen my intelligence, but that I had lost it. After all, she pointed out, many people lose their intelligence over the course of a lifetime. She then proceeded to name several politicians so obviously empty headed that it was difficult not to wonder whether she might be right. But I just knew my intelligence had been stolen, because I had thoroughly searched my entire house for it in vain. Perhaps, she pointed out, I had lost it somewhere other than at home. At this point, I was feeling like I, and maybe she, had lost it altogether, and suggested as much. But the discussion continued, and eventually we decided both that I must have misplaced it, and then a thief found it unattended and stole it. Having synthesized an explanation that took both our points of view into account, we parted ways. After she had left, my confidence in our synthesis decreased. It didn’t really matter, though, because I still had to recover my lost treasure. With this in mind, I decided to visit the next town on Epistemologia. The Langlidies and the Moshmans The Langlidies and the Moshmans lived on opposite sides of the same town. Like others on the island, they were very concerned with living life logically. But there was a definite differencein their approaches both to life and education. The Langlidies seemed to be more concerned with living the logical life for its own sake, whereas the Moshmans were constantly accusing the Langlidies of logical irrationality. ’So what? was the oft-repeated question of the Moshmans. ‘How can you use the logic?’ ‘Is that what people really do? The Langlidies seemed to believe that teaching their children to think logically was a good in
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its own right, whereas the Moshmans were more the pragmatists. If people weren’t shown how to use what they learn in their instruction, they may never learn. Or worse, they may use their logical abilities for rather perverse ends. The difference between them was shown when I asked each group if they knew where my intelligence was. Their reactions were rather different. The Langlidies showed me by logical proof that they couldn’t possibly have any intelligence, whereas the Moshmans concentrated on why they would never have wanted my intelligence in the first place: It was of no use to them. So off I went again, once more empty-handed. The Demetrons and the Fischerites Here lived two peacefully coexistinggroups, the Demetrons and the Fischerites. A few conversations taught me that though there were differences between them, what they had in common was the ability to think in a complex manner. I spoke with several people about my problem and realized that due to the loss of my intelligence, I was completely out of my depth. The fourth person I spoke to, for example, said that he knew what my problem was even without hearing it from me, because he knew what Number Three knew from what Number Three told him that Number Two had told him based on what he had heard from Number One who had heard all directly from me. I thought of asking him to repeat all this, but figured I probably wouldn’t understand it the second time either, and so I deferred. Fortunately, he had a very specific hypothesis about who the thief might be and where I might find him. ‘Over to your left 1.355 miles in a gully atop a ravine at the northern end of the southwestern tip of the third highest point on the second from the last peak of the Relational Mountain you will find a man who has been known to steal anything he can lay his hands on. He may well have your intelligence.‘ I was in a horrible situation, as well you might imagine. Having lost my intelligence, I not only couldn’t remember all that he said-I couldn’t even understand it. What was worse, I wasn’t sure I would have been able to understand him had I still possessed what intelligence I once had, which I now realized wasn’t very much and might not even be worth finding. Flustered, I nonetheless offered the man good money to take me to this notorious thief, and off we went. Without a hitch, we arrived at the lair of the infamous man. He certainly did not look like a thief. He was nattily dressed in a frock coat. ‘I want to help you,’ he said, ‘but first let me assure you that contrary to what you may have heard, I am not thief. What I am depends on how you choose to view me. From a qualitative point of view, I am someone who helps redistribute wealth, whether it be financial, intellectual, or of whatever kind. From a spatial
226 R.J. Sternberg
point of view, I am someone who goes here and goes there, collecting what at one time belongs to me, and later belongs to another. From a quantitative point of view, I am someone who takes fixed and quantifiable proportions of assets from paper, and make them my own. From a causal point of view, I am someone who causes distress to one person when I appropriate his assets, and cause joy to another person when that second person receives the assets of the first. And from a verbal point of view, I am, quite simply, the local tax collector.’ My own hypercognitiveanalysis of this discourse left me feeling that ultimately, the tax collector had said the same thing five different ways. But that, I realized, was his point. But perhaps he was trying to sidetrack me from what was to me the fundamental issue. I confronted him, demanding my intelligence back. I wasn‘t sure he had it, but figured that a direct approach might give me a clue as to whether this was really my man. He looked at me with disdain, coughed, and responded that he had never been to Crimesville, would never go to Crimesville, and that if he had gone to Crimesville, which he hadn’t, he would never steal my paltry intelligence, but given that he hadn‘t gone to Crimesville, he couldn’t have stolen my intelligence, which he could have found only somewhere other than the Crimesville to which he had never been. Clever chap, I thought, trying to argue his way out of culpability. I demanded that he let me search his house. He laughed and told me to go ahead. I soon realized why he laughed: Every nook seemed to have a cmnny embedded within it, within which was embedded another nook containing at least several crannies, and on it went. To search the house would take forever. I wasn’t getting anywhere-that much was clear. I set sail for the very next island I could find.
