20 Thinking Tools: Collaborative Inquiry for the Classroom

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Collaborative Inquiry for the Classroom ACER Press

First published 2006 by ACER Press Australian Council for Educational Research Ltd 19 Prospect Hill Road, Camberwell, Victoria, 3124 Copyright © Philip Cam 2006 All rights reserved. Except under the conditions described in the Copyright Act 1968 of Australia and subsequent amendments, 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 written permission of the publishers.

Edited by Ronél Redman Cover and text design by Anita Adams Typeset by Anita Adams Printed by Hyde Park Press

National Library of Australia Cataloguing-in-Publication data: Cam, Philip, 1948- . Twenty thinking tools. Bibliography. For primary and secondary school students. ISBN 978 0 86431 501 4. ISBN 0 86431 501 5. 1. Philosophy - Study and teaching (Primary). 2. Philosophy - Study and teaching (Secondary). I. Title. 372.8 Visit our website: www.acerpress.com.au

Explanatory Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Practical Beginnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 The Tools of Inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Introductory Toolkit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31 The Question Quadrant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Reasons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Agreement/Disagreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Distinctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Borderline Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Thought Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Thumbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Intermediate Toolkit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 Agendas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Counterexamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Generalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Discussion Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Advanced Toolkit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89 Fact, Value, Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Deductive Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Reasoning Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Disagreement Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

The tools in this book have been classified using the system below. It is important to ensure that your students demonstrate a basic proficiency with the more elementary tools before proceeding to those at the next level. In general, the rate of progression will vary with the educational stage of the students, with older students being able to progress to the Intermediate and Advanced Tools more quickly. Progression will also depend on the amount of time and effort devoted to acquiring proficiency in the use of the tools, and on whether or not attention has been paid to their acquisition in earlier years. While I have linked the tools to different educational stages, students of any age will need to acquire facility with the Introductory, Intermediate and Advanced Tools, in that order. Teachers should also note that most of the tools can be used in elementary, as well as more sophisticated, ways.

Introductory These tools can be introduced to students at any age and level of attainment. They are particularly suitable for students in their early school years.

Intermediate The Intermediate Tools can be introduced to students once they have learned to use the Introductory Tools. They are particularly suitable for students in their middle primary years.

Advanced The Advanced Tools require some logical sophistication and/or a capacity to reason abstractly. They are particularly suitable for secondary school students, but may also be introduced to experienced students in the final year of primary school.

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Suppose for a moment that students were to graduate from our schools almost entirely innumerate. Imagine the outcry. Now picture them turning out to be more or less illiterate and how appalled the community would be. By contrast, students actually do leave our schools basically insocratic, and it is barely noticed. Given that until now there has not even been a word such as ‘insocratic’ to stand alongside ‘illiterate’ and ‘innumerate’, it is hardly surprising. Yet I am referring to something quite comparable and so basic that it demands the most serious attention. I derive the word ‘insocratic’ from ‘Socrates’. Socrates was fond of engaging people of all ages in dialogue aimed at getting them to think for themselves about the central issues of life. He held that the unexamined life was not worth living, and that the kind of open-minded inquiry in which he engaged with his fellows was really the best way to live. In coining this term, I do not suggest that we should be engaging students in Socratic dialogue in the classroom. Were you to inspect Socrates’ practices closely, you might not altogether agree with his methods, and you might even wonder whether the specific kind of knowledge that he sought actually is central to a good life. Yet there can be no doubt that the ability to think about the issues and problems that we face in our lives, to explore life’s possibilities, to appreciate alternative points of view, to critically evaluate what we read and hear, to make appropriate distinctions and needful connections, and generally to make reasonable judgements are among the attributes of anyone who has learnt to think effectively in life. People who cannot adequately think for themselves in these ways are to that extent insocratic. And my claim is that our education system systematically fails to teach people to think for themselves to any significant degree. Introduction

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We attempt to teach people to reason mathematically and to read fluently—though there are perennial calls for schools to teach these things better than they do. We try to teach people to comprehend the various subject matters that form the basis of the school curriculum—although this comprehension tends to rely heavily on memory work and basic routines. Yet virtually no attention is given to teaching people to think well in the context of their lives away from school, in those everyday social, familial and personal contexts in which the great bulk of decisions and actions take place. There is a Reading Recovery program, but no Thinking Recovery to rescue the ‘insocratic’ student. And the kind of attention that we normally pay to thinking in the curriculum has at best a diffuse effect when it comes to these contexts, and for the most part provides no preparation at all. This is a source of social and personal tragedy. All too often individuals, families, organisations, communities and sections of society live with the consequences of poorly thought-out decisions, faulty reasoning, biased judgements, unreasonable conduct, narrow perspectives, unexamined values and unfulfilled lives.

If only people were better at asking appropriate questions, articulating problems and issues, imagining life’s possibilities, seeing where things lead, evaluating the alternatives open to them, engaging in discussion with one another, and thinking collaboratively, then we would all be so much better off.

A wide-scale improvement in such abilities would be no panacea, no cure for all the ills that life presents, but surely it would be one of the most significant educational achievements that we could envisage in combating the problems of life and society. To draw a medical parallel: no developed society would tolerate unchecked endemic disease in the way that we suffer the consequences of widespread poor thinking in our society. Something needs to be done. This book is designed to assist teachers to begin to rectify the situation. It provides a practical means of helping students to improve their ability to think about problems and issues of all kinds.

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When introduced to students through classroom discussion and small group activities, and reinforced by regular use, the array of tools outlined in these pages will prove useful throughout a lifetime.

Many of the tools that I have assembled will be somewhat familiar to you and your students, but it is one thing to use such tools in a relatively uneducated and intuitive way, and quite another thing to have an explicit and well-schooled knowledge of their use, so that the user both knows what tools to reach for and how to use them effectively. It is not sufficient for students to be brought up to respond to the teacher’s requests to give an appropriate reason for something, for example. They need to develop the habit of giving and seeking reasons when it is appropriate to do so. They need to do it knowing what they are about and to do so with increasing sophistication and skill. In the kind of classroom activity that I recommend, you will find that there are countless occasions when students will instinctively make an intellectual move, or when you will be able to request them to do so. Underlining these moves when they occur, requesting them and explicitly reinforcing their use are an essential part of the practice. In addition, however, I have found it a great advance to give students activities that explicitly introduce and reinforce the tools used to make these intellectual manoeuvres. This book provides the teacher with the kinds of resources that are needed.

Introduction

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Introducing the toolkits It is never too early to begin to teach our students to think, and we should start early if we want to have a truly formative influence. Yet teachers can adapt most of the activities included in this book to suit students of just about any age. Regardless of age, students who start off with an empty toolbox will, with work and support, gradually assemble a kit of tools. As a general guide, the tools have been divided into three groups. They comprise the Introductory Toolkit, to which we can add a set of Intermediate Tools, and then a further set of Advanced Tools. The Introductory Tools are definitely foundational and need to be acquired first, and reinforced until they become a normal part of the thinking process. The Intermediate Tools can then be introduced as and when you feel that your students are ready for them. Advanced Tools are intellectually more difficult, and many students are likely to find some of them beyond their powers until they reach secondary school. The table on the next page gives a list of the tools to be found in each of the three kits. Any elementary discussion will make some use of most of the tools in the Introductory Kit. Discussion cannot proceed without problems or questions. While the teacher may introduce them at the beginning in the early grades, it is desirable to move to students’ questions as soon as possible, and then you are likely to find The Question Quadrant very useful in helping to improve the quality of their questions. Again, you cannot have an inquiry without students’ Suggestions, and the inquiry will have no critical edge unless it involves the exploration of Agreement and Disagreement through the give and take of Reasons. These become tools to be used in conducting discussion. It will also be natural for students to introduce Examples and make Distinctions as they proceed. Yet it is important to distinguish between students happening to introduce examples or to make distinctions during discussion, and teaching students about the various uses of examples or introducing them to the art of making distinctions. They need to learn to use such things as tools to do thoughtful intellectual work. So the teacher might place particular emphasis on learning to make distinctions over several sessions, for example, and supplement it with exercises in distinction-making so that students become reasonably proficient in the elementary use of that tool. Similarly, the use of Thought Experiments, Borderline Cases and a device like Target can be introduced in turn. I recommend that teachers introduce the reflective device that I call Thumbs early on, as it provides students with the opportunity to review their practice and to think about how they might improve it.

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Once you begin using students’ questions as a basis for discussion, you will soon discover the benefits of working with Agendas. I also recommend that teachers make use of Discussion Maps as soon as they begin to introduce students to the Intermediate Tools, in order to help keep track of the growing complexity of discussion. The explicit use of Counterexamples, Criteria and Generalisation, which can be introduced in succession, also makes demands on the mapping process. Fact, Value, Concept gives students an Advanced Tool for analysing questions and uncovering further questions that may be necessary for the purposes of their inquiry. The introduction of formal Deductive Reasoning and the various kinds of diagrams that can help them structure and track discussion completes the set of Advanced Tools that this book provides. When introducing diagrams, teachers should begin with Reasoning Diagrams, and only proceed to Assumptions and Disagreement Diagrams when this basic device is well understood.

Introductory Tools

Intermediate Advanced Tools Tools

The Question Quadrant Suggestions Reasons Agreement/ Disagreement Examples Distinctions Borderline Cases Target Thought Experiments Thumbs

Agendas Counterexamples Criteria Generalisation Discussion Maps

Fact, Value, Concept Deductive Reasoning Reasoning Diagrams Assumptions Disagreement Diagrams

Introduction

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There are three general pieces of advice about introducing these tools that I should give you at the outset:

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There is no substitute for discussion: While many of the tools can be introduced to students through exercises and specially devised activities, resist the temptation to treat these tools as things that can be taught without students learning to use them in discussion. Class discussion and small group activities involving discussion should be the primary means by which students learn to use the tools. Here I am rejecting the common assumption that you can effectively teach thinking skills on their own apart from dealing with rich content and engaging students in genuine inquiry. My reasons for insisting on this will become apparent in the following section on the theoretical background to this work, but for now suffice it to say that it is by this means that the tools will most readily enter into ways of thinking that your students come to habitually employ.

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Maintain a balanced approach: Any moderately successful discussion will incorporate intuitive attempts by students to make a variety of intellectual moves, providing you with opportunities to call attention to them and to teach their proper use. But be careful not to place too heavy a cognitive load on your students. It interferes with the process of consolidation and the joy they take in discussion. You need to strike a balance between allowing discussion to proceed and diverting attention to intellectual procedures. Hold off on introducing students to new tools until those previously introduced have passed through the initial learning phase and your students are using them habitually. In the learning phase, there will be a need for regular intervention, which will diminish as the use of a tool becomes part and parcel of the students’ discussions. If you attempt to introduce too much intellectual apparatus too quickly, you will overburden the discussion with intervention.

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Make the tools as visible as possible: Be sure to make the tools as visible and concrete as possible. Particularly for younger students, I recommend that you use the idea of a toolbox and ask them to visualise it. When first acquiring a tool, get them to think of placing it in their box, and then subsequently ask them to think of reaching for it as the need arises. You can even build a Thinking Tools Box as a teaching aid and keep cut-outs of the tools in it. You should encourage your students to identify the tools that they use by name, and have the names of the tools they are learning to use posted up in the classroom. It will help if you also display examples of the students’ work in such a way that they can readily identify their own successful use of the tools.

Twenty Thinking Tools

This book follows John Dewey (1966, 1997) and Matthew Lipman (2003) in emphasising the centrality in school education of learning to think. Both these philosophers of education belong to what we may call the tradition of reflective education, in which learning to think lies at the core of educational aims and practices. Furthermore, both writers understand thinking as a process of inquiry. Dewey’s model of inquiry owes much to the patterns of thought in experimental science, although he applied it to inquiries into matters of value as well as matters of fact. Indeed, Dewey was particularly concerned with the need to develop an inquiring intelligence in regard to values, and he thought that we had much to learn in our deliberations and disputes over values from modes of thought that have been successful in science. Lipman’s model of inquiry draws more heavily on philosophy, a discipline that pays a great deal of attention to good thinking and its improvement. Lipman emphasises such things as conceptual exploration and logical inference, which are central to philosophical thinking, and he pays much less attention to experimental testing, which is the mainstay of scientific inquiry. I am not overly concerned with these differences between Dewey and Lipman, however, and have generalised on the inquiry process in such a way as to minimise their significance. In doing so, my aim has been to construct a toolkit that covers the most important moves in thinking that we need to have at our command if we are to think effectively in everyday life. Both Dewey and Lipman also lay stress on the notion of community. Dewey had a particular notion of community in mind that was tied to democracy. Dewey’s idea of democracy does not centre on representative government, but Theoretical Background

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on the ways in which people relate to one another in their everyday lives and the kinds of arrangements that facilitate their relations. In short, it centres on an ideal of community life. For Dewey, democracy is a way of life marked by inclusiveness in the range of interests to which it caters and the maximisation of free cooperative interplay between individuals, as well as between the various groups that make up a community. Relations and arrangements that give everyone’s interests due consideration, not setting some people’s interests over and above those of others, are to that extent democratic, as are those that allow individuals and groups to fully and freely engage with one another, as opposed to being excluded or coerced. According to Dewey, a scheme of education that befits democracy and contributes to its growth ought to foster this form of community life. No matter how much attention is paid to topics in civic education and suchlike, if the system of school education, individual school and classroom practices, and interpersonal relations in our schools are exclusive, discriminatory, hierarchical, authoritarian or cliquish, the development of democratic citizenship is undermined. The tie between education and a democratic way of life also underlies Lipman’s conception of the classroom as a Community of Inquiry. Here the classroom is thought of as a pluralistic community, centred on dialogue and collaborative activity, in which all of its members have an active and equitable share. Through discussion and dialogue, students learn to actively listen to one another, to share their views, to build on each other’s ideas, to consider a variety of opinions and perspectives, and to explore their disagreements reasonably. Lipman’s classroom forms an inclusive cooperative community in which communication and inquiry sow the seeds of democracy. The Community of Inquiry forms the guiding ideal of classroom practice advocated in this book. A brief introduction to the general practices and procedures of collaborative classroom inquiry follows in the next section, Practical Beginnings. These practices and procedures will be reinforced throughout the book. This kind of collaborative inquiry encourages the social communication and mutual recognition of interests that Dewey identifies with a democratic way of life. Such an engagement develops the social and intellectual dispositions and capacities needed for active citizenship, while liberating the powers of the individual. That is to say, in learning to think together in these ways, students acquire the forms of regard and the practices of social exchange that help to sustain an open society at the same time as they learn to think for themselves. These two things go together.

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Twenty Thinking Tools

On the one hand, we are developing in students the kinds of attitudes, habits and capacities that characterise people who have learnt to think for themselves, such as:

• an inquiring outlook coupled with an ability to articulate problems and issues • a tendency to be intellectually proactive and persistent • a capacity for imaginative and adventurous thinking • a habit of exploring alternative possibilities • an ability to critically examine issues and ideas • a capacity for sound independent judgement.

On the other hand, by having students learn to think together, we are also developing social habits and dispositions, such as:

• a habit of actively listening to others and of trying to understand their viewpoints • a disposition to give reasons for what you say and to expect the same of others • a habit of exploring disagreements reasonably • a disposition to be generally cooperative and constructive • a disposition to be socially communicative and inclusive • a habit of taking other people’s feelings and concerns into account.

These interlocking individual and social outcomes build on the tradition of reflective education, while mirroring John Dewey’s vision of a more deeply democratic way of life. They form a package of outcomes that are achievable by systematically implementing and building on the educational practices recommended in this book. The practices being recommended also have a theoretical basis in the work of the educational psychologist Lev Vygotsky (1978, 1986). Vygotsky tells us Theoretical Background

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that a person’s social and intellectual development is primarily a process in which the interpersonal communicative functions of language are transmuted into verbal thought. Vygotsky calls this process ‘internalisation’, by which he means the transformation between an interpersonal communicative function and an individual psychological use. According to Vygotsky, this transformation and incorporation of the social is a universal feature in the development of all the so-called higher cognitive functions:

Every feature in the child’s cultural development appears twice: first on the social level, and later, on the individual level; first between people (interpsychological), and then inside the child (intrapsychological). This applies equally to voluntary attention, to logical memory, and to the formation of concepts. All the higher psychological functions originate as actual relations between human individuals. (Vygotsky 1978, p. 57)

When it comes to developing children’s capacities to think, it would be a natural implication of Vygotsky’s remarks to suggest that children come to think for themselves through the internalisation of social practices. And this provides a way of understanding the relationship between thinking together and thinking for oneself in the Community of Inquiry. For example, learning to ask questions of others as a move in collaborative inquiry can be seen as a prelude to becoming reflective by asking oneself questions. Learning to explore reasons with others can be seen as the social scaffolding by means of which students come to ask themselves for reasons. Learning to consider the viewpoints of others—rather than merely asserting one’s own—forms the basis for coming to consider alternatives to one’s own first thoughts and to generally being prepared to explore a range of views and possibilities in one’s own thinking. In general, learning to think for oneself is, on this view, to convert the practices of open collaborative inquiry into ways of thinking for oneself through the process of internalisation. Vygotsky is better known to teachers for what he calls ‘the zone of proximal development’. This zone is defined by the difference between what a student can do unaided and what he or she can do with prompting or with scaffolding provided by an adult, or by more competent peers. The zone of proximal development focuses on the student’s potential, and instruction proceeds ahead of the actual level of development, drawing on socially available functions

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Twenty Thinking Tools

that are in the process of being assimilated. Working within the zone of proximal development is therefore not just a matter of shifting students ‘out of their comfort zone’. It also requires a supply of interpsychological practices that can be progressively internalised by the student. This places a premium on interpsychological or social training with the tools that students can be encouraged to gradually transmute into their own repertoire of thinking practices. Given its emphasis on students learning to think for themselves through intellectual-cum-social interaction, and the scaffolding provided in this context by both the teacher and more competent peers, the Community of Inquiry thus provides a rich Vygotskian learning environment. These brief remarks are meant to convey something of the theoretical background to what is otherwise a practically oriented book. I hope that I have said enough to alert the busy classroom teacher to its intellectual underpinnings. It is all too easy to lose sight of this larger perspective in the busy daily work of teaching. If you take the time to reflect on these theoretical remarks and bear them in mind when attempting to put this book into practice, then your effort will be much rewarded.

Theoretical Background

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The basic pattern of inquiry What I am about to describe is by no means an invariable procedure. It is a framework for inquiry that can be adapted to different circumstances, entered into at various points, and augmented in many ways. Like most live inquiries, actual inquiries in the classroom are likely to include all sorts of deviations from this basic model. Nevertheless, the following is a pattern with which you will become familiar.

The basic pattern of inquiry INITIATING

problematic initial situation

problem formation, agenda setting

SUGGESTING

ideas, conjectures, hypotheses

CREATIVE PHASE

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Twenty Thinking Tools

EVALUATING REASONING & CONCEPTUAL EXPLORATION implications, assumptions, meanings

evidence, tests, criteria

CRITICAL PHASE

CONCLUDING

conclusion, resolution, implementation

Introducing a problematic situation Inquiry begins with a problematic situation. In daily life we find ourselves in such a situation when something unexpectedly goes wrong and we don’t know why, or when we encounter difficulties or problems that are out of the ordinary, or when something peculiar or puzzling happens that we cannot explain or fully comprehend. When it comes to the classroom, a problematic situation may be either actual or fictional. It may be generated by a literary narrative, say, or by a newspaper report. Whatever its source, it is essential for the situation to be one that students will see as problematic. Unless their curiosity is aroused, inquiry will not begin. Routine matters—problems that the students acknowledge to have established right answers, and issues that students view as just another teacher-set task—will not do. You need material that calls for thinking. This means material that will help to generate genuine questions in students’ minds. It means problems where there may be many different possible solutions rather than one single correct response. It means issues where students can be expected to have a variety of opinions that would be worth exploring. Unless we are dealing with very young students, it is generally not good practice for teachers to begin with problems or questions that we have formulated ourselves. We need to provide the opportunity for students to do that. A standard approach is to present students with material that can be used to get them to raise issues or that provokes them to ask questions that can be used as a basis for inquiry. Such material will typically treat whatever subject matter it contains as problematic and in need of further explanation or understanding. It may challenge students’ attitudes, values, beliefs or conceptions. It may raise alternative possibilities or invite consideration of different points of view. In any event, it needs to be the kind of material that will encourage students to ask questions, to seek explanations and to offer their own thoughts and opinions. The material will need to be sufficiently related to their experience and interests to enable them to draw on personal understandings and feelings. Quality children’s literature is often of this character, and appropriately chosen social or other issues from the media, from the local environment, or from the students’ daily lives can also be used. Stories and other materials that have been expressly written for the purpose of classroom inquiry will obviously fit the bill, and I have included a selection of this material under Classroom Resources in the Bibliography (see pp. 115–16).

Practical Beginnings

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Initiating inquiry Collaborative learning that typically moves between class discussion and discussion-based small group activities requires the right kind of physical arrangement. While small group activities can be carried out at desks or on the floor, as appropriate, class discussion really requires a circle. If students are going to learn to respond to one another, they need to be able to see each other face-to-face. It is not a good idea to have students at their desks or to adopt the formation that is familiar in primary schools of grouping students on the floor in front of the teacher. You do not want to have something as elementary as the physical setting working against what you are trying to do. Now you are ready to initiate a problematic situation. Don’t forget that having the ability to alight upon a problem, to articulate it, to formulate appropriate questions and to separate out the issues is integral to a capacity to inquire. Therefore, whatever material you choose—a picture book, story, artwork or other image, a documentary film, newspaper article, local issue—it should be used to raise issues and prompt discussion among your students. Teachers will need to provide much more scaffolding for very young students, of course. With students who are just beginning to learn to articulate problems or to ask questions when called upon to do so, the teacher may need to help them to probe the stimulus by raising appropriate questions for them to address. For example, if I were going to have a discussion with very young students based around Eric Carle’s The Very Hungry Caterpillar, I might begin by asking whether they think that the butterfly in the story is the same living creature as the caterpillar. And we might concentrate on the use of Reasons in order to think about that issue in our discussion. Then we might proceed to think about whether we will be the same people as we are now when we grow up, or whether we will have changed so much that we will have become different people. In other words, I will have alighted upon an aspect of the story that is likely to stimulate the students’ curiosity, and then built on their sense of puzzlement in getting them to think about themselves. Once students are able to ask their own questions, however, it is usually best to get them to do so. When you do this for the first time, gather your class into a circle and tell everyone that today they will have the opportunity to discuss whatever it is that you are going to present. Tell them that while you are reading the story or presenting other stimulus material, you want them to be thinking about a question they might ask. The question can be about an issue that the material raises, something that they see as a problem, something in it that puzzles them or with which they may not agree, or indeed anything that the material prompts them to think about that they would really like to discuss. Tell them that you are looking for good ‘meaty’ questions, ones that will get people in the class to think hard about some problem or issue.

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If your students are slow to come up with questions at first, give them a little time; then take the questions as they arise and write them on the board or on a sheet of butcher’s paper. It is a good idea to write the students’ names next to their questions for future reference and to give them a sense of ownership. You may need to ask students to clarify or otherwise improve their questions as you go, and to invite other students to help someone who is having difficulty formulating their question. However, don’t reject any serious attempt to ask a question at this stage. Be inclusive and show your students that you value their questions.

When your students have become familiar with this practice, you should vary the procedure. For example, you might divide the class into pairs or threes and have each pair or threesome negotiate a question among themselves and, if they are able, write it with a felt pen on a strip of paper. This will actively involve all your students in the process of question formation and should improve the quality of the questions asked. You might like to adopt the practice of having your students keep a reflection book in which they record questions about their lives that occur to them in the course of the day, and which they bring to class for discussion. Once they have mastered the basics, you will be able to help them make their questions more deeply exploratory, as will be explained later when we come to the device referred to as The Question Quadrant. When students are familiar with the Introductory Tools, it is usually a good idea to invite them to draw connections between their questions in the way described under Agendas later in the book. While individual questions can be connected in all sorts of ways, depending on the material with which you began, you will often find that questions are connected to central topics, concepts or underlying themes. Giving your students the opportunity to bring out the connections between their questions helps them to organise those questions into a more coherent agenda and to get their bearings in the problem domain. Use coloured markers or some other coding scheme to make their connections explicit, then ask them whether they can supply a word or a phrase that captures the topic, theme or concept and add that to the board. While students sometimes find this difficult to do at first, do persevere, as they

Practical Beginnings

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will quickly get better with practice. They will soon be able to supply deeper connections in place of more superficial ones; and they will see that sometimes questions are logically connected, so that, for example, it would be important to try to answer one question before turning to another with which it is connected. Having assembled the questions, the students are ready to begin their discussion. They will almost certainly have generated many more questions than can be discussed in the time available, and may well have generated sufficient inquiry starters to keep the class going for several sessions. Provided that interest is maintained, that is all to the good. You do not need to start every session by generating questions, and next time you may begin by asking the students to provide a brief review of their previous session and then invite them to take up the discussion from where it left off, or to proceed to other questions that remain to be discussed.

There may be an obvious or natural starting point for discussion, but more often than not the students will have grouped the questions into several larger issues or themes—any one of which might serve as a starting point. It is often a good idea, therefore, to get a sense of the class’s interest in different groups of questions, and a simple way of doing this is to ask them to vote for the issue or theme that they would most like to discuss. You may find that the centre of interest is not where you had supposed.

While your students are just beginning to learn what makes a question good for inquiry, you might proceed more directly by yourself selecting a question (or group of questions) that seems to have real promise. The discussion will almost certainly fall flat if you don’t alight upon a question of substance. Having said this, it can be useful briefly to address a question or two that can be easily answered; or to consider one where different hypotheses might be suggested that lead nowhere, because, for instance, there is no way of testing them out. It helps students to get a sense of the difference between these kinds of dead-end questions and those that open up a really stimulating discussion. Quite reasonably, teachers often feel that they would like the time to reflect on the chosen topic or question before commencing discussion. This is often a good idea. Among other things, it provides the teacher with the opportunity to formulate some supplementary questions or to devise an exercise or an

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activity that might be useful in extending the discussion once it is underway. It is therefore quite common for teachers to take the process described above up to this point in one sitting, and then to come back to discussion on the next occasion, allowing time for further preparation.

Generating suggestions The first object of discussion is to generate ideas, hypotheses, conjectures or expressions of opinion—or what I call Suggestions, in short. That is to say, there is some question, problem or issue under discussion and we are looking for possible answers, explanations, solutions, or remedies in response. If the question with which we began is one appropriate for inquiry, it will leave room for various possible responses of this kind. Attending to these different possibilities is crucial, because it enables us to move on to the business of reasoning, analysis and evaluation that is needed in order to reach a considered judgement or conclusion. Just how the discussion proceeds will depend to some extent on what kind of question is under discussion. One standard beginning is to ask the questioner to address their question in a preliminary way. It may be helpful for the questioner to explain what prompted their question, to clarify it if need be, and also to offer further thoughts if he or she has any. By now, other students will be ready to respond. Since we are looking for a variety of opinions, different points of view or alternative ideas or possibilities, it is important to allow a number of students to speak briefly at this stage. During the process, students can be encouraged to build on each other’s ideas, to express agreement or disagreement, to offer alternatives, or simply to try out an idea. Some clarification of their ideas may be needed, including making distinctions and connections of various sorts between the suggestions themselves. While it is right and proper for students to express their differences and disagreements by giving reasons for them, you should ask students to put aside detailed debate on any suggestion for the moment, until some alternatives have been collected. We need different points of view, rival hypotheses, or alternative ideas in order to suspend judgement in the community as a whole. The suspension of judgement is central to the intersubjective practice of inquiry. It may be that some students begin with fixed ideas about the matter under discussion, but the fact that other students express different ideas, or that alternative possibilities are suggested, means that the community has not made up its mind and discussion will ensue. Let us take, for example, the following suggestions from a secondary classroom in which students are addressing the question of what makes an action fair. In this case the suggestions were generated by discussion in small groups.

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An action is fair if it treats people as they deserve to be treated. What makes an action fair?

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An action is fair only if it treats everyone equally. An action is fair enough if it does no one any harm. An action is fair if everyone’s interests are taken into account.

The students making these suggestions may not necessarily be committed to them. They may be just thoughts that came to mind, or an idea that seemed reasonable at the time, to which other alternatives or more refined statements might be added in due course. In whatever spirit they have been put forward, clearly a lot more will need to be said in order to develop and evaluate these suggestions properly if we are going to reach a considered judgement, irrespective of whether we arrive at a consensus in the end. Given these various possibilities, intersubjective suspension of judgement occurs and students are drawn into examining their ideas by testing them against their experience, comparing and contrasting the different possibilities, and exploring disagreements. And as they continue to work in this way with one another, they gradually internalise this pattern in their own thinking, and habitually suspend judgement in their own thinking in order to explore alternative possibilities and different points of view.

Conceptual exploration and reasoning It may not be immediately apparent what students’ conjectures, tentative explanations, suggestions, suppositions and so forth come to. In order to tease out the meaning of such things, they may need to explore the connotations of the concepts that they employ, as well as to draw out the implications of the claims that they make. These are intimately related activities. For example, the deeper meaning of a suggestion may not be clear until the concepts being employed are more fully grasped—just as its import may only become apparent when the students reason about its implications. This raises the twin topics of conceptual exploration and reasoning.

Conceptual exploration In order to get an initial feel for conceptual exploration, let us go back to the question we were considering a moment ago: What makes an action fair? You

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can hardly imagine proceeding very far with this question without people coming up with examples of actions that they take to be either fair or not fair, and this almost inevitably leads into controversy about one case or another. This is because the question with which we began effectively calls on us to state the criteria for saying that an action is fair; and like just about all of the central concepts we employ when we talk about things of importance to our lives, the tacit criteria that govern the concept of fairness turn out to be somewhat uncertain and surprisingly contentious. So first of all we need to make our unspoken criteria explicit, and then we need to examine them. This may not result in a consensus about the meanings of concepts we employ, but it will enable us to more deeply understand the import of our ideas and to better appreciate where we stand in the intellectual terrain. Distinction-making is one basic kind of conceptual move. Here we insert a divider between things that might otherwise be treated as the same. This can bring greater clarity and precision and save us from a multitude of errors. In the discussion of fairness, for example, one group’s suggestion was that an action is ‘fair enough’ if it does no one any harm. We may well want to ask whether the notion of something being ‘fair enough’ is the same as something being fair. After all, to say that something is fair enough is often just to say that it is merely sufficiently justified to be acceptable in the circumstances. To be ‘fair enough’ is therefore, arguably, to be only good enough to be allowed to pass. And qualified fairness is not what we were asking about. It could therefore be important to distinguish being fair from merely being ‘fair enough’. In the case in point, even were an action fair enough so long as it did no one any harm, ‘not doing harm’ may be too weak a constraint to ensure that an action is completely fair. Distinction-making is to be found whenever we try to sort out ambiguities or vagueness in the meanings of words.

For example, in the suggestions made about fairness, when it is said that an action is fair if it takes everyone’s interests into account, does ‘interests’ mean ‘those things that we are interested in pursuing’ or, alternatively, ‘those things that contribute to our happiness or welfare’? Or does it perhaps mean something else? How we understand a word like ‘interests’ in this context is crucial to the issue. After all, it is one thing to claim that considerations of fairness require us to consider the welfare of all the individuals affected by our actions in deciding what we should do, and quite another to claim that an action cannot be fair unless it takes into account whatever people are interested in doing. Practical Beginnings

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Conceptual exploration also involves paying attention to connotations and other conceptual connections. This can be as simple as seeing that words belong to clusters or families of words that have bonds of meaning, that form conceptual oppositions, or are ordered along some dimension. Consider, for example, the suggestion that an action is fair if it treats people as they deserve to be treated. We usually speak of what people deserve in the context of reward and punishment. ‘To get what you deserve’ is to get your just reward or punishment. In the context of fairness, ‘punishment’ and ‘reward’ belong to a cluster of terms that have to do with appropriate penalties (according to offence) and the differential treatment of people (according to merit), including such words as ‘payback’, ‘retribution’, ‘forfeit’, ‘compensate’, and ‘prize’, ‘award’, ‘reward’ and ‘entitlement’. On the face of it, they belong to a different family of ideas than those tied to equality. So those who suggested that an action is fair if it treats people as they deserve to be treated appear to be looking at fairness from a different angle than those who said that an action is fair only if it treats everyone equally. (In more advanced discussions, we might refer to the distinction between retributive and distributive justice.) Perhaps, with some work, these two perspectives can be made to align, but there is certainly a difference between them. It is a difference that we can begin to articulate by exploring the connotations of the words being used, and that is a very useful conceptual exercise.