CONTEXTADOR The next island was an oddly-shaped one whose name, I was later to find out, was Contextador. It had one unusual property that I had never before seen: It kept changing shape. This made a landing difficult, because what at one moment was land, at another was water. I was feeling very frustrated not being able to locate exactly where the island was and wasn‘t, but eventually I managed to execute a smooth docking. As I beached my boat, I saw a city in the distance, and started walking toward it. Frustratingly, its location, like that of the island, seemed to keep changing. But eventually I reached it and found myself amid multiple clans living happily together-Bronfenons, Cecans, Rogons, Berrons, and Colons. I was impressed quite favorably by such different peoples coexisting in relative harmony. Still, something was odd about all these people. At first I couldn’t figure out
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what it was, but then, eventually, it was clear. As they moved from place to place, from context to context, they changed. I engaged one Rogon in conversation, but as we walked from one end of the street to the other, he disappeared before my eyes. Another, an intelligent upstanding businessman when I first started talking to him, became a babbling idiot as soon as we crossed the street in search of a cup of coffee. Nothing seemed very stable on Contextador, neither the people nor the geography. I spoke to one Rogon long enough to ask about known criminals on the island, but this also proved frustrating. She declared that my question was poorly constructed, because a thief in one island context probably would not be one in another. Moreover, she certainly couldn’t predict from the context of Contextador who would be a thief in the very different context of Crimesville, U.S.A. This exchange wasn’t making much progress until we walked to a different part of town where she changed her point of view. ‘I only believe what I just told you when I’m in the north side of the town,’ she explained. ‘As soon as we crossed the line to the south side, my view changed. I think I may be able to help you find the thief.’ But in fact she wasn’t, because as soon as we were firmly planted in the south side, what had been a black-haired, brown-eyed woman of age 45 or so became a chameleon who couldn’t even talk. I tried to converse with the chameleon, stupidly enough, but soon the lizard had so blended into the scenery that I couldn’t even find it, much less talk to it, so I gave up. Although I was at the center of the island, what had been the center suddenly transformed into the shore, and I found myself right back next to the HMS Metaphor. This constant shifting was making me nervous, especially since I had the feeling that I was beginning to get shifty myself. I decided to set sail and embarked just in time, because as I pulled away I saw what had been the shore change into a major market place with no water at all. I was glad to be on my way once again.
GARDENERIA The next stop had to be the strangest of all. It was a small archipelago of seven islets whose inhabitants each referred to themselves as living on ‘the island,‘ paying as little attention as possible to the others. They all referred to themselves as Gardeners, but there were different branches of the Gardener family, one on each islet. I picked one at random, called the Bodilino-Kinesthesians; a strange name, but no stranger than its inhabitants.