Conceptual exploration also includes categorical thinking in which systematic distinctions and connections are made in organising some subject matter. This is the kind of thinking that belongs to classification or taxonomy, which is as essential to organising the display shelves in a supermarket as it is to scientific work. However, categorical thinking is important for all kinds of purposes.

Perhaps the most elementary task of this kind is to divide a set of things into those that have some property and those that do not. Suppose that we had a set of scenarios involving various actions, some of which are clearly fair, others of which are clearly not fair, and some of which we could argue either way. In attempting to categorise each of these scenarios as either FAIR or NOT FAIR we need criteria. Our criteria are our reasons for saying that one action is fair or that another is not, which are implicit in the judgements we make about the various cases. Unearthing and scrutinising our criteria can be a demanding task.

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We may use a variety of criteria, some of which may be more important than others, and which may conflict with one another in certain circumstances. This can lead to uncertainty and disagreement. We may need to determine whether the features we are relying on are ones that something must have in order to be categorised in a certain way, or ones that identify only some things of that kind; or whether one criterion takes precedence over another when they come into conflict, and so on. From a seemingly simple task of categorisation, therefore, we can find ourselves facing intellectually sophisticated and demanding issues. How far students pursue such matters will depend on their age and experience as well as their interests, but the possibilities of categorisation tasks are rich and rewarding. In sum, conceptual exploration gives us a clearer, more coherent view of just about any rich and complex subject matter. When it comes to the classroom, acquiring some basic tools for conceptual exploration—and learning how to use them effectively—paves the way for deeper understanding in all areas of the school curriculum. This provides strong grounds for saying that the art of conceptual inquiry ought to be built into the learning process throughout the school years.

Reasoning Reasoning is an extensive topic that forms the subject matter of both formal and informal logic, and yet it is hardly touched upon in school education. The fact that scant attention has been paid to reasoning in school education is sufficient to explain why most teachers were not trained to be aware of patterns of reasoning, and often have difficulty in determining when those patterns are valid or fallacious. This would not be such a disaster if poor reasoning skills did not get people into all sorts of difficulties in their lives. The fact is that muddle-headed and fallacious reasoning, and such things as jumping to conclusions, acting on unwarranted assumptions and failing to appreciate consequences, can be costly and dangerous. Even so, in a general book such as this, I cannot hope to do more than alert teachers to the importance of this topic and to provide a starting point for dealing with it. By introducing a few simple reasoning tools that are particularly useful in the context of inquiry, I hope to give teachers who are unfamiliar with the teaching of reasoning the confidence to begin to tackle it and an appreciation of its importance, so that they will want to extend their repertoire. Going back to the basic pattern of inquiry, it is obvious that in order to fully understand and evaluate what has been suggested, we need to see what else either must, or would likely, be the case if our suggestions were to be accepted. Notice that these implications are of two kinds. First, there are those propositions that simply follow from our suggestions, in the sense that if the suggestions are true then the implications must also be true. They are said to be Practical Beginnings

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logically implied. Secondly, however, there are those implications that follow with only some likelihood or degree of probability. Let us look at these in turn. From some propositions others simply follow. For example, from the claim that an action is fair only if it treats everyone equally, it follows that any action that fails to treat people equally must be unfair. This implication is important because we can now cast about for an example that treats people unequally but which seems to be fair. Someone might suggest, for instance, that when a younger brother or sister is required to go to bed earlier at night than their sibling, this is unequal treatment and yet it is fair (or fair enough!) given that they are younger. If this were accepted, it would provide what is called a counterexample to the original claim, which would have to be revised or given up. I am not saying, of course, that everyone is likely to agree that such treatment is indeed unequal (or that such a policy is fair). We would certainly need to look at what ‘equal treatment’ means here. It may well be argued that being different in age is itself a difference that makes a difference—‘equal treatment’ implying that like cases should be treated alike, rather than that different cases should be treated the same. Take a second example: From the claim that an action is fair when everyone’s interests are taken into account, does it follow that an action cannot be fair unless it takes everyone’s interests into account? To some people’s surprise, the answer is that it does not follow. It is a common fallacy to think that it does. For students to come to see that this is a fallacy in reasoning, and why that is so, would be progress indeed. Later in the book, we will be learning about how to teach students to avoid this kind of fallacy. In learning to reason, we come to take account of the way that words such as ‘if ’ operate, and so to be mindful of what statements containing ‘if’ clauses do and do not imply. Students who were used to thinking about their reasoning would also immediately notice the difference between ‘if ’ and ‘only if ’ as they occur in the suggestions in our example. To say that an action is fair only if it treats everyone equally, implies that if an action does not treat everyone equally then it is not fair. By contrast, the claim that an action is fair merely if it treats everyone equally does not have this implication. To think that it does is to fall for the fallacy in reasoning that we met a moment ago. Students who are practised in reasoning are alert to such implications and choose their words carefully. Most of the implications that students need to think about in examining their ideas do not follow from them in the manner of what is known as deductive logic. One thing is thought to imply another because they are regularly found to accompany each other, or because there is some thread of evidence linking them, or simply because this is what we have been brought up to believe. Reasoning here covers a great deal of territory with which students will become increasingly familiar as they learn to find their way in inquiry. This includes learning to probe around in a situation where there may be more than one live possibility, rather than assuming that the most salient possibility

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is the only one. It involves learning to take the full range of circumstances into account, rather than focusing on a single aspect or looking at something from only one point of view. It includes learning to trace out the likely consequences of different possibilities in order to properly compare and evaluate them. It involves learning to be critical rather than gullible in judging reasons and evidence that are proffered by sources that may not be reliable. It extends to students learning to look for evidence in their own experience and that of their classmates, and not just to accept blindly what is handed down on authority from the adult world.

By learning to do such things, students are learning to make more reasonable judgements. This means that they will be able generally to make good judgements about things of importance in their lives. They will be less susceptible to manipulation and better able to judge the evidence for themselves. In learning to explore reasons and evidence through collaborative inquiry, they will become both less dogmatic and more balanced in their judgements. They will be more willing and able to develop shared understandings and to actively contribute to decision-making in familial, social and workplace settings. Good judgement, in all its complexity, ought surely to be a central outcome of school education, and learning to reason well forms a large part of its development. So reasoning is something to which we should pay very close attention.

Evaluating and concluding The process of analysing our ideas and drawing out their implications is intimately connected with their evaluation. We often draw attention to an implication of some suggestion just because we see it as problematic. For example, we may reason as follows: ‘If the suggestion put forward were correct, then we would expect to find certain evidence. But there is no such evidence. So the suggestion is doubtful.’ This is a common form of reasoning used to give a negative evaluation of some suggestion. Again, someone may wish to explore a particular concept because they feel that a suggestion relating to it is misleading, ultimately incoherent, a mere truism, or not really distinct from some other Practical Beginnings

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suggestion that has already been rejected. In short, in an inquiry process, reasoning and conceptual exploration are primarily directed towards evaluation, with which they are very much entwined. While acknowledging this interrelatedness, it is important to keep these things separate for the purposes of teaching the tools of inquiry. Students need to be able to focus on their evaluative tools in order to learn to use them effectively. They need to learn to be careful in giving and evaluating reasons, to develop skill in employing evaluative criteria, to make effective use of examples and other evidence, to search for counterexamples, and generally to see what is involved in evaluating suggestions. Similar remarks apply to reaching conclusions, which is the last phase in the basic pattern of inquiry. Reasoning is a process directed towards a conclusion, and so it obviously incorporates something of this last phase within it. Once again, however, it is important to distinguish between them. Even though we may have reached a conclusion by faultless reasoning, this does not show that the claims with which we began are true, and if someone calls them into question we will need to go back and more carefully consider them. Even more strikingly, we may reason to some conclusion which, on reflection, turns out to be inconsistent with our own experience, so that we have cause to doubt our initial assumptions. Or we may reason to some conclusion, while they reason to a quite different conclusion on other grounds, and together we are left to weigh competing considerations by criteria, which themselves may turn out not to be entirely agreed upon. In sum, the conclusion of an inquiry is generally not the same thing as the conclusion of any particular piece of reasoning. It is more usually the outcome of evaluating many lines of thought and different points of view. It cannot be stressed too heavily that the conclusions we arrive at in classroom inquiry are very often not unanimous. Resolutions may be partial or vary between students because of unresolved disagreements and different understandings, albeit ones that are better informed, more reasonable and less opinionated than would otherwise be the case. This lack of consensus is hardly surprising, given that we are often dealing with perennial questions of meaning and value that do not have anything like single correct answers. Educators who are used to dealing with questions that have settled correct answers sometimes feel uncomfortable with such questions, and may even regard the lack of authoritative or agreed-upon answers as a mark of the educational futility of addressing them. Yet such questions are among the most important ones that we face in our lives and our answers to them can make a significant difference to the kind of society in which we are to live.

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Open intellectual questions about freedom, right action, fairness, personhood, beauty, truth, and the like, tend to remain open in the sense that every society and generation, and indeed every individual, ends up answering them for themselves. This is not to say that anything goes, or that it is all just a matter of opinion. Our answers can be more or less intelligent, well thought out, insightful, compassionate and life enhancing, or they can be more or less obtuse, stymieing or pernicious.

Nor do we avoid these questions by adopting ready-made responses that were the work of earlier generations. This is simply to unreflectively adhere to answers that were themselves reflections on the conditions of life in other times and places. We do not emulate those who produced them merely by resting on their answers, but rather by engaging, as they did, in a reflective and thoughtful life. Evaluation is fundamentally of two kinds, being either logical or evidential. By ‘logical’ evaluation I mean testing for such things as the coherence of our ideas and their consistency with one another. Evidential evaluation, by contrast, is the evaluation of suggestions and their implications in terms of background knowledge, predictive success, personal experience, and the like. We may speak here in terms of logical and evidential criteria. Coherence and consistency are logical criteria that any suggestion would need to satisfy. Any suggestion (idea, conjecture or hypothesis) that is found to be incoherent would need to be modified or abandoned. A conjecture might be perfectly coherent in itself, however, and yet inconsistent with some other conjecture that has been made. Therefore the two conjectures cannot both be true, so that at least one of them must be false. In this case, the logical demand for consistency is an important part of the evaluative process that can help to point the way forward. It may send us looking for evidence of one kind or another to sort out the matter. In fact, what we have just described is a commonplace in science, where the implications of competing hypotheses are subject to assessment through controlled experimental test and the analysis of data. Science makes use of reasoning to derive testable predictions from hypotheses or theories, and then uses experimental procedure and systematic observation and analysis to check whether they conform to the evidence. One of the distinctive features of classroom inquiry is that it uses student experience as evidence. Students draw on their experience to back up their Practical Beginnings

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claims. A simple case might involve students giving an example from their own experience. Examples are an elementary evidential tool that can be used in the evaluation of many suggestions. We need to be mindful, however, that experience is a complex construction that varies from one student to another—along with individual differences in intellectual and social maturity, competence, temperament, likes, dislikes, interests, family life, friendships, social circumstances, and all of the happenstance of their individual histories. Thus for students to test their ideas and understandings against each other’s experience, and to develop new thoughts and ideas by reflecting on their combined experience, is an important part of the learning process. By sharing their experiences and reflecting on them, students are learning to open themselves up to a wider range of experience, to become more sensitive to the experience of others, and to take a more objective view of their own experience. Experience also provides students with a valuable source of what I referred to earlier as ‘counterexamples’. A counterexample is an example that shows that a general claim is mistaken. If someone were to say, for example, that Indigenous people are all lazy folk who don’t try to do anything for themselves, students will know of Indigenous people who do not fit this stereotype. Even if this does not come through personal acquaintance, it may come from other forms of experience, such as television or the Internet. Many Australian students could cite the Olympic athlete Cathy Freeman, for instance. She supplies a counterexample to the generalisation that was made, and forces the student who made it to reconsider what they said. Counterexamples provide an important evaluative tool for the purposes of inquiry, and students can become quite adept at drawing counterexamples from their own experience. Students engaged in classroom inquiry often find that in order to evaluate their suggestions they need information that they do not have to hand. Such background knowledge provides an important source of evidential material that can be used for evaluation. This includes information that might be supplied by the teacher, knowledge derived from textbooks or library resources, through the Internet, and so on.

It is a matter of some significance that in the context of the classroom Community of Inquiry such facts are not delivered to students as so much information simply to be memorised. They are not unwanted pieces of information being crammed into the heads of students, but information that they seek. They become sought-after facts—facts that enter into their deliberations, facts that are needed to make informed judgements. They become, in short, materials with which to think. 26

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In this context, facts and information become meaningful because they are used in these ways. They are useful facts rather than so much unusable information. In seeking information, students must make judgements about the reliability of their sources. Are they trustworthy? Are some sources more authoritative than others? Do the sources provide unquestionable knowledge, or are they merely reliable guides? If the latter, just how likely is the information to be correct? Moreover, what standards of proof or evidence should we require in one context or another? And how should we decide these things? Such questions lead us into that branch of philosophy known as epistemology, or the theory of knowledge, and thus into a philosophical discussion in its own right. Since questions as to what constitutes knowledge and how can we come by it hover about all inquiry, students will need to engage in epistemological discussion from time to time. More generally, however, it is important for students to develop their critical faculties in evaluating sources of knowledge or evidence, and not to uncritically treat all sources as equal or to favour some sources over others for reasons that do not stack up. It is often a good idea to conclude an inquiry with a short reflection session on what has been accomplished. This is not an occasion for teachers to summarise the conclusions that have been reached. It would be better to ask the students what they have learnt from their inquiries, than to try to state the outcomes yourself. Since there is often room for a range of reasonable judgements, be prepared for a variety of responses. While many students are likely to agree on what has been discovered, others may express a somewhat different view, or even outright disagreement. In any case, it is important to note that such summing up addresses only one aspect of the inquiry. It is useful to ask the students questions that lead the class to reflect on both the process and the outcome of various aspects of their inquiry. Note that Thumbs provides a tool for such reflection (see pp. 61–63). Different kinds of inquiry differ in their methods of evaluation and the outcomes that they are expected to deliver. The experimental method evaluates scientific hypotheses by conducting critical trials or tests to see whether predicted observable consequences materialise, and then draws theoretical conclusions accordingly. Practical suggestions are evaluated in everyday life by criticism and formulation into plans that we implement, and often continue to monitor and evaluate further down the track. Conceptual suggestions, such as that an action is fair only if it treats everyone equally, are more likely to be evaluated against actual and possible cases that could provide counterexamples, the conclusion being the adoption or revision of some idea. Some cases, therefore, conclude with the concrete implementation of suggestions; other cases result in theoretical confirmation or repudiation; and yet others bring about a shift in our understanding, the practical bearing of which may be indirect and diffuse. Practical Beginnings

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While the last kind of result is more common in the classroom, it is important for students to put their results into action in one way or another. Most notably, in the educational context, this means the students seeking to apply what they have learnt to other school work: written, verbal, graphic, dramatic, and so on. That is to say, the work that they have done through collaborative inquiry should make a difference to the quality of their work overall. It is important to see what happens, therefore, when collaborative inquiry is integral to teaching and learning in a school. Since this is unfortunately all too rare, we still have a lot to learn in this regard. Although the results to date are somewhat limited, we can be much encouraged by the fact that where persistent immersion in collaborative inquiry has been implemented throughout a school, we see significant improvements in both academic outcomes and social attitudes and behaviour. And where this kind of work has been systematically carried out over several years, the results can be quite dramatic. (For example, look at the results from Buranda State School in Queensland, Australia, available from the school through www.burandass.qld.edu.au)

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TLFeBOOK

It is somewhat artificial to conceive of tools of inquiry as belonging to a particular phase. We may begin by raising questions, respond with suggestions, and go on to reason about them and explore them conceptually, until by a process of evaluation we arrive at a conclusion. However, we may need to explore the central concepts that lie behind a question before we go on to make suggestions, or find that exploring a concept only raises further questions. Just as obviously, questions may arise at any point in the inquiry, distinctions may need to be made at various times, and we may need to attend to assumptions built into questions or reason about examples. So while we may think of our tools as featuring most prominently in specific phases of inquiry, the same kind of work may need to be carried out in many places as the inquiry proceeds. Therefore it may be more useful to think of our tools of inquiry in terms of the functions that they perform. A division of the tools contained in this book is set out in the table on the next page according to their primary function. Some of the tools are used for working with questions, others are used for reasoning, for conceptual exploration or for evaluation, and so on. Even then, it is worth noting that some of the tools could almost equally well be classified under more than one heading. To arrange questions into Agendas, for example, is to group them under some theme or topic, which is itself a way of conceiving of them, and therefore is a conceptual activity. Similarly, Disagreement Diagrams provides a way of keeping track of the reasoning that occurs in a disagreement, so that it is equally a tracking tool; and to give and consider reasons is at once to justify or evaluate as well as to reason. The scheme provided is a useful one all the same. It recognises that in our classroom inquiries we basically engage in the following kinds of intellectual work: we raise questions, hypothesise or suggest, reason with each other, engage in conceptual exploration, and evaluate claims and suggestions. For each of these broad kinds of tasks there are tools to assist us, whether we are beginners or more advanced students. The Tools of Inquiry

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QUESTIONING TOOLS The Question Quadrant Fact, Value, Concept Agendas HYPOTHESISING TOOLS Suggestions

CONCEPTUAL TOOLS Distinctions Borderline Cases Target Thought Experiments Criteria

EVALUATIVE TOOLS Reasons Agreement/Disagreement Counterexamples Examples

REASONING TOOLS Generalisation Deductive Reasoning Reasoning Diagrams Assumptions Disagreement Diagrams

TRACKING TOOLS Discussion Maps

META-INQUIRY TOOLS Thumb

We also need to keep track of the proceedings of course, as well as to reflect on how well we are going and how we might make improvements. These are needs that Discussion Maps and Thumbs are designed to satisfy. In the remainder of the book you will find an introduction to each of the twenty thinking tools provided for use in the classroom. For ease of reference, they have been grouped according to whether they are Introductory, Intermediate or Advanced. That is to say, first you will find an Introductory Toolkit, and then you will be able to add to it successively. If you are working in early childhood education, do look at the Intermediate Tools, some of which you may be able to adapt to your purposes as things progress. If you are working with primary school students who are just beginning on this kind of work, you are likely to find that you progress to some of the Intermediate Tools quite quickly. If you are a secondary teacher, you should eventually be able to introduce the Advanced Tools, but you will need to ensure that the ground has been well prepared. John Dewey made the extraordinary claim that ‘all which the school can or need do for pupils, so far as their minds are concerned ... is to develop their ability to think’ (1966, p. 152). Since by ‘think’ he meant ‘inquire’, it was the development of inquiring minds to which he referred. Even if Dewey’s claim may be criticised for blithely ignoring a whole raft of outcomes that look to be legitimate ones for school education, he was certainly right to stress the central place of developing students’ ability to think. And although our schools are in many ways much closer to Dewey in this regard than those he addressed some ninety years ago, we still have far to go. I hope that this book may in some small way help us to continue to move in Dewey’s direction, and accordingly I wish you every success in your attempts to improve the quality of your students’ thinking.

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It is a common procedure in the Community of Inquiry to organise discussion around students’ questions that have been prompted by reading a text. While it is also normal procedure to accept questions of all kinds that students raise, the effectiveness of this procedure largely depends on the quality of students’ questions. The problem is that all too commonly students ask questions that are not very deep and do not readily lead to the kind of discussion that is desired. If only we could teach them to ask better questions—really meaty inquiry questions—we would be off to a far better start. In thinking about this issue some years ago I developed a simple scheme for classifying students’ questions. This scheme is what I call ‘The Question Quadrant’. Teachers to whom I have introduced the scheme have found it a very useful device for sorting out questions in their own mind. Moreover, when some variant of The Question Quadrant is introduced to students as an exercise, it almost immediately improves the quality of their questions and thereby provides a much more productive basis for discussion. The Question Quadrant that I have been using for categorising questions with teachers is explained below, followed by suggestions of how it can be introduced into the classroom.

Four types of questions Pooh and Piglet can be seen trudging along a snowy track. The day is clear but the sun is low and it casts a yellowish-orange glow over the scene. Piglet is wrapped in woollens and a scarf, while Pooh has nothing on but an old short-sleeved top that is several sizes too small for him. Piglet says to Pooh touchingly, ‘We’ll be friends forever, won’t we Pooh?’ ‘Even longer,’ Pooh replies.

Here are some questions about this little scene: 1 2 3 4 5 6 7 8

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Twenty Thinking Tools

Is the season summer or winter? Who is dressed more warmly, Pooh or Piglet? Who wrote the stories about Pooh and Piglet? What are the names of the other characters in those stories? Where are Pooh and Piglet going? Why isn’t Pooh dressed more warmly? Is it important to have lifelong friendships? Can something last even longer than forever?

The questions above are of various kinds: some are ‘open’ questions and some are ‘closed’. An open question does not have a settled answer, whereas a closed question does. If there are facts to hand that settle the answer to a question beyond all reasonable doubt, say, or if the answer is a matter of general knowledge, then the question is normally regarded as closed. This applies to the first four questions on our list, two of which demand nothing more than what is generally thought of as reading comprehension, while the other two refer to matters of general knowledge. When I say that these questions are closed, I do not mean that they need to be settled in the minds of every person who reads the passage or has it read to them. The first question, for instance, might not be settled in a reader’s mind for all sorts of reasons. The reader might not know the relevant facts of climate, for instance, or be uncertain about where Pooh and Piglet live. Even such a straightforward question is settled only in the context of relevant background knowledge and assumptions. Nonetheless, the question is almost certain to be regarded as closed because on standard background assumptions the scene is set in winter. Similarly, it is easy to imagine someone tossing up as to whether the answer to the third question on our list is A.A. Milne or, say, Kenneth Grahame (author of Wind in the Willows), so that the question is not settled in their mind. Once again, however, the question can be regarded as closed because there is no serious dispute that A.A. Milne wrote the stories about Pooh and Piglet. There is a single, established correct answer in this case. Stories leave many things indeterminate. It need never be explained to us why Pooh is out walking on a winter’s day dressed only in a short-sleeved top. We might be left to guess. Perhaps it is because he already has a warm furry coat. Maybe the top is the only thing that he has that isn’t too dirty to wear. It could be that, being a Bear of Very Little Brain, it simply didn’t occur to him to dress for the weather. Such suggestions may be more or less plausible or fitting, but neither the text nor the background knowledge and assumptions that we bring to it need rule them out. They are open possibilities. Questions 5 and 6 on our list ask us to imagine such possibilities. Although they provide very elementary examples of open imaginative questions, it is easy to see that they can help to fulfil a very important educational function. Imaginative exploration of the possibilities within a story is a means to its interpretation. We engage in it whenever we make guesses about what a character will do, where their behaviour is likely to lead, what possibilities are open to them, or how a plot will turn. We also do exactly the same thing in daily life when we attempt to discern people’s motivations, try to predict how they would behave in a given set of circumstances, or think about our own life’s possibilities. Obviously we can do these things either more or less intelligently and with varying degrees of insight and understanding. In the long run, the difference between a welldeveloped capacity of this kind and a poorly developed one will have such farreaching consequences for our lives that we should pay considerable attention to its development. The nurturing of such a capacity is one of the benefits that the study of literature can confer, and this alone provides a quite compelling reason to give students ample opportunity to study it. Introductory Toolkit—The Question Quadrant

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The final two questions on our list are open questions of a rather different sort. They are ‘larger’, more general questions about what we should value in life and our conceptions of what is possible. And while there is little point in arguing in favour of one imaginative possibility over another (such as Pooh’s warm furry coat rather than his forgetfulness being responsible for his state of attire), the same is not true of these last two questions. Here a proper exploration will require us to critically examine what we say, to discuss our disagreements, and test out alternative points of view. We will need to do such things as: clarify what we are saying, give and evaluate reasons, examine assumptions, draw relevant inferences, make necessary distinctions and connections, examine concepts, and appeal to appropriate criteria. In short, in order to address these final two questions we will need to engage in intellectual inquiry. Hence we may call them ‘inquiry questions’. Let me summarise the discussion so far by means of The Question Quadrant. I do not claim that it exhausts all possible questions that students might raise, or that its compartments are completely watertight. Nevertheless, I have found it good enough for practical purposes. The particular version shown below assumes a set of questions that are stimulated by a text, and somewhat different labels would obviously be needed if some other form of stimulus were used to generate the questions. This is a complication that can be set aside for the present purpose.

TEXTUAL QUESTIONS

Is the season summer or winter? Who is dressed more warmly, Pooh or Piglet? READING COMPREHENSION

Where are Pooh and Piglet going? Why isn’t Pooh dressed more warmly? LITERARY SPECULATION

CLOSED QUESTIONS

OPEN QUESTIONS

FACTUAL KNOWLEDGE Who wrote the stories about Pooh and Piglet? What are the names of the other characters in those stories?

INQUIRY Is it important to have lifelong friendships? Can something last even longer than forever?

INTELLECTUAL QUESTIONS

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It is hardly surprising that if we want to stimulate inquiry in the classroom, then open intellectual questions would serve us best. Once students have some idea of these requirements, they are unlikely to ask very many closed questions. If they do ask questions of basic comprehension, they will need to be addressed. In all probability they can be answered by other students in the class, before moving on. Again, questions of background factual knowledge might arise, but students will quickly come to see that they are more properly addressed by asking the teacher, by a trip to the library or by an appropriate web search. The persistent problem is that many children continue to ask questions of the kind that I refer to here as ‘literary speculation’, which can occupy a great deal of discussion time with very little pay-off as far as intellectual inquiry is concerned. The question is how we can get our students to raise a greater preponderance of questions that naturally belong to the lower right quadrant. Experience gives us reason to believe that an effective way of doing so is simply to introduce them to the distinctions between questions that we find in The Question Quadrant.

Introducing students to The Question Quadrant I don’t propose that you begin paying attention to students’ questions by introducing them to The Question Quadrant—just as in the first year of school when children are only beginning to learn to ask questions, you are unlikely to begin the process of inquiry with their questions. But I have included The Question Quadrant among the Introductory Tools because once you have ventured into using students’ questions as a basis for inquiry, and had mixed results, it is probably time to turn to this tool. In order to introduce The Question Quadrant to students you will first of all need a version that they can readily understand, and this will vary somewhat depending on the age of the students in your class. Rather than ‘closed’, you might want to have ‘There is one right answer’; and rather than ‘open’, you might have ‘There may be many possibilities’. One teacher told me that she uses ‘Look and see questions’ in place of ‘Reading comprehension’, ‘Ask an expert questions’ in place of ‘Factual knowledge’, ‘Use your imagination questions’ in place of ‘Literary speculation’ and ‘Thinking questions’ in place of ‘Inquiry’. When working with The Question Quadrant in the classroom, I like to lay it out on the floor with such labels on pieces of card. As an introduction to The Question Quadrant, you might first discuss the various kinds of questions with your students, using a made-up example or two that they can easily relate to for each of the quadrants. Then give your students some further made-up questions to sort out for themselves. You might do this as a whole class, but when the students are sufficiently confident you could divide them into small groups, with each group being given a minute or two to sort out a number of questions for themselves. (If you give all the groups the same questions they will more easily be able to discuss any disagreements between the groups when they report back.) Introductory Toolkit—The Question Quadrant

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Once the students are familiar with the device, you can get them to think about their own questions in terms of The Question Quadrant. As an example, below is a set of questions and labels that I used with an upper-primary school class who had read a story by Philip Guin called ‘The Knife’ from my book Thinking Stories 1 (1993a, pp. 42–48). Most of the questions came from the students themselves, but I added a couple of others for the purpose of the exercise.

THE ANSWER IS IN THE BOOK Did Carl plan to steal the knife from Beecham’s hardware store? Did Mr Beecham turn Carl in to the police? ONE RIGHT ANSWER

Does the law allow children who steal to be sent to jail? Are hardware stores allowed to sell knives to children? ASK SOMEONE WHO KNOWS THE ANSWER

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JUST USE YOUR IMAGINATION If Carl had taken the knife home what would his parents have done? What would Mr Beecham have done if he saw Carl steal the knife? MANY DIFFERENT POSSIBILITIES

Did Mr Beecham do the right thing in his proposal to Carl, or not? How can stealing ever be all right? YOU REALLY HAVE TO THINK ABOUT IT

The creative phase of inquiry relies on generating suggestions for possible answers to questions, ways to solve problems or to resolve issues. By suggestions I mean the various species of thought that we call proposals, speculations, conjectures, hypotheses, explanations and ideas. These are our first attempts to apply our broader experience, background knowledge or more general understandings to the matter in hand. As such, suggestions have a vital role to play in the inquiry process. If the answer that we sought were clear to see, then there would be no need for inquiry. We would have our answer already. But where this is not the case, we need to move beyond the given by thinking of possible ways in which the situation presenting itself may be understood, unravelled, resolved or explained. This is the role that suggestions perform. Suggestions are intermediaries between questions and conclusions or resolutions. To inquire is to question, and to question is to seek answers. As stabs at answers, suggestions are still exploratory—they are not yet conclusions or resolutions, but only provisional or working ideas. They are like keys tentatively inserted into locks in the hope that they might work. In the context of inquiry, different kinds of suggestions correspond to different kinds of questions, of which the following are the most common: • Explanations: Suggestions as to possible explanations are answers to questions about how we should understand matters of fact or why they are so. They are attempts to interpret something or to account for it. Explanatory suggestions include conjectures or hypotheses put forward to account for the facts of a case or as starting points for investigations that aim to either confirm or disprove such possibilities, as well as assumptions made in support of an interpretation of events and generalisations from which we may draw explanatory conclusions. • Proposals: Proposals are suggestions as to possible courses of action in response to practical questions about what we are to do. Proposals loom large in everyday affairs, but are often less carefully scrutinised than prudence would advise. By engaging students in collaborative inquiry we can help them to develop the habit of considering their options and being somewhat more circumspect when conditions require. • Value judgements: Value judgements are suggestions about right conduct or preference in answer to evaluative questions calling for a consideration of appropriate norms and standards. Both questions and responses are most often framed in terms of ‘ought’, ‘should’, ‘right’, ‘wrong’ and other such Introductory Toolkit—Suggestions

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indicators. To say that value judgements may act as suggestions is to indicate that, in the context of inquiry, values are something to be inquired into and not just dogmatically asserted. This is especially so when it comes to areas of disagreement about values. • Meanings: Attempts to define a term or to analyse the meaning of a concept are suggestions made in response to conceptual questions. Such suggestions are a starting point for conceptual exploration. As with students’ questions, the quality of their suggestions is a cardinal determinant of the outcomes that they achieve. So it is a discouraging thought that, while teachers may often be delighted by the fertility of their students’ suggestions, the production of suggestions seems to be one of those things that can be encouraged but not taught. The fact is, however, that, once their interest is engaged, students will spontaneously come up with suggestions. The teacher’s task is to provide the means by which students can learn to improve the quality of their suggestions. Fortunately, this is something that we can do. Implausible suggestions, unworkable proposals, wild conjectures and naïve hypotheses can be discovered to be such when they are carefully considered by the class, because they involve such things as false or unwarranted assumptions, erroneous implications, failure to fit with the evidence, or likely but undesirable consequences. By learning to subject their suggestions to systematic scrutiny your students will gradually internalise habits of thought that help them to discard more obviously unworkable ideas with increasing ease. Of course, nothing can substitute for a rich store of knowledge and understanding, and in many areas students’ suggestions will inevitably betray their relative lack of experience. By critically examining their suggestions in the light of what knowledge and experience they do have, however, your students will definitely improve the quality of their suggestions over time. The other major factor in using suggestions in an inquiry is the importance of alternative possibilities. Open intellectual and practical questions generally leave room for alternative possible answers for which something can be said. Even when, at the end of the day, there must be a unique right answer or truth of the matter, we are unlikely to discover it without considering at least some of the more likely possibilities. In many practical matters and in questions of value, however, there is no such thing as the right answer or the solution to our problems, but rather there are alternative possible courses of action and ways of living. Almost all actual problems and issues that we face in our lives are of this nature, and wisdom lies in seeing the range of possibilities and then choosing well. While we should make it a rule to actively explore the problem domain, at any given point in the inquiry it remains a matter for judgement whether there are further significant alternative suggestions that we ought to bring forward. Sometimes we discover that we need to look for another possibility after an initially plausible suggestion runs into serious difficulty. At other times we discover that the difficulties with one or more suggestions themselves suggest a new possibility that does not suffer from those defects.