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The Bodilino-Kinesthesians These people were muscular and exceedingly well-coordinated. I saw one traversing a narrow pole with perfect balance. Another was walking on his hands without any loss of speed or direction. I asked this particular athlete if he could direct me to the center of town, and his response was ’Duh, I dunno!’ He did not seem very intelligent, and so it surprised me to learn as I passed time on the island that this very person (who didn’t even know the sum of 1+1) was considered one of the brightest Gardeners on the Bodilino-Kinesthesian islet because of his great physical coordination. Another whom I met was able to solve highly complex mathematical and logical problems, but was not considered very intelligent because he had a physical deformity that limited his mobility. Stupidest of all were people who were physically handicapped. I asked for leads regarding the theft of my intelligence, but it became clear to me that despite the theft, I was in better shape mentally than they were, so I sailed elsewhere in the island chain. The Musicalians The next set of Gardeners were called ’Musicalians.’ People didn’t talk herethey sang. The sweeter the singing voice, the more intelligentone was considered. This seemed odd to me, especially as I’ve never had the best of singing voices myself, and it was obvious that I was immediately labeled as stupid. I tried to solicit suggestions, but when I spoke to people they didn’t understand; when I sang, they ran away in horror. I got nowhere. The Gardeneria archipelago was becoming as frustrating as everywhere else, to say the least, but I decided to make at least one more stop. The Intrapersons The third islet was Intrapersona. Here, self-knowledge was the measure of a person’s intelligence. This idea dated back, I knew, to Aristotle, and so I suspected I would be more comfortable here than I had been on the other two islands. ‘Excuseme,‘ I said to one of the IntrapersonGardeners. ’Could you tell me where I might catch a thief?’ The woman gave me a long, hard look, and inquired why I asked. I explained that my intelligence had been stolen. ‘But why, really, do you ask? What is it in you that compels you to find what was stolen, and to ask me for advice? I explained that there was nothing very complicated about what I wanted-just to recover my stolen property. She was not impressed and wondered, Why do you need to see the situation as not very complicated?‘
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This was not going well, so I said good-byeand queried a second person nearby. Why do you feel a compulsion to ask me?' he answered. I guess I'll never know, for at this point I decided self-analysis was not my virtue, and I immediately left. Gardeneria
I was quite depressed. I had visited one island after another and still had not found my intelligence. Repeated self-tests with the Wechsler Adult Intelligence Scale showed my mind nearing nonexistence. Near panic, I didn't know how much time I had left before I would lose the ability to navigate my boat. I set my sights on one more island, after which I would declare the whole business a lost cause. Steeling myself, I sailed to what for me would be the last stop. STERNBERNICUT It took me exactly three hours, three minutes, and three seconds to arrive at Sternbernicut,which was a mere three miles square and divided into three regions: the mountain, the piedmont, and the plain. The island directory, conveniently located near where I landed, said that the inhabitants were called Sternberns. As in Gardeneria, there were different branches of the Sternbern family. Since this was my last chance, I decided to investigate thoroughly. The Sternberns
I decided to head first for the mountain, which had at its foot a big sign declaring it 'Mt. Component, Home of the Componentheads.' The mountain residents did have rather large heads, I thought, hoping it was a sign of particularly welldeveloped intelligence. I picked one at random, asking him whether he could help me find a stolen object. 'Sounds like a very practical problem. I can't solve practical problems, but if you want to know the square root of 50, or the value of pi, I can tell you to any number of decimal places you would like,' he replied. None of that sounded relevant, and so I thanked him and moved on. The next person I encountered also had no idea where my intelligence might be, but assured me that his was intact and that even if he gave me half of his, he would still be extremely intelligent. Definitely a miss, I thought. I tried one more person, who, in response to my question, starting reciting the complete works of Shakespeare.
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The Novelnoggins Things were looking bad on Mt. Component, so I clambered down to the piedmont region, home of the Novelnoggins. There was practically nothing familiar about the landscape at all, and the inhabitants were equally unusual. I politely greeted the first person I saw, but he turned his face away from me and shouted, ‘Gech greech pleach!’ I fared no better with my next encounter, having more gobbledygook shouted at me from the corner of another man’s mouth. Besides the language problem, these people apparently heard with their eyes and saw with their ears. This made communication not only difficult but awkward, because they always averted their faces in conversation. Another failure, I thought, and hiked down to the plain. The Practici The plains-dwelling Practici had normal-sized heads, and looked more like regular people. The first person I asked for advice stared at me for a moment. ’Have you thought of looking inside yourself?‘ he asked. Actually, I hadn‘t. My strategy, of course, had been to look outside, hoping that someone more knowledgeable than I could help me find my intelligence. After all, what expertise had I in these matters? But I eagerly considered the possibility of looking inside myself and was about to look in the mirror when I realized that wasn’t what he meant. During my travels, I had met many people who considered themselves experts on intelligence. They didn’t seem to know much more than I did, though, and many of them actually seemed to know less. Some of their answers got awfully far afield of anything I had ever thought intelligence to be, and it was no wonder that I couldn’t find it among them. Perhaps I wasn’t so stupid after all. Perhaps my intelligence was not to be discovered merely by finding out just what or where my intelligencewas, but by using good judgment in the process of looking for it. The answer was not everything-I might never find the answer, not in my whole lifetime-but getting there was what counted. As I walked back to the HMS Metaphor I felt a lot smarter, and suddenly realized that, appearances to the contrary, I had never lost my intelligence! Rather, I had lost my confidence. My confidence restored by this revelation on Sternbernicut plain, there my intelligence was, waiting for me, safe in its little black box in the stern of my boat under a life preserver. I must have left it there the last time I went water-skiing on Lake Crimesville! I retook the Wechsler, and my score increased 100 points. Perfect it wasn’t, but good enough. I had no desire to return to Crimesville. Rather than return, I would sail the islands in search of new people, new ideas, new experiences-and the best way