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Whatever happens, all suggestions put forward by students in the spirit of inquiry deserve to be taken seriously, even if a brief airing is often all that is needed for them to see which ones are worth taking forward. Obviously, you may be aware of important possibilities or other points of view that have not occurred to your students. And as teachers we sometimes have in mind particular possibilities that we would like our students to suggest, but which do not seem to be forthcoming. You need to exercise caution in such cases. If a suggestion is important and does not come up, you might eventually and tentatively introduce it—‘Suppose that someone were to suggest the following ...’, ‘What do you think of that?’ In collaborative inquiry-based learning, suggestions are tools that students use to make progress with an issue or headway with a problem. In pointing out a direction that an inquiry might take, offering a suggestion is like indicating that we should try a certain path when hiking across unfamiliar territory. Just as with hiking, one cannot sensibly offer such a suggestion without taking in the general lie of the land, having a sense of how that path will help us to get to our destination, and of how it compares to other alternatives that present themselves.

Introductory Toolkit—Suggestions

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One of the most elementary tools of inquiry is the giving of reasons for claims made. So in inquiry-based learning, from the very beginning, we need to encourage students to give reasons. We might even begin the very first inquiry session in the early years by teaching students to use the word ‘because’ to give a reason. Of course, many students will intuitively use the word to give a reason when asked to do so, but we want everyone in the class to have the word in their toolkits so that they can consciously reach for it in order to give reasons. We need to make reason-giving a move that they consciously and deliberately make, and ask others to make, when that seems appropriate. In order to establish reason-giving with young children, I might begin with the following activity. • I will tell the students that I am going to ask them about their all-time favourite movie, or perhaps their favourite television show, or whether they think that dogs or cats make better pets—anything, in fact, for which they can be expected to have preferences or opinions, and for which they might be able to supply a reason. I will not tell them about the word ‘reason’ or anything like that, but simply say that I want them to be thinking about which one is their favourite and why that is their favourite. • I will also tell them to listen for a magic word that people might use when they say why something is their favourite. • Then I will go around the class and ask various people what is their favourite, and then why that is their favourite. • Often I will repeat what they say and maybe emphasise the word ‘because’ when it gets used. When it begins to become apparent to the students that this is the word, I will stop to ask who can guess the magic word. I will have this word prepared on a sheet of card and ‘magically’ lay it on the floor when students name it as the word for which they have been listening. • I will then ask the students what people went on to do when they used the word ‘because’. After a brief discussion we will see that they went on ‘to say why’ or to give a reason. I will also have the word ‘reason’ on a sheet of card and lay it on the floor. • I will conclude by saying that when we come to discuss the story or whatever it is that we are going to talk about today, I want them to keep the word ‘because’ handy because they might need it to give a reason for what they say.

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• At the end of the class I might ask the students what we started off with today, and have them tell me about ‘because’ being a reason-giving word. Then I will end by telling them that I want them to imagine that they have a toolbox on the floor beside them and to pretend to open it up and look inside. ‘Look,’ I will say, ‘it is empty! There is nothing inside.’ I will then ask them to pick up the word ‘because’ and put it in their toolbox. So that when in future they need to give a reason for something they can reach into their box and grab the magic word. • I will also tell them that we will be placing more tools in our box as we go along, so that by the end of the term we will all have a kit of tools that we can use in order to talk and think about things.

because

Do bunyips exist? In the Community of Inquiry, giving and evaluating reasons is a collaborative affair. Often students can be broken into small groups to explore reasons for what they want to say, and then they can present their reasons to the class as a whole for further deliberation. Depending on the age of the students, each small group might be given a sheet of butcher’s paper and asked to write their reasons down on the paper for presentation to the class. The following illustration comes from a middle primary class who were discussing the question ‘Do bunyips exist?’—a question raised in response to reading the children’s picture book The Bunyip of Berkeley’s Creek by the Australian author Jenny Wagner (Puffin Books, 1990). For the uninitiated, bunyips are mythological Australian creatures said to be found in billabongs or lagoons in the Australian bush. The illustration represents one small group’s reasons for saying that bunyips do not exist, together with the beginnings of the class’s evaluation of their reasons.

Introductory Toolkit—Reasons

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How do we know when a report is reliable?

reliable

no photographs of bunyips no reports of bunyips bunyip pictures are different in different books ‘bunyip’ sounds like a vegetable We all look different but we exist.

???

One of the students in the class objected to the claim that there were no reports of bunyips, saying that his cousin had told him that she had seen a bunyip when she was camping with her family over the summer. Several students were not prepared to accept this report at face value, some saying that it was a tall tale and others that the cousin may have caught a glimpse of something else and mistaken it for a bunyip. In light of this, the class decided that they needed to distinguish between reliable and unreliable reports of bunyips and the group whose reason it was agreed to modify their claim by saying that there were no reliable reports of bunyips. The student who had related the report of the bunyip was not quite willing to give up on the issue, however, and insisted that, while his cousin could have been mistaken, his classmates were not there and so they could not say that she had made a mistake. This led to a student asking how we can tell whether a report is reliable, and the quick-witted teacher thanked the student for her question and added it to the board. It was something she said that the class might like to discuss later. Another student ventured that just because bunyip pictures look different in different books does not mean that there are no bunyips. ‘We all look different,’ he said, ‘but we exist.’ While some students seemed to think that this was a good point, others suggested that the reason why bunyips look different in different books is because they are made-up creatures, and the fact that we all look different from one another is no reason to say that the original reason is not a good one. Throughout all of this, I was sitting quietly at the back of the class waiting to see what would be said about the last reason on the list—that ‘bunyip’ sounds like a vegetable, presumably by analogy with ‘turnip’ or ‘parsnip’. Unfortunately we didn’t get to that one.

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I make no particular claim for the quality of this real-life example, and introduce it only to recommend the general procedure that the teacher used. The use of small groups is an excellent vehicle for an initial consideration of reasons. Having to communicate to one another what they think, and to collaborate in coming to a written formulation of their reasons, fully involves the students in the consideration of reasons. When the small groups then present their reasons to the class as a whole, each group gets to test out their reasons with their classmates and to think about the broader spectrum of reasons that other groups have raised. The mix of small group activity and whole class discussion is one that I generally recommend, and the activity we have been viewing on reason-giving and the follow-up evaluation gives us a clear example of how to make that mix work. I have treated reason-giving and evaluation as an introductory topic in order to suggest some simple ways of getting started in this area. Later we will move from simple reason-giving to more complex reasoning, where students attempt to provide evidence for the truth or falsity of a claim by relating it logically to other claims. Before we come to these more sophisticated tools, however, it is important that students become used to the elementary business of giving reasons where it is appropriate and also to be expecting this of one another. In developing inquiring minds, nothing is more powerful than hearing others say things that fascinate or surprise you and to want to know why they say what they do. And then, sometimes, to begin to wonder why you think what you do, and whether what you think can be justified by good reasons.

Introductory Toolkit—Reasons

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It may seem odd to suggest that agreement and disagreement can be thought of as a toggle-headed tool, but the reasoned expression of agreement and disagreement is central to the dynamics of collaborative inquiry, and their vigorous combination gives the process much of its critical edge. Agreement and disagreement are the basic alternative responses to a suggestion. When students express their agreement with someone’s suggestion, they are normally expected to supply reasons that add to its plausibility; just as when they express their disagreement, they are expected to give reasons for their reservations. So discussing a suggestion involves a critical evaluation on the basis of reasons both for and against it. The interplay of agreement and disagreement gives direction to the proceedings. For example, a succession of students may build a case for a suggestion, but then students who do not agree begin to make observations that pull us in the opposite direction. Students who come to a decision in a small group then discover that another group has reached a different conclusion; and now they find themselves together at a fork in the road, with each group having to respond to the other’s reasons for heading down a different path. In collaborative inquiry, agreement and disagreement represent patterns of convergence and divergence in thought that enable us to tack back and forth into the wind, and give our inquiry its forward movement.

Debate versus inquiry It is important to note that the dynamics of an inquiry differs from that of a debate. In a debate, opposing teams present arguments either for or against a proposition. One must play one’s part in arguing the case that one’s team has been assigned, regardless of one’s own opinions and the suggestions that one might otherwise make. The object is to win the debate, not to offer helpful suggestions no matter where they may lead. In debate, one expresses agreement with one’s team members and disagreement with the opposition. It would be an act of treachery to do the reverse and a sign of weakness to not know where one stood. Debating points often do not depend on soundness of argument, but on rhetorical devices designed to cut the ground from under the opposition and to sway the audience to one’s side. These are the tactics of lawyers and politicians and which—for better or worse—are deeply entrenched in the way that they conduct their affairs.

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By contrast, in inquiry we are free to express our agreement or disagreement as we see fit, provided that what we say is constructive. We do not take sides on an issue except when we feel we should, we may speak both for and against a suggestion as we continue to deliberate, and may change our minds if reason dictates. Rather than striving to see our opinions prevail, we are reflecting on them in the hope that we may receive instruction. It would be misleading to suggest that in an inquiry people should never express opinions or give reasons other than those they hold. Someone may disagree with a proposition in order to play devil’s advocate, for example, and insofar as this helps to put that proposition to the test it can be an entirely legitimate role to play. The danger of this and similar stances in the classroom is, of course, that they can become a kind of game. Students who delight in contradiction or who constantly play the sceptic, may bring a sense of fun to the proceedings, but their input needs to be tempered by recognition that inquiry is an attempt to make headway with the matters under discussion. There will also be occasions when a suggestion that is either generally agreed to or else dismissed in the classroom may be regarded quite differently by some members of the broader community. Students may need to be reminded of this, so that a wider range of considerations is canvassed. Often the teacher can draw attention to such considerations simply by asking the students whether they can think of someone who might express a different opinion or look at the matter in a very different way. If all else fails, the teacher may proceed to identify the view in question and ask the students to consider it. There can be many shades of agreement and disagreement. Students may say that they ‘kind of ’ agree or disagree with what someone said, or that they both ‘agree and disagree’. In such cases students need to tell us the respects in which they concur or differ. Students expressing partial agreement may be sympathetic to the proposition being put, but wish to improve on it in some respect; or they may wholeheartedly agree with the proposition, but for significantly different reasons than those previously given. Likewise, students who qualify their disagreement may want to express only some shade of difference in the proposition or emphasise the importance of a different reason. Students who both ‘agree and disagree’ with what someone says are usually making much the same kinds of moves. They may wish to agree with the proposition being put, but to disagree with the reason given in support; or they may agree with a statement in some respects but not in others, thereby wanting to improve on it. In whatever way students qualify their expressions of agreement and disagreement, the development of these more nuanced judgements is to be encouraged. It represents a move away from an ‘I’m right/you’re wrong’ mentality to one that recognises that we can often arrive at better understandings and more reasonable decisions by looking for points of agreement and disagreement rather than by making blanket judgements. Introductory Toolkit—Agreement/Disagreement

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As your students learn to explore their disagreements thoughtfully they will be acquiring the habit of dealing with their differences without recourse to the destructive tendencies that otherwise so readily prevail. Verbal abuse, physical violence, ostracism and gang rivalry all involve an element of antagonism built on differences of one kind or another. It is therefore a social imperative that we learn to deal with our differences on the basis of being reasonable with one another, and learning to explore disagreements through the give and take of reasons is a means of doing just that.

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The giving of examples is such a familiar way of supporting what we say, that little comment may seem to be required. Even so, it is well worth giving some thought to the various uses of examples in inquiry, as well as to distinguishing the use of examples from the merely anecdotal remarks that students may make. An example is sometimes an illustration. As such it is an attempt to explain a general claim or to make a concept clear. Having introduced the term ‘iconic architecture’, for instance, I might offer the Sydney Opera House and the Eiffel Tower by way of illustration. Both structures are national icons, I might say, and are examples of the kind of architecture to which I refer—they help to make the meaning of my expression clear. When the terms being employed in classroom discussion are none too clear, it can be helpful to ask students what they mean by requesting them to give an example. Again, if I were introducing the claim that monumental architecture is an expression of a culture’s most deeply held beliefs and values, I might illustrate it by reference to medieval cathedrals or, perhaps, to New York’s former World Trade Center. In this case I am using examples that illustrate a general statement in order to explain its meaning. Once again, it can be very helpful if students give examples to illustrate general claims that they make. It is also worthwhile for the teacher to ask other members of the class if they can add further illustrative examples. This enlarges the meaning of what has been said and helps to construct a common understanding. My examples of monumental architecture actually do double duty. They are meant not only to illustrate my claim but also to provide evidence that what I say is true. They both exemplify and support my assertion. Evidential support is a common reason for introducing examples. If someone says that global warming is a reality, they might cite the disintegration of Antarctic ice shelves in evidence. In that case, the breakup of the ice shelves is offered as an example to prove what they say. Care must be exercised when an example is used in evidence, as it might not be typical or representative. That something is sometimes so does not mean that it is always or even normally the case, and we need to take care that we are not led astray by examples that we already have in mind just because they appear to confirm what we are saying. When students supply examples in support of a claim, it is therefore often useful to ask them whether they can think of other examples that might provide contrary evidence. By encouraging students to search for evidence against a claim as well as to provide evidence for Introductory Toolkit—Examples

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it, you are teaching them to evaluate claims critically. When appropriate, we need to remind our students that the critical evaluation of their claims is a key requirement of inquiry. Sometimes a single contrary example can be sufficient to defeat a claim. Only one clear contrary case is required for us to reject a categorical assertion that something is always the case, or that it is never the case. Such knockdown examples are called counterexamples and are of sufficient importance to be regarded as a thinking tool all on their own. Counterexamples will be introduced later. More general or abstract talk about a subject matter needs to be brought into contact with relevant firsthand experience wherever possible in the classroom. This will help your students to make sense out of the things that they are discussing, and encourage them to think about their own lives in the context of their learning. Examples drawn from experience are one way of making such meaningful connections and should be encouraged. Given that your students are engaged in inquiry, however, it is important that the sharing of experience is a means of pursuing the inquiry and does not relapse into some other form of discourse that deflects us from our objectives. Insofar as drawing examples from experience is concerned, it may be necessary to ask a student whether they are giving an illustration or providing evidence, as the case might be, or merely engaged in the anecdotal retelling of some experience that the discussion brought to mind. Sometimes such anecdotal material can form the basis of an example, of course, but it is very important that students understand this and learn to treat it accordingly. It is the difference between students who are reminded of something that happened to them and then simply proceed to tell the class about it, and students who say that they can provide an example from their own experience and then proceed to tell the class.

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Drawing a distinction is one of the most common things that we need to do in inquiry. We can all make distinctions, of course, but it is one thing to be able to do so implicitly, and quite another thing to understand how distinctions work and to learn to use them effectively. While there are many ways in which we can learn to draw distinctions, I have found that giving students exercises similar to the examples on page 50 is an excellent way of helping them to learn to make the right kinds of moves in their thinking. Once again, it is important to note that exercises of this kind are to be used as a supplement to, and not a substitute for, drawing appropriate and useful distinctions in discussion. We make many distinctions effortlessly and almost without notice. But sometimes we fail to distinguish between things that are different in ways that matter. This can be because the relevant differences are subtle or complex, or because the things with which we are concerned are normally lumped together, or simply because we are inattentive and do not bother to think with sufficient care. By paying attention to the kinds of processes involved in distinctionmaking, we can help our students to handle more difficult cases, to think critically about the distinctions that other people draw, and to be more attentive to the need to make distinctions with care. We usually draw distinctions between things that are the same or similar in many respects, but that we need to keep apart for certain purposes. We would be puzzled by the suggestion that we need to draw a distinction between things that appear to be quite unrelated. ‘Let’s draw a distinction between a fish and a bicycle.’ This may all be very well as an attempt at humour, or just fine as an exercise in creative imagination, but it is definitely deviant as distinctionmaking. Given that a distinction is normally a way of dividing things that are similar, we can draw a distinction by stating it as a difference within a shared domain. To say that red and green are different colours is to acknowledge a shared domain—that is, colour—within which we wish to mark a distinction, just as we might say that circles and squares are different in shape. Of course, it is not always so easy to say just what the things we wish to distinguish have in common. To take an example from below, what is it that entrances and exits have in common? A satisfactory answer may not be immediately obvious and we will have to think about it. To proceed to make a distinction is to identify the property or properties within the specified domain in which the things in question differ. To take another simple example from below, we might say that a pebble and boulder are Introductory Toolkit—Distinctions

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both pieces of rock, but that they differ in size—size being the relevant property. A pebble is a small piece of rock, while a boulder is a much larger one. That is a simple statement of the distinction. Of course, once again, it can be far more difficult to specify the property in question. Suppose that someone asked you to distinguish between a fort and a prison. It is not entirely obvious what property to alight upon. Here is one possibility. Prisons and forts are both enclosures designed to make it difficult to breach their boundaries, being distinguished by the fact that a fort is an enclosure designed to prevent those on the outside from getting in, while a prison is an enclosure designed to keep those on the inside from getting out. Variations on this theme are also possible. For example, we could say that a fort protects those on the inside from those on the outside, while a prison protects those on the outside from those on the inside. The following exercise is designed for middle to upper primary students to learn to pay attention to both the domain within which a distinction is made and the property that distinguishes the things in question. In distinguishing between a knife and a fork, for instance, it is not sufficient to say that a knife has a blade but a fork has prongs. While that is true, a more complete answer is that they are eating utensils that differ in these respects. Of course, we might also make the distinction in other ways, such as the differences in the purposes for which they are used. It is important to remember that there isn’t just one way to make a distinction. You might work on a couple of examples with the whole class and then have students work on examples in pairs. It is useful to ask different pairs to work on the same examples so that they will be able to examine differences in their results.