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to employ my intelligence. To do this, I now realized, I would have to find a way to open the hermetically sealed box, something I had never tried before but certainly a worthy challenge. Now I am something of a wanderer, not content to settle on any one island. None of them has the answer to how I can best open the box and use my intelligence. Ultimately, I will have to solve the problem; no one can give the answer to me. In the meantime, I am content with the search. Knowing that I will never come home again, I write this message and seal it in a bottle for another to tell my tale.”
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Name Index
Ackerman, P. 14 Adey,P. 180 Alexander, J. 126,136,137,139 Amse1,E. 139 Anastasi, A. 13 Anderson, A.R. 180,181,183,184 Aristotle 174 Astington, J.W. 111,139 Baddeley, A. 89 Baker, G.P. 207 Balke, G. 52,53 Balke-Aurell, G. 13,53 Ball, L. 139 Bangert-Drowns, R.L. 13 Bara, B.G. 175,194,196,197,198,200 Barclay, C.R. 119 Baron, J. 34,139,141,143 Bassok,M. 23 Beckett, S. 135 Beilin, H. 138, 143 Belnap, N. 180,181,183,184 Bennett,N. 54 gentler, P.M. 158 Bereiter, C. 13 Berg, C.A. 151 Berry, T.D. 141 Bickhard,M.H. 138,140,141,142,143,169 Bill, V. 96 Binet,A. 46 Bjorck-Akesson, E. 49 Black, J. 154 Bond, T. '180,182 Boom, J. 142 Boyes,M. 139 Braine,M. 137,138,141,152,153,154,158, 166,167,177,182,183,184 Brown, R.V. 143 Bransford, J.D. 138,139,141,142,143
Bruner, J.S. 22 Bryant,P. 174 Bul1,D. 204 Burt, C. 47,48,52 Butterworth, G. 174 Byrne,R.M.J. 151,152,175,196,197,206 Byrnes, J. 138,139,140,180,194,205 Campbell, R.L. 138,140,169,142 Carey, S. 119,130,139,142 Carroll, J.B. 12,46,47,69 Case, R. 75,94,99,101,151 Cattell, R.B. 14,15,29,38,39,46,48,49 Cavalier, L. 113,127 Ceci, S.J. 35,38,46 Cederblom, J. 143,145 Chandler, M. 139 Chapman, M. 174 Cheng, P.W. 143 Cherniak, C. 173 Cholson, B. 139,140,141 Chomsky, N. 143,144,146 Cohen, L. J. 173 Croft,K. 129 Cronbach, L.J. 11,47,48 Demetriou, A. 12,69,75,76,77,83,85,86, 87,89,93,95,96,97,10O,l02,105,137,138, 139, 140, 151, 153, 155, 156,168,169,175, 184,207 Dennett, D.C. 12 Denton, S.M. 119 Dionnet, S. 182 Ducret, J-J. 186 Economou, A. 83 Efilides, A. 12,69, 75, 76,77,83,85,86, 87,89,95,100,105,137,139,140,151,153, 155,156,168,169,175,180,184,207
234 Ekstrom, R.B. 46 Erickson, J.R. 193 Evans, J.St.B.T. 193 Everett, B.A. 129 Ewert, G.D. 144,146 Eysenck, H.J. 35,36 Fabricius, W.V. 105,111,112,113,116,117, 118,119,126,127,128,130 Falmagne, R.J. 166 Farrar, M.J. 101 Ferguson, G.A. 14 Fischer, K. W. 75,101,139 Flavell, E.R. 9,129 Flavell, J.H. 86,95,125,129,130,155 Fodor, J.A. 12 Fong, G.T. 143 Fortier, L. 138 Franks, B.A. 138,154 French, J. W. 46 Freudenthal, H. 192 Frye,D. 111 Gallistel, C.R. 96 Galotti, K.M. 138,141 Galton, 34,35 Garcia, R. 154,180,181,183,184 Gardner, H. 12,32,33,41,151 Gelman, R. 96,104,141 Gibson, J.J. 16,18,20 Glaser, R. 14,23,45,69 Gleitman, H. 104 Glick, J. 137 Goldman, S.R. 137 Goodman, D. 101 Gottlieb, G. 141 Green, F.L. 129 Greenberg, C. 138 Greenberg, M. 151 Gresswell, M. 180 Grice, H.P. 200 Grize, J.B. 181 Gronbach, 11 Guilford, J.P. 12,29,30,39,46,51
51,52,53,58,59,76,92,104 Gustafsson, K. 41 Guttman,L. 12
Haack, S. 177,180,182,183 Hacker, P.M.S. 207 Hadkinson, B.A. 138 Hagen, J.W. 112,127 Halford, G. 75,101,184 Hare, V.C. 136 Harman, H. 46,69 Harnqvist, K. 13 Harris, P.L. 111,138 Hawkins, J. 137,138 Heinonen, V. 14 Hick, 34 Hill, S.A. 151 Hintikka, J. 174,175 Hintikka, M. 174,175 Hoepfner, R. 46 Horn, J.L. 12,30,39,46,48,49,52 Hughes, G. 180 Humphreys, L.G. 12,16,38,47 Hunt, E. 34,174 Hunting, R. 137,174,176,180,205 Inhelder, B. 96,151,179,181,183,191,193, 206 Jackson, I. 182 James, R.L. 54 Jenkins, J.J. 137 Jensen, A.R. 52 Johansson, B.S. 154 Johnson-Laird, P.N. 39,151,152,153,154, 175,176,177,178,179,184,186,193,194, 196,197,198,200,204,206 Joreskog, K.G. 39 Kai1,R. 31 Karmiloff-Smith, A. 96,104,138,140,141 Kassin, S.M. 114 Kitchener, K.S. 139,154 Klatzky, R.K. 155