Drawing distinctions: The same but different Can you state some respect in which the following pairs are the same and some other respect in which they are different? For example, a brother and his sister might be said to have the same parents, but to be of the opposite sex.

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1 a mother and father

8 an entrance and an exit

2 slippers and shoes

9 a rifle and a cannon

3 a lake and an ocean

10 a fort and a prison

4 pushing and pulling

11 a door and a gate

5 a hill and a mountain

12 a nail and a screw

6 a pebble and a boulder

13 a planet and a moon

7 a tunnel and a cave

14 a genuine reason and an excuse

Twenty Thinking Tools

One of the most useful tools for conceptual exploration is the problematic or borderline case. If we wish to think about what makes something fair, for example, it can be very helpful to consider cases that are neither obviously fair nor clearly unfair. • Suppose that Maria stole something from you, and so you stole something from her. Was that fair? • Robert works very hard at school, although he nearly always receives poor marks. Is that fair? If you were to present these cases to a group of ten-year-olds and to ask them whether they were fair or not fair, you would almost certainly provoke mixed reactions. Disagreement or uncertainty among the members of your class would be an indication that these cases do not sit altogether comfortably within their collective understanding of fairness. Such cases will therefore encourage students to consider reasons for and against counting them as fair, and that will lead to a deeper understanding of what it means for something to be fair. We can even use a borderline case as a provocative stimulus, discussion of which will lead to open intellectual questions. Consider an example: The photograph below shows an elephant from northern Thailand that has been taught to paint by holding a brush in its trunk. Such elephant paintings do not appear to represent anything, but they often contain pleasing, colourful patterns, which look somewhat like the works that some artists make. At the elephant camp where I took this picture, the paintings were on sale under a sign that read ‘Elephant Art’. In fact, there is a worldwide market for ‘elephant art’ and there have been numerous exhibitions of their work.

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Do you think that the paintings produced by elephants might properly be regarded as works of art? They present us with a problematic or borderline case from which many questions arise that make us think about what we should say. For example: • What does the elephant understand about what he is doing? Is the elephant’s painting just a mindless, mechanical scribble? And could a mindless scribble be a work of art? • Suppose that the elephant has been trained merely to move the brush back and forth. Could that be enough for the elephant to be an artist or the work to be art? • Does a work of art have to be produced by an artist? • Do you have to be a person in order to produce art? Were the class of ten-year-olds to discuss the question of whether an elephant’s paintings could be works of art, they would very soon be likely to find themselves raising such questions and thus beginning to address the more general question: What is art? The students’ reasons for saying that elephant paintings either are or are not art will begin to reveal possible criteria for something to count as art. The students are likely to be uncertain about these criteria and at least some of the criteria that they suggest will certainly be contentious, and require careful consideration of different points of view. But then the question ‘What is art?’ does not have a settled right answer. It is one of those open intellectual questions to which many different answers can be given, albeit that some answers reveal a deeper understanding than others. By having to really think about the concept of art in this way, your students will be trying to come to a more considered view of what makes something art and thereby deepening their understanding of it. Such a discussion could be extended through a small group activity with what I call ‘Floor Sets’. Suppose that you have prepared three cards which read ‘ART’, ‘NOT ART’ and ‘?’. These might be laid out on the floor inside your discussion circle, with ‘ART’ at one end, ‘NOT ART’ at the other, and the question mark in the middle. Each small group of three or four students could then be given a card with a more-or-less borderline case on it, such as the following:

a bower bird’s nest

a photograph

a spider’s web

graffiti sprayed on a wall

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an idea

rocks shaped by the weather an architect’s drawing

a colourful hat

a drawing made by a computer

Twenty Thinking Tools

Copyright © Philip Cam 2006

a child’s scribble

The groups may be given a few minutes to discuss whether the thing in question should be placed with ‘ART’ or with ‘NOT ART’. If they are uncertain or cannot agree among themselves, then it will need to be placed with the question mark. After they have had time to deliberate, you can ask one group to place their card where they think it belongs and to give their reasons for placing it there. Then you can open the case up for discussion. You can then move from group to group, as time permits, gathering reasons for calling something art, or denying that it is art, as you go. By the end you should have unearthed and discussed a large range of criteria for calling something art. You can even label them ‘criteria’ if you like, because as the students advance we will be introducing them more formally to thinking about criteria. With a little thought you can find borderline cases for the application of any large and contestable concept. Whether it is beauty, goodness, fairness, friendship, existence, evil, intelligence, personhood, bullying, freedom, right, bravery, racism, knowledge, or what have you—all these concepts can be explored in this way. I will leave you with a set of scenarios for the concept with which I began: justice.

JUST 1 2 3 4 5 6 7

UNJUST

?

Maria stole something from you, and so you steal something from her. Chi found some money in the playground and handed it to the teacher. As no one came to collect the money, the teacher let Chi keep it. Jackson pulled the cat’s tail, and the cat scratched him. No one would own up to having broken the classroom window, so the whole class was made to clean up the schoolyard. Bethany knew who had broken the window, but she wouldn’t tell. So the teacher punished her. Although Robert worked very hard at school, he nearly always received poor marks. Leah writes wonderful stories without even trying. She won the school writing prize.

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By thinking about borderline cases, we can discover many of the criteria that implicitly govern the application of our concepts, yet we can also make good progress by considering a wider variety of cases. These may range from paradigm cases, to questionable or borderline cases, to what we may loosely call contrary and ‘crazy’ cases of the concept in question. While we used a range of borderline cases in the previous discussion of art, if we were using the Target tool we would keep just a few of them, replacing the others with paradigm cases—works like Leonardo da Vinci’s painting of Mona Lisa or Michelangelo’s statue of David—and one or more crazy cases, such as a sneeze, say, or a snail’s trail. We would then attempt to place these cases on a target, with the paradigm cases in the bullseye, the borderline cases in the surrounding circle, and the crazy cases in the outside ring. The use of such an array of cases helps us to triangulate the concept in question. While borderline cases can help us to unearth the criteria that we unselfconsciously use in applying our concepts, it is often useful to compare borderline cases with paradigm cases. For example, suppose we were discussing the concept of ‘being alive’, and were considering ‘seeds’ as a borderline case. Someone may say that seeds cannot be alive because they lie dormant until the conditions are right for them to germinate. This suggests that something cannot be alive if it is dormant. We can discuss this suggestion by returning to our paradigms. We might ask whether anyone can think of something that is obviously alive (a paradigm case) but may be dormant. If we can find such a case, we can say that being dormant does not prevent something from being alive. This may prompt someone to think of a hibernating bear, lying dormant in the depths of winter. The bear is alive, but dormant. So merely being dormant does not disqualify seeds from being alive. On the other hand, that a particular paradigm case has what seems to be a significant attribute that is lacking in a borderline case, does not automatically discount the borderline case. Someone might say that a playful puppy is obviously alive because it is always running around. But there are paradigm cases of living things that do not move about like the puppy. Plants are alive, for instance, but they do not run around. So we need to be careful not to become too fixated upon a particular case. Paradigm cases can vary in significant ways, and a wider survey may reveal that certain attributes are not really essential to the concept.

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‘Crazy cases’ are crazy because we suggest that they fall under the concept when it is perfectly clear that they do not. To suggest that stones are alive is to invent a crazy case. Stones may contain living things, but they are not themselves alive. When we attempt to say why stones are not alive, a long list of candidates suggests itself: Stones are not born and do not die; they do not produce baby stones that mature and grow up; they do not gain sustenance from their environment; and so on. Each of these reasons is a potential requirement for something to be alive. By asking what seems to be missing in the case of a stone, we have generated a broad spectrum of attributes to consider. It can therefore be quite a good idea to introduce a crazy case early on, as a brainstorming exercise. It is important to note that this is the sole purpose of the crazy case, and it is beside the point for someone to try to argue that a crazy case really could be a genuine case. With some concepts it is useful to introduce a contrary case rather than a crazy case. If we were exploring the concept of ‘justice’, for example, it would be silly to invent a crazy case; but a contrary case—a case of manifest injustice—would be instructive. We could then ask why that would be a clear case of injustice, and our answers would once again yield a provisional list of the criteria that define our concept of justice. With the concept of ‘being alive’, we can use both crazy cases and contrary cases. Here a contrary case is simply something that is no longer living—a piece of fish, for instance. Contrary cases are obviously restricted to those concepts that have genuine opposites, such as justice and injustice, alive or dead, good and evil, knowledge and ignorance, and beauty and ugliness. So it is useful to note at the outset whether your concept is of this kind. As with concepts generally, a concept like ‘being alive’ has a history. In this case, our understanding of what makes something alive has been very much influenced by the growth of scientific knowledge. Yet, like ancient and primitive animists, young children are likely to believe that all kinds of things are alive. They may begin by taking anything that moves to be alive, later restrict the concept to anything that moves of its own accord, and only with the acquisition of scientific knowledge come to think about life in terms of biological criteria, such as metabolism and reproduction. Again, children are likely to assume that their toenails are alive because they grow, and only later (if at all) learn to think of them as accumulations of dead cells. While it is obviously an important educational task to inform students’ understanding of significant concepts through the delivery of conventional curriculum content, it is also important for them to develop their powers of conceptual thinking. Target is a tool that will assist in this process. A word of warning: Sometimes students get into a debate about whether or not a case has a given attribute. For example, in discussing whether their hair is alive (which anyone without the relevant scientific knowledge is likely to think of as a problematic or borderline case), your students might get into a dispute about whether the cells that make it up are living or dead. While the discussion Introductory Toolkit—Target

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should motivate them to go and check the facts from an authoritative source, their newfound knowledge will avail them little so far as exploring the concept of ‘being alive’ is concerned. They may establish that their hair is not alive because it is made up of dead cells. But that does not tell them much about the concept of ‘being alive’. In other words, the work with Target is conceptual rather than factual. So beware of getting sidetracked into disputes of this kind. One final tip: As proposed criteria are suggested, do make a list of them on the board. You can always modify them or cross them off your list as you move along. With more advanced students you might also make notes about various criteria, as to whether the attribute specified by a criterion is: • necessary: anything that falls under the concept must have the attribute • merely common: paradigm cases commonly, although not invariably, have the attribute • sufficient: having the attribute, or set of the attributes, is all that is required for something to fall under the concept. Sometimes you may even be able to arrive at a set of both necessary and sufficient conditions for something to satisfy the concept in question. At other times, however, you will not be able to do so, and not necessarily because the discussion was not up to the task. Many concepts are not plausibly construed in that way. As the philosopher Ludwig Wittgenstein said about the concept of ‘games’, the things that fall under our concepts often bear only a family resemblance to one another, and we should look for similarities or analogies rather than trying to construct a watertight category. I will leave you with a target for the concept of ‘being alive’, a concept which is especially fascinating to younger children, and which has been much studied by researchers, famously including the developmental psychologist Jean Piaget in his classic work The Child’s Conception of the Mind. I have mixed together a range of cases that I would invite students to pin on the target, giving their reasons for placing them where they do, and thus beginning our discussion.

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not alive ? alive

an apple

your hair

a playful kitten

the wind

a stone

a piece of fish

toe nails

a seed

Twenty Thinking Tools

an egg about to hatch

thoughts

the sun

a hard-boiled egg

Copyright © Philip Cam 2006

Introductory Toolkit—Target

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One way of testing out an idea is to conduct a thought experiment, that is, to imagine a scenario or situation that will enable us to test the idea against our intuitions. For example, the seventeenth-century English philosopher John Locke was interested in the topic of personal identity and, in particular, what makes you the same person over time. He held that being the same person depends on the persistence of your consciousness and not the persistence of your bodily form. In testing out this claim against our intuitions he asks us to imagine that the soul of a prince enters into the body of a cobbler whose soul has just departed. This soul ‘with all its princely thought about it’ ensconced in the cobbler’s body is the same person as the prince, says Locke, who is responsible for any actions previously committed by the prince but not those of the cobbler. To outward appearances, of course, he is the same man as the cobbler. But, says Locke, this only shows that the bodily being or man is not the same as the person; and we need to distinguish between being the same man and being the same person over time and changing circumstances. Locke’s thought experiment is reminiscent of the folktale in which a handsome young prince is turned into a slimy old frog that can be transformed back into the prince only by the kiss of a beautiful princess. To suppose that the frog really is the prince, as children so readily do, is effectively to entertain Locke’s thought that the person of the prince persists through these transformations, and therefore to distinguish the person of the prince from the bodily form that misfortune has cast upon him. (For a modern version of this story with a humorous twist, see Babette Cole’s Princess Smartypants, Hamilton, 1986.) The prince is that inner being who suffers from his predicament and is all too well aware of the need to convince the princess of his true nature. Of course, if Locke is right, it is also not the true nature of the person of the prince to be a handsome young man; and no doubt this is something that the princess will discover as the years go by when they live together happily ever after. In any event, such a story can be used as a thought experiment with quite young children to help them test their preliminary suggestions regarding the significance of physical and psychological factors in maintaining our identity as persons over time.

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While such ready-made thought experiments can help students to test out their ideas, they should also be encouraged to construct their own thought experiments. Typically these will begin with a student saying, ‘Let us imagine that ...’ or ‘Just suppose ...’, followed by a scenario in which some suggestion that has been made can be tested against their intuitions. Here is an elementary example from a Year 6 classroom in which the students are discussing the topic of value: Lorena: I think you should value whatever comes, whether it’s good or bad, because if something bad comes and it’s your fault, you can learn from your mistakes. Kirin:

I want to challenge that. Just imagine that you burnt down your house. Everyone in it was killed. Value that!

Here Kirin’s dramatic scenario provides a challenge to Lorena’s claim that we should value the bad things that happen in life along with the good. ‘Just imagine …,’ says Kirin, as he introduces a made-up but entirely conceivable situation in which Lorena’s claim seems hard to sustain. In this case, Kirin’s simple thought experiment is also meant as a counterexample to Lorena’s general claim, which may encourage her to modify it in order to take account of what he has to say. Here is another example from a Year 5 classroom: The students had been discussing whether it is ever acceptable to lie, and Max expressed the view that you should always tell the truth because you will only cause more trouble by lying. Other students suggested that sometimes ‘little white lies’ don’t matter, and that whether or not you should tell the truth depends on the situation. A couple of students tried to convince Max that sometimes you really ought to lie—or at least not tell the truth—such as when telling the truth might hurt someone’s feelings. Here is how one student put it: Introductory Toolkit—Thought Experiments

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Cathy: Max, well picture this. There is this kid who likes you but you do not like him. He asks you if you want to come over. Do you lie?

Like Kirin, Cathy is appealing to Max’s intuitions regarding a readily imagined case. She supposes that, when he thinks about it, Max will find that his intuitions agree with hers. It is a simple thought experiment that, again like Kirin’s, is supposed to supply a counterexample to Max’s claim that we should never tell a lie. As a final example, let us look at a more extended discussion of imagined possibilities that test our intuitions about some idea or claim. In this case a Year 4/5 class is discussing whether we could have a mountain that is half on the earth and half on the moon. The question comes from a set of questions designed to provoke the students to try to imagine possibilities and thereby to conduct thought experiments. (See ‘What can happen and what can’t happen?’ in Lipman and Sharp, 1984.) Some students think that they can imagine a mountain that is half on the earth and half on the moon, but some say ‘you can’t’. One student who thinks that it can be imagined says, ‘You can imagine a mountain so big that it goes right up and touches the moon.’ This meets with the response: ‘That wouldn’t be half on the moon. A mountain that went up and touched the moon wouldn’t be half on the moon.’ ‘Okay,’ comes the reply, ‘but you could have a mountain that was solid all the way from the earth to the moon.’ After some discussion, the student adds, ‘It would be a solid shaft.’ Another suggests: ‘It would be like a stalagmite and stalactite that joined into a column.’ ‘But would that be a mountain?’ someone asks. ‘Yes,’ it is asserted. ‘It would be one mountain because it was one column.’ ‘But it doesn’t have a top,’ insists the questioner. ‘Does a mountain have to have a top?’ asks the teacher. The students have different opinions about this. One says, ‘No, a mountain could go on forever.’ In reply, another says that even if a mountain went on forever, it must have a bottom. And that is a problem for the mountain that is being imagined as a shaft or a column. ‘Where would the bottom be?’ After further discussion, someone suggests a new possibility for a mountain that is half on the earth and half on the moon. ‘You can imagine,’ says the student, ‘a mountain that was cut down the middle from top to bottom, and one half taken up to the moon.’ This case meets with general agreement until someone says, ‘That would make two mountains—one on the earth and one on the moon.’ The teacher asks why we would say that, and the student responds, ‘They would be physically separate, and so they would be two mountains.’ Other students suggest that whether we should say it is one mountain or two mountains depends on what we think about a range of similar cases, such as whether, if one half of a building were moved to another site, that would be two buildings or just two halves of the building in different places. And so the discussion continues. This playful imaginative thinking is a kind of conceptual exploration. By examining what can and cannot be imagined or conceived, the students are exploring the possibilities and limits of their concepts.

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(How did we go today?)

The final tool in the Introductory Toolkit is designed to assist students to reflect on their inquiry, both in terms of surveying its outcomes and evaluating its conduct. It is therefore a tool that can be employed whenever we need to evaluate progress, but in the classroom it is most often used to round out a session. It takes the form of a question or series of questions, to each of which students respond with a ‘thumbs up’, ‘thumbs down’ or ‘thumbs in-between’. This means either that some aspect of our performance was good, bad or indifferent, or that we agree with, disagree with, or are undecided about the matter in question. The teacher and students can then use these simple indications as a starting point for exploring individual evaluations and differences of opinion, thus reflecting on the inquiry—conducting an inquiry into the inquiry, if you like—as an aid to consolidation and a guide to the direction of further inquiry. It can also lead to suggestions from students about aspects of their practice, thereby functioning as a tool for self-evaluation and improvement that uses the student’s assessment of their past conduct to direct future conduct. Teachers can use Thumbs to direct attention to any aspect of the inquiry they would like their students to consider. It should normally be used to canvass a mixture of what are called ‘procedural’ aspects and ‘substantive’ aspects of the inquiry—although the distinction between them is sometimes moot. • Procedural aspects are those that belong to the process or method of inquiry, such as the general order in which inquiry proceeds, the management of an agenda and keeping on track, or how we proceed to answer a certain kind of question or use a particular tool. In terms of learning, the focus here is on the acquisition of procedural knowledge—what we are learning to do. Introductory Toolkit—Thumbs

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• Substantive aspects go to the subject matter of inquiry, including the questions, issues or problems dealt with, the suggestions that are made, the concepts explored and the conclusions reached. Here we focus on discursive knowledge and understanding—what we can discern as a result of our inquiries. On the procedural side, the teacher may wish the students to attend to anything from not calling out and learning to take turns in discussion, to the ordered use of specific tools, such as exploring the concepts that we need to understand before we attempt to answer certain questions, or avoiding the tendency to become too narrowly focused on giving and evaluating reasons for some suggestion without bothering to think about possible alternatives. Here the teacher may ask questions such as the following: • How well did we share the discussion today? • Have we learnt to use counterexamples? • Do we always explore concepts when we need to? • Are we sufficiently aware of alternative possibilities? On the substantive side, we will want to see what we have learnt from the inquiry so far, and we may wish to draw attention to certain aspects of a problem that we have dealt with or highlight a particularly significant insight or finding, as well as to identify further matters that still need attention. This may involve questions such as: • Were all the questions on our agenda genuine inquiry questions? • Did we achieve depth in our discussion? • Have we arrived at a satisfactory answer to our question? • Do you have a better understanding of such-and-such a concept? It is possible to straightforwardly ask students to summarise what they have learnt from the class, of course, or to explain a particular concept, or to define what is meant by a counterexample, and so on. While that approach can be productive, Thumbs is specifically designed to fit with the inquiry process. It asks students to express an opinion that they can be expected to justify in the same terms in which the inquiry itself was conducted. Because students are unlikely in most cases to have come to total agreement about matters of substance, Thumbs enables them to distinguish those aspects of the problem or issue that are still live from those that are settled, and this provides them with both a measure of collective progress, as well as a guide to the direction that further inquiry might take. Thumbs also affords them the opportunity to reflect on how well they are progressing with overall procedures and particular tool use so that they may aim at improvement. It is tailor-made to provide that support. Reflection leading to self-correction is a natural extension of the inquiry process. By spending a few minutes at the end of the class thinking about what we did during it, we can help our students to become more reflective about their behaviour and to learn to take responsibility for improving or correcting it. If Sally’s thumb is down when the teacher asks about whether we listened well today, and she says that this is because when she was making a contribution

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some other students were talking among themselves, then the teacher can agree that Sally has provided a good reason for having her thumb down. Now that a student (and not the teacher) has raised the problem, the question about what we should do to deal with it can be thrown back to the students themselves, who will usually have sensible suggestions to make. In this way, the students become involved in formulating rules and managing practices, rather than simply having them laid down and enforced by the teacher. Obviously the sophistication of the questions that get asked under Thumbs will vary with the age and experience of your students, and the things that you highlight will depend on the state of progress and your students’ particular needs. You might also ask only one or two questions or you might ask several, again depending on the circumstances. The following list is therefore offered only as a further indication of the kinds of questions that you might ask, and you will need to exercise judgement in framing such questions for your class.

Some Questions for Reflection Procedural questions 1

Did we listen well?

2

Did we build on one another’s ideas?

3

Did we search for alternative possibilities?

4

Did we look at different points of view?

5

Did we explore our disagreements reasonably?

6

How well did we use such-and-such a thinking tool?

7

Did everyone get a chance to contribute?

8

Did we generally manage to stay on track?

Substantive questions 1

How good were the questions that we asked today?

2

Did we come up with really good ideas or fruitful suggestions?

3

Did we sufficiently examine the concepts that we used?

4

How good overall were the reasons that we gave for what we said?

5

Did we make good progress in answering our question(s)?

6

Did we resolve any significant problem or issue?

7

Did we deepen our understanding of any significant idea?

8

Are there other matters that still need to be resolved?

Twenty Thinking Tools

Copyright © Philip Cam 2006

Introductory Toolkit—Thumbs

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Notes

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Introductory Toolkit—Notes

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Earlier I said that inquiry begins with a problematic situation to which we respond with curiosity, concern, doubt, hesitation or puzzlement. As we begin to inquire, the interest that we take in the situation becomes more articulate and results in the formulation of problems or questions, which provide the agenda for our deliberations. Sometimes our agenda is limited to a discrete problem or a particular question, while at other times it may deal with a number of interrelated matters. An agenda is a means of establishing the focus and scope of our inquiry. It is a tool that we use to bring order to the proceedings. It can also be a tool for limiting or manipulating an inquiry, of course, as when an inquiry has been set up with unduly narrow terms of reference, or an agenda is hijacked by special interests. Setting aside such misuse in the wider community, there are several tasks that deserve our attention when establishing and following an agenda in the classroom. Problems, issues or questions need to be identified, clarified and arranged in order, and as we proceed we need to allow for further elaboration in our agenda and adjustments to its scope. • Identification: Students need to learn to accurately identify a problem or issue. This involves being able to articulate it by describing it, giving an example of it, or relating it to other issues or problems. It also involves being sensitive to the possibility that characterisations may be incomplete, misleading, biased, or based on dubious assumptions. We need to acknowledge these possibilities because inquiries that are based on poorly articulated problems or issues are unlikely to produce fruitful results. • Clarification: The problem may be obvious to everyone, or the question may be clear; but, where this is not the case, inquiry should not proceed until an attempt has been made to clarify things. If students initially offer vague characterisations or ambiguous questions, they should be asked to supply: – further details – more carefully qualified statements – more precisely worded questions. • Ordering: Where an agenda consists of a number of items, it needs to be organised and not left as a rag-tag collection of things. This may mean that issues need to be separated, problems ordered according to priority, or questions grouped according to topic or placed in a logical sequence.

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• Elaboration: Further thought may reveal that our problem or issue should be broken down into a number of constituent parts, or the question with which we began may lead to a series of subsidiary questions that need to be addressed. This is normally the case when we attempt to address problems or to answer questions of any complexity. This means that we need to keep a careful eye on the agenda. As one question leads to another, or we successively investigate different aspects of a problem, it is all too easy to lose our way. This often means that we need to map or otherwise keep track of the discussion in terms of the unfolding agenda. • Adjustments of scope: While we need to ensure that we stick to our agenda, we must also be prepared to adjust it as we proceed. We may discover that our initial formulation was too narrow and identified only part of a larger or more general problem or issue with which we need to deal. Or we might discover that we can dispense with some part of our initial agenda because it is not as relevant as we had assumed. Except with very young children, I have recommended the use of students’ questions as a standard procedure for inquiry in the classroom. Here an agenda is a question or series of questions that addresses a problem, issue or other item of interest. When teachers use narrative or other complex material to stimulate questions, students are likely to respond with questions that cover a range of topics unless the general topic has been set in advance. In any event, it will almost certainly be necessary for the students to group their questions according to the issues or problems that have been raised, and thereby to begin to arrange them into various possible agendas. An obvious way of doing this is to ask your students whether they can see connections between their questions and to identify the problem, issue or theme that connects them. As students’ suggestions gain acceptance, some scheme can be used to identify them on the board. The following is an example from an upper primary classroom, where students have identified several agendas in questions sparked by a story. Notice that the agenda dealing with ‘growing up’ lies within the broader one of ‘change’, showing that the students are interested in change, both in terms of personal development and at the general (metaphysical) level of what it is and how it occurs.

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Students group their questions 1 How does change occur? (Angela) 2 Do you suddenly grow up or does it happen in stages? (Annie-Kate) 3 Why did the adults think that what the children had to say wasn’t important? (Tim) 4 What is change? (Serena) 5 How can you change in such a short period of time? (Kris) 6 Why is noise pollution? (Melody) 7 Is anyone superior to anyone else? (Tom) 8 Does the way you see things now change when you grow up? (Carlos) 9 Is change a living thing? (Emily) 10 How do you define intelligence? (Miriam) 11 Why do adults respect other adults more than they do children? (Aaron) 12 Why is it that children have to respect their elders if the adults aren’t known to respect the younger ones? (Sharon) CHANGE

GROWING UP

AGE AND RESPECT

POLLUTION

INTELLIGENCE

When proceeding in this way, the questions that initially frame each topic may need further ordering. For example, on the topic of ‘growing up’, Kris’s question relates most closely to the story entitled ‘Bizzy Road’ (in Cam, 1997a), in which a girl experiences a sudden burst of social and emotional growth. He seems to be questioning whether so sudden a change is possible. Annie-Kate’s question leads on from this to ask, more generally, whether growing up is something that happens suddenly or in stages; while Carlos’s question about whether growing up changes your perception of things, relates to what it is like to be a grown-up rather than about how quickly it occurs. This would be a natural order in which to address these questions, and with a little thought and experience these upper primary school students will be able to work that out. Sometimes the agenda is set by a single question, as with Miriam’s question about how to define intelligence. For the purposes of discussion, however, we might end up dealing with a single question, even when there are more questions on the agenda. Tom’s question, ‘Is anyone superior to anyone else?’, could make for a rich discussion all by itself, and if the students had a particular interest in that question there would be nothing wrong with sticking to it.

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Since we would almost certainly be making use of several sessions to discuss the various topics that have been raised, we could always begin by restricting our agenda if that were thought to be desirable. In regard to scope and elaboration, it can be very useful for the teacher to take the time between sessions to develop some follow-up questions that might help the students to broaden the scope of their discussion or to more deeply probe various aspects of the topic. We can call a set of such additional questions a ‘Discussion Plan’. While it takes time, real effort and some experience to develop a well thought-out Discussion Plan, it is worth your while to develop the practice. It provides the opportunity for you to question these matters more systematically, and the additional depth of your questioning will help to guide your students to question and explore more deeply. Look, for example, at the following Discussion Plan that builds on Annie-Kate’s question.

DISCUSSION PLAN: Growing up 1

Do you suddenly grow up or does it happen in stages? (Annie-Kate) 2 Do things sometimes happen to young people that make them suddenly grow up? 3 Have you now reached a certain stage in the process of growing up? 4 At what stage are people completely grown up? 5 Do some people never really grow up? 6 On the basis of what we have said so far, what is it to ‘grow up’? 7 If you could, would you choose to be like Peter Pan and never grow up?

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A class of third graders had begun reading a story called Elfie (Lipman 1988b), but were not yet sure about the identity of the central character. Was Elfie a little girl, an animal of some sort, or perhaps an elf? This raised the question, ‘What is Elfie?’ In discussion the following episode ensued, which is transcribed almost verbatim. Susan: I think that Elfie is a rabbit. Teacher: Why do you think that Elfie is a rabbit, Susan? Susan: Well, because it says here that Elfie curled up into a ball to sleep. And that is what rabbits do. Robin: That doesn’t prove anything, Susan. Susan: I think it proves that Elfie is a rabbit. Robin: No, it doesn’t. What about kittens? They curl up into a ball to sleep, and they’re not rabbits. Tom: I agree with Robin because I curl up into a ball to sleep and I am certainly not a rabbit.

I was observing this class and wondered what the teacher would do at this point. She was relatively new to classroom inquiry, and didn’t seem sure what to say. After asking Susan what she thought of what Robin and Tom had said, she simply passed on. While that was perfectly understandable, she missed a golden opportunity to draw attention to the students’ reasoning, and after the class I recommended that next time she should return to this little exchange. On my understanding of it, Robin and Tom implicitly took Susan’s reasoning to be as follows: 1 Elfie curls up into a ball to sleep. 2 Rabbits curl up into a ball to sleep. 3 Therefore, Elfie is a rabbit. In reply, they show that by the same form of reasoning Susan would have to accept that kittens are rabbits and that Tom is a rabbit. You might as well say, for example, that: 1 Kittens curl up into a ball to sleep. 2 Rabbits curl up into a ball to sleep. 3 Therefore, kittens are rabbits.

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Since kittens are obviously not rabbits, there is something wrong with Susan’s reasoning. Here Robin’s parallel reasoning provides a counterexample to Susan’s reasoning. It shows that Susan’s way of reasoning is not reliable, because by that form of reasoning it is possible to end up concluding something false from premises that are true. So Susan’s reasoning cannot prove what she takes it to prove. Here is a simpler way of looking at the matter. What could Susan be thinking? She appears to have in mind the following general claim: If something curls up into a ball to sleep, then it’s a rabbit. Robin’s and Tom’s responses are counterexamples to this general claim. They show it to be false. This gives us two ways of defining counterexamples: 1 A counterexample is an example which demonstrates that a general claim is false. 2 A counterexample is reasoning of the same form as the original, showing that form of reasoning to be invalid because in the parallel example the premises are known to be true and the conclusion to be false. (We will look at this way of talking about reasoning more formally under Deductive Reasoning later on.) Children as young as these third graders can learn to supply counterexamples. Although they may have more difficulty with the second formulation than the first, it is clear that at least some of the students in this class are able to intuitively supply counterexamples to what they take to be erroneous reasoning, and so there seems little reason to suppose that they could not come to supply what is needed in simple cases, consciously and deliberately. Exercises are useful in giving students practice in constructing counterexamples, and with a little thought teachers should be able to devise them. For example, take the following two general claims to which our third graders could probably provide counterexamples. All they need do is to find an example of the thing in question that does not have the attributed feature. A counterexample to the first would be any kind of flightless bird, such as a penguin or an ostrich; and for the second we might cite mammals such as the whale or the dolphin.

A bird is a creature that flies.

Mammals have either two or four legs.