Gustafsson, J.-E.12,13,35,39,40,42,49, Kline,P.
35
235 Komatsu, L.K. 138 Kosslyn, S.M. 83 Kripke,S. 183 Kuhl, J. 16 Kuhn, D. 139,140,141 Kyllonen, P. 23,119
Mulaik, S.A. 54 Murphy, G.L. 119 Murray, F. 175 Muthen, B.O. 65
Neimark, E. 154,166 Newstead, S.E. 194,196 Landau,B. 104 Nickerson, R. S. 139,143 Langford,P.E. 105,137,138,174,176,180, Nisbet, J. 137,141,143 191,194,203,205,206,207 Nisbett,R.E. 112,113,137,141,143 Lehman, D.R. 143 Nordvik,H. 41 Lehrer, K. 142,136 Noveck,I. 154 Leiman, J.M. 51 Lesgold, S. 96 Oakhill, J. 204 Lewis,D. 34,183 OBrien, D. 152,154,158,182 Ljung, B. -0. 59 OBrien, T. 151 Lickliter, R. 141 OLoughlin, M. 139 Lind,S. 54 Olson, D.R. 11 1 Lindstrom, B. 49 Overton, W. 140,141,151,154,180,193, Loehlin, J.C. 55 194,205,206,207 Lohman, D.F. 11,15,16,23,48,69 Loizou,L. 85 Papadaki, M. 83 Lovett, S.B. 130 Papantoniou, G. 83 Lukin, L. E. 139,140,142,141,143 Paul, R.N. 140,143,144,145,146 Lunneborg, M. 34 Parsons, C. 207 Pascual-Leone, J. 75,94,101 Markman, E.M. 121,123 Pawlik,K. 46 Markovits, H. 138,176 Pea,R.D. 137 Marks, M.B. 138 Pellegrino, J.W. 31 Marshalek, B. 23 Perfetti, C.A. 34 Marvin, R. 151 Perkins, D.N. 141 Matalon, B. 179,181 Perner, J. 95,111,113,129,139 Mays, W. 181,179 Pettersson, A. 59 McGuinnes, C. 137,141,143 Piaget, J. 75,76, 103,105,151, 154,173, McNemar, Q. 47 174,175,176,177,178,179,180,181,182, Medin, D.L. 119 183,184,185,191,193,206,207 Metallidou, Y. 83,85,105,156 Pieraut-le Bonniec, G. 180 Molenaar, P.C.M. 103 Pillow, B.H. 130 Montangero, J. 174 Platsidou, M. 76,85,93,151,153 Moore,C. 111 Pressley, M. 138,139,141,142,143 Morf,A. 179 Prevez,M. 76 Moshman,D. 105,138,139,140,141,142, Price, L.A. 46 143,144,145,146,154,175,207 Mossler, D. 151 Rachlin, H. 167 Moynahan, E. 113,127 Reichenbach, H. 185
236 Rescher, N. 140 Resnick, L.B. 14,45,46,96 Revlis, R. 193 Ricco, R. 154,180 Richards, D.D. 33 Roberds, S. 116,117 Robinson, M. 146 Roth,S. 34 Rumain, 8. 154,167,183,184 Rumelhart, D.E. 34 Russell, B. 136,137,174
Stilwell, C.D. 54 Stroop, J.R. 92 Stroud,B. 176 Swanson, J. 21,22,23,24
Schallert, D.L. 136 Schleifer, M. 138 Schmid, J. 51 Scholnick, E.K. 137,138 Schwanenflugel, P.J. 111,119,126 Scribner, S. 137 Segal, J.W. 141 Seltman, M. 207 Seltman,P. 207 Shanker, S.G. 192,207 Shapiro, B.J. 151 Shayer, M. 76,85,180,207 Siegel, H. 140,143 Siegler, R.S. 33 Simon, H.A. 16,18,46 Sirmali, K. 93 Sjoelin, B. 154 Slotnick, N. 154,166 Smith,L. 105,137,138,154,174,175,176, 179,182,184,186,207 Snow,R.E. 11,12,13,14,15,16,18,21,23, 47,48,69 Sodian, B. 138,139,140 Somerville, S.C. 138 Sorbom,D. 39 Spearman, C.E. 14,46,47,51 Spelke, E.S. 104 Sperber, D. 182 Stankov, L. 48 Starkey, P. 104 Steedman, M.J. 204 Sternberg, R.J. 12,15,30,31,32,33,35,41,
Ullstadius, E. 59,61 Undheim, A.M. 41 Undheim, J.O. 30,35,37,39,40,41,47,49, 56,68
42,43,141,143,151,173
Tabossi, P. 175 Terman, L.M. 46 Thomson, G.H. 16 Thorndike, E.L. 16,47 Thurstone, L.L. 12,29,30,46,51,53 Tsakiridou, E. 93
van Alstine, J. 54 van der Maas, H.L.J. 103 van Geert, P. 103 van Haften, W. 176 van Wright, G.H. 180 Voss, J.F. 141 Vernon, P.E. 12,47,49,51,52 Vye,N.J. 137 Vygotsky, L.S. 22 Wagner,R. 15 Ward,S.L. 154 Wasik, 138,139,140 Wason,P.C. 151,175,176,177,178,179 Wefald, E. 136,137 Wellman, H.M. 111,112 Westerlund, A. 59,61 113 White,€'. Wilson, D. 182 Wilson, T.D. 112,113 Wimmer, H. 129,138 Wing, C.S. 137,138 Wittgenstein, L. 174,191 Woltz, D.J. 23 Wood,D.J. 22 Zaitchik, D. 139 Zhang, X.K. 93 Zwahr, M. 116,117,118
237
Subject Index