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Note that for a counterexample we want something that is an example of the kind of thing mentioned in the generalisation that does not have the feature in question. So an airplane would not be a counterexample to the first claim, for instance. Beginning students sometimes succumb to this confusion, so be on the lookout for it. Here are a couple of examples of the kinds of reasoning that could be used to help students learn to construct counterexamples. Just as in the case taken from the classroom, remember that we need parallel reasoning that takes us from premises we may assume to be true to a conclusion that we know to be false.

1 2 3

Gabriel has wings. Birds have wings. So Gabriel must be a bird.

1 2 3

Sonya believes that Mount Everest is the highest mountain in the world. Knowing something involves believing it. So Sonya knows that Mount Everest is the highest mountain in the world. Hint: Substitute ‘The Space Shuttle’ for ‘Gabriel’ in the first example. In the second example, for the statement that Mount Everest is the highest mountain in the world you can substitute a false statement that Sonya might be assumed to believe, such as that Mt Kosciusko is the highest mountain in the world.

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A criterion is a more or less decisive reason that we appeal to in making judgements or decisions. In employment, for example, applicants for a position are evaluated against a set of criteria, which are the considerations we appeal to in ranking them and making an appointment. If someone were to dispute a decision, properly speaking that could only be because they thought the stated criteria were not adhered to or because they disagreed with the choice or relative weighting of the criteria. When such disputes arise, we attempt to justify (or sometimes revise) our judgements by reference to the criteria, or to justify or revise the criteria themselves. Criteria are therefore tools that we need to examine and refer to if we are to come to reasoned agreement through deliberation. While just about anything might serve as a criterion in the right context, examples of some common kinds of criteria may be helpful in clarifying the idea. Aims: Committees sometimes reject proposals because they lie outside the aims of the organisation that they represent. Here the organisation’s aims provide the criterion for making a decision. Codes: Clubs may impose dress codes. Such codes provide criteria that determine acceptable standards of dress. Definitions: The taxation department has a definition of taxable income that is used in determining the amount of income tax payable. This is a criterion the tax department will appeal to in cases of dispute. Evidence: Courts admit the testimony of witnesses as evidence in the determination of verdicts. Subject to admissibility and examination, the evidence of witnesses is a criterion members of a jury will appeal to in determining their verdict. Ideals: Judges at a cat show appeal to ideals of breeding, condition, temperament and behaviour in awarding prizes. The cat that comes nearest to satisfying these criteria in the judges’ estimation will win first prize. Norms: Having an IQ either greater than or less than 100 is a criterion used to judge whether a person is either more or less intelligent than the average. Policies: Claims against an insurance company may be rejected because they are not covered by the policy that was in force at the time. Being covered by the policy is an essential criterion used in determining claims. Purposes: A manufacturer may refuse to repair or replace a damaged product because it was used for purposes other than those for which it was designed. A statement of that condition or criterion was no doubt included in the manufacturer’s warranty. Intermediate Toolkit—Criteria

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Rules: Board games have rules that determine which moves are admissible. In cases of dispute, players should refer to these criteria. Standards: Dietitians use the Recommended Dietary Intake in evaluating diets. These standards provide dietitians with criteria for making their recommendations. Testability: Following the philosopher Karl Popper, we might adopt the criterion that what makes a hypothesis scientific is whether it is testable. Tests: Medical laboratories conduct tests on specimens to assist doctors in diagnosing their patients. A positive test result is a decisive factor in forming a doctor’s opinion. In making a judgement or reaching a decision, criteria can be decisive in a variety of ways, of which the following are among the most important: • A criterion can be a necessary condition: A criterion can be an essential or necessary condition in the sense that nothing which fails to satisfy the criterion can be classified as a thing of that kind or evaluated in that way. For example, no belief can be said to amount to knowledge if that belief is not true. Being true is a necessary condition for a belief to amount to knowledge, and therefore it is essential for this criterion to be satisfied before someone can be said to know something rather than merely to believe that it is the case. • A criterion can be a sufficient condition: A criterion can be a sufficient condition for making a determination all by itself. Being a prime number other than 2, for instance, is sufficient for being an odd number. A number satisfying that criterion is guaranteed to be odd without further ado. (By the way, notice that being a sufficient condition does not make it a necessary one. There are plenty of odd numbers that are not prime numbers—e.g. 9.) • A criterion can establish something with certainty: The criteria that are said to govern the application of our concepts are held by some philosophers to be those conditions which establish with certainty that something is the case. On this understanding, a criterion amounts to a condition that is both necessary and sufficient. For example, the criterion for having been found guilty in a court of law is the pronouncement of that verdict. The return of the verdict is both necessary and sufficient for having been found guilty. It is therefore the criterion that we use. (It is worth pointing out that in the case of a guilty verdict, the jury must have found the accused guilty before the verdict was delivered. Otherwise it could not deliver that verdict. This illustrates the fact that a criterion of something is not the thing itself, but the means we use to determine that it is so.) • A criterion can be a very reliable condition: Sometimes factors that we can generally rely on in making a judgement or reaching a decision are regarded as criteria. In this broader use of the term, things such as natural signs and distinctive characteristics may be treated as criteria because they are such very good indicators. That a solution turns a litmus paper red, for instance, is such a reliable sign of it being an acid that we use it as a criterion for establishing the presence of an acid in the laboratory.

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• A criterion can be a desirable condition: When it comes to evaluative judgements, we sometimes also treat merely desirable conditions as criteria. By ‘desirable’ we do not mean something that is ‘wholly desirable’, which in that case would be tantamount to a necessary condition, but rather we mean a condition that is nevertheless desirable to some significant degree. In setting out an advertisement for employment, for example, we may list what we regard as desirable criteria in addition to the essential criteria for appointment to the position. These admittedly lesser criteria are criteria nevertheless.

Absolute and comparative judgements Criteria are used to make both descriptive and evaluative judgements that may be either absolute or comparative in nature. This gives us four types of judgement: • absolute descriptive judgements • comparative descriptive judgements • absolute evaluative judgements • comparative evaluative judgements. Thus, in turn, we may judge that some action was a punch, that it was a harder punch than some other punch, that the punch was totally unjustified, and that it was less justified than some other punch. Absolute descriptive judgements rely on categorical criteria and form the basis of classification. For something to be a mammal, for instance, is for it to be included in a class of things that satisfy certain classification criteria (warmblooded, vertebrate, suckles its young, etc.). At least for current purposes, we may think of such criteria as essentially definitional. Criteria that are used as a basis for descriptive comparison allow us to refer to relative positions on some scale. When we say that boat X is bigger (broaderbeamed or more buoyant) than boat Y, the criteria for our judgement are at least implicitly scalar. To judge that boat X is bigger than boat Y is to place them on some scale that enables us to compare them in length or tonnage, or it may be that we have only some implicit and vague scale in mind. Scales may be rudimentary or sophisticated, rough or exact, and qualitative or quantitative, but in all these cases we implicitly rely on what we may call ‘scalar’ criteria. It must be admitted that this simple division leaves room for exceptions and anomalies. For example, consider judgements about family relationships, such as that X is a cousin of Y. For X to be a (first) cousin of Y, X must be Y’s mother’s or father’s brother’s or sister’s child. (Did you get that?) In this case the criterion is the definition of what it is to be a cousin, and X and Y must satisfy that definition if they are to be cousins. Given that the criterion is definitional, we might expect that the judgement is absolute. Yet ‘cousin’ is a relational notion, albeit not a scalar one. Here we may say that the judgement is relative rather than comparative. (Hence we call our cousins relatives.) Again, consider the commercial classification of medium eggs. While hens’ eggs have a natural weight range, and some eggs naturally fall in the middle of that range, Intermediate Toolkit—Criteria

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to regard a medium egg as one in a precise weight range is to impose a classification standard for commercial purposes. This is a conventional classification imposed on the natural variability of hens’ eggs, and hence a classificatory criterion that ought to support an absolute judgement. Yet surely the notion of a medium egg implies that some eggs should be described as smaller and others as larger by comparison, ‘medium’ being a comparative notion. Such cases are of considerable interest. It appears that by designating a band on the weight scale as the criterion for what counts as a ‘medium’ egg, we have turned a comparative scalar notion into one that can be used to make an absolute judgement. Similar remarks can be made about criteria in regard to both absolute and comparative evaluative judgements. Suppose that Peter insists on action X being morally right and action Y being morally wrong, while Paula claims that Y is merely morally less acceptable than X. Peter’s evaluation is absolute, while Paula’s is comparative. Let us also suppose that Peter and Paula agree that the relevant criterion for making their evaluative judgements is the maximisation of pleasure and the minimisation of pain, and they also agree that X maximises pleasure and minimises pain, while Y fares somewhat less well in this regard. They regard this criterion differently, however, with Peter taking ‘maximises pleasure and minimises pain’ to define the category of right action, while Paula conceives of the criterion as presenting us with a scale of wellbeing along which actions may be spread. So Peter and Paula are in agreement about the facts of the case, but their different conceptions are producing different kinds of evaluative judgements. Some kinds of criteria naturally lend themselves to absolute or categorical judgement, while others tend to support relative or comparative judgement. Reverting to my earlier examples, we categorically reject something because it is inconsistent with our aims, outside the code, incompatible with policy, or banned by the rules. While these kinds of criteria often admit of borderline cases—where, for example, it is not clear whether something is incompatible with policy or banned by the rules—one aim of such things as policies and rules is generally to enable clear-cut decisions wherever possible. They provide grounds for absolute judgement. By contrast, when deciding which product to buy or who to believe, we typically need to make comparative judgements, and the criteria to which we appeal are very often what I have called ‘scalar’. Products may vary in their suitability to our purposes and we will need to weigh the evidence for competing claims. Short of finding a product that is absolutely ideal—there being, as we say, no comparison—or of obtaining positive proof as to who is right, our judgements will rely on criteria that allow for degree. By now you may have quite rightly formed the opinion that dealing with criteria can be complex and tricky. We would not expect any but the most advanced secondary students to learn to examine their criteria and knowingly employ them in all the ways that I have set out above. Yet criteria are implicit in all judgements and decisions, and it is therefore important for us to learn to use these tools well. Even in the early years of school, it is entirely possible to get students to make explicit the criteria that they are tacitly using in applying some

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concept or making a comparative judgement. We can begin by having students construct a list of criteria without necessarily worrying about such things as necessary and sufficient conditions. And we can introduce our younger students to the difference between absolute or categorical judgements and comparative or relative ones. By such means we can lay foundations on which we can build. I will leave you with an exercise (adapted from Cam, 1993b) designed for middle-to-upper primary school students that is meant to help them draw out and discuss the criteria they use to say that something counts as stealing. This is an exercise in conceptual exploration where the criteria are made explicit by the students through the consideration of a number of simple scenarios. Sometimes a scenario will provoke a ‘that depends’ response from students, but that is just fine. Once they specify what the case depends on and why, they will again have supplied a tentative criterion. The teacher should establish a list of suggested criteria and add items to the list as they arise, allowing for discussion of any difficulties or disagreements. The exploration is likely to include discussion of the role of such things as intention, permission, ownership and dishonesty in making something a case of theft. I would normally carry out such an exercise through discussion with the whole class.

EXERCISE: Stealing Are the following examples of stealing? Be ready to give a reason for your answer. Stealing

Not stealing

?

1 You borrow something and forget to return it. 2 You are lent something that you never intend to return. 3 You use someone’s things without asking. 4 You take something that you know the owner doesn’t want any more. 5 You give away something that belongs to someone else. 6 You cheat on a test by copying your neighbour’s work. 7 You find something that someone in your class lost and you keep it. 8 You take something belonging to someone else, mistaking it for your own. 9 You pick fruit from a neighbour’s tree that is hanging over your fence. 10 You secretly eat a big piece of your little sister’s Easter egg. Twenty Thinking Tools

Copyright © Philip Cam 2006

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Generalisation is often viewed negatively. We are likely to be critical of people who have a habit of making sweeping statements, or who are prone to making ill-informed and rash generalisations, or are inclined to view people and situations in stereotypical terms. Such generalisations have a deservedly bad name, and the habits of mind that underlie them ought to be countered by any socially responsible system of education. Yet generalisation is also a vital means of making sense of our world by learning from experience. In generalising, we abstract recurrent patterns from experience that we can apply to future conditions. Without such powers we would be trapped in endless particularity and have no systematic understanding of our world. Generalisation attains formal expression in laws and rules that help to guide conduct, informing the moral and social domain as well as scientific inquiry and technological development. Such guides represent the cumulative and often hard-won wisdom derived from the experience of success and failure in the past. Educationally, we want students to make warranted generalisations and not to make unwarranted ones. This means that they need to become used to seeking the grounds that may be supposed to warrant generalisations and to engage in the process of evaluating them. In order to do that, however, students first need to become aware when generalisations are being made and to become clear about what kind of generalisation is involved. Let us look at this in terms of the following remarks: Johnny: Dogs make better pets than cats. Alison: Migrant kids can’t speak English properly. William: The planets are solid balls of matter. Emily: Fish can’t fly. Hee-Min: It is wrong to tell a lie.

All of the above are general statements. They are statements that make some claim about groups or classes of things, rather than about some particular thing. For example, Johnny is comparing dogs to cats, not Fido to Fluffy. If need be, you should construct an exercise or two in which students are asked to pick out general statements from statements about particulars to ensure that they are familiar with the distinction. Such general statements are often implicitly of the form ‘All X’s are Y’s’ or of the form ‘No X’s are Y’s’. For example, William’s claim is an implicit ‘All’

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statement, while Emily’s pronouncement is naturally interpreted as the ‘No’ statement that no fish can fly. Most people would take Hee-Min to imply that it is always wrong to tell a lie, making her remark implicitly an ‘All’ statement. Can we analyse Johnny’s and Alison’s assertions as ‘All’ or ‘No’ statements? Here we may need to ask what they had in mind. Does Johnny mean to say that dogs always make a better pet than cats, or merely that they usually do? Does Alison mean to imply that no migrant kid can speak English properly, or that it is almost always or perhaps generally the case? When we are dealing with general statements, it is particularly important to become clear about whether the statement in question is to be interpreted as an ‘All’ or a ‘No’ statement, or whether it is to be qualified by ‘almost always’, ‘usually’, or whatever. This initial step of clarification can save a great deal of confusion, and it can help students read more critically and think more carefully about what they say. Commonly such general statements are formed by what is called ‘induction’. That is to say, the general claim is inferred from knowledge of particular cases that fall within the person’s experience or other learning. William might know that the earth is a solid ball of matter and that so is Mars. So he might suppose that all the planets are alike in that respect. Emily might think that fish can’t fly based on the kinds of fish that she knows. (By the way, do so-called flying fish fly?) In other cases the basis of the claim is very unlikely to be induction, or at least not one that the claimant has made. When Hee-Min claims that it is wrong to tell a lie, for instance, she is almost certainly just asserting a rule of conduct that she has been taught. Even if this rule of conduct has a distant basis in our collective experience of the consequences of truth-telling and lying, it is not likely to be the student’s warrant. Still, students could easily supply plenty of examples where it seems clear that it would be wrong to lie in order to supply the generalisation with inductive support. One standard way of testing a generalisation is to search for counterexamples. For instance, if Hee-Min means that it is always wrong to lie, then we might test her claim by considering cases where it might not be so clear that it is wrong to lie. Would it be wrong to lie if telling the truth would do great harm, for example? What if she could save the life of a friend only by telling a lie? Such questions are likely to reveal counterexamples to the claim that lead to its modification. In the same way, a student might site Saturn or Uranus as counterexamples to William’s claim, or someone might remind Alison that Hee-Min is a migrant who has a good command of English. Counterexamples can defeat ‘All’ and ‘No’ kinds of generalisations. Other kinds may need to be tested by a variety of other means. We may need to assemble the evidence, or to find out whether expert opinion is agreed. Sometimes a thought experiment may reveal what would be the case if the generalisation were either true or false. If Hee-Min’s statement were meant as the claim that lying is generally wrong, for instance, we might ask: What would our world be like if people couldn’t generally be trusted to tell the truth? Would the world be different in ways that we would not like? Would it be sufficiently disagreeable to show that it would generally be wrong to lie? Intermediate Toolkit—Generalisation

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Inquiry begins with a problematic situation, then seeks its resolution through a pattern of systematic exploratory activity. I have provided an outline of the exploration process in terms of students: 1 raising, analysing, organising and selecting inquiry questions 2 generating suggestions as to alternative possible resolutions of whatever matter is in question 3 drawing