ability 37,41 - broad 32,48 - cognitive 46 - general 4,11,14,46,69 - narrow 48 - primary 29,32,47,48,49 - specialised (see specific) - specific 4,13,14,46,69 action control 16 affordances 16,18,19,20 aptitude treatment interaction (ATI) 3,11, 14,21,23 artifacts 16,18,19 awareness - online 155 - epistemic 155 - personal-model 155 change (see development causality) contingency 159,161,166,167,184 contingent tutoring 21,22,23 competence 194 development - causality 4,97 -nature 101 epistemic cognition 154 factors nested models 52,53,55-58,92 formal operations 178,179,180 hypercognitive system 4,12, 86,87,90,95, 97,104,139,153 - development 95 - structure 86 inference schemas 152,167 intelligence 1,3,7,11,103
- academic 14-15 - adaptive 3,16 - and experience 3,13 - cognitive approach 1,4,31,77 - cognitive components approach 31, 32,33,37,40
- cognitive content approach
(see knowledge approach) - cognitive correlates approach 31,32, 34,40 - constructive 3,16 - crystallized 12, 13, 14,15,21,29,35, 36,48-49,53,76 - development 13 - developmental approach 1,3,4,76 - fluid 12, 14, 15,21,29,34,35,48-49, 53,76 -function 15 - general (factor) 4,12,13,35,39,41,46, 48 - hierarchical 3,12 - hierarchical models 4 , 1 5 40,45,47, 51 - information processing approach 3, 29,31,43 - knowledge approach 3,31,36 modular 3,12,41,104 - multifaceted 3,12 - multileveled 3,12 - novice-expert approach 29,31,36,37 - personal 3,15 - pervasive 3,13-14 - practical 14-15 - psychometric approach 1,3,4,29,30, 42,76 - relational 3,15 - selective 3,15 - situated 3,13-14 - structure 2,12, 29
238 interface redesign 19 logic 138,175,192 - certainty 183,193,194,205,207 - coherence 174,186 - competence 6,205 - connectives 5,158,163,165,166,167 - entailment 6,180-185,194,207 - formal 204,207 -mental 152 - modal 180,184 - nature 142 - necessity 6,138,153,154,174,176,181, 183,184,186,193,194 - predicate 6,180,207 - premises - modelling of 197 - combination of 198 - deriving conclusions from 199 - propositional 6,152,180,181,207 - relations 5,158,159,160,161,163,164, 166 - validity 5,153,159,177
- structure 4,75,80,105,153
- theory of 4,111,119,129 modules 41
performance assembly 16 person-situation-interaction 11,13,15,23 person-situation-interface 17,19,21 person-task-interface 23,25 principles of cognitive organisation 77, 85 - developmental variation 79 - domain specificity 78 - formal procedural specificity 78 - subjective equivalence of abilities 79 - symbolic bias 79 processing system 4,33,69,89,90,91,93, 97,101,104 - control of processing 89,90,91,93,94, 99,101,153 development 93 -means 153 - speed of processing 89,90,93,94,99, 101,153 - storage 89,91 -structure 89 - working memory 91,101,153,155
-
memory - information acquisition theory 116 - information processing theory 117, 118,128 rationality 5,135,136,138,139, 140,142, - theoriesof 112 143,145,146,173,193,204 mental models 6,152,175-177,180,185 reasoning 1,3,5,7,103,105,135,138,142, metacognition 33,86,111,155,168,174 180 - metacognitive experiences 6,155 - deductive 7, 31,32, 33, 83, 191, 192, - metacognitive knowledge 155 193,194 metalogic 155 - development 5,6,141,151,154,163, metareasoning 5,135,136,146,154,169 167 - conceptual 5,136,138,140,142,146 - inductive 7, 31,32,33, 83,177,191, - constructive 5,136,140,141,142,143, 205,206 146 - logical 5,6,151 - procedural 5,136,138,140,142,146 -models 173 mind 1,3,5,7,75,93,103,105 -nature 151 - architecture 4,77 - process 151,154 - constructivist theory of 4,5,128,129, - propositional 5,151,153,163 130 - schemas, 164 - development 4,75 - structure 6,151 - dynamics 75,93 - syllogistic 196,197,203,204
239 - without logic 175 relevance-criterion 180,181,182 representational communication approach 191 response-sampling model 16
selection task 178,180 specialized structural systems (SSSs) 4, 12,69,78,79,80,84,90,97,99,101,103,104, 153,167 - causal-experimental 82,95 - development 95 - qualitative-analytic 80 - quantitative-relational 81,95 - spatial-imaginal 83 - verbal-propositional 5,82
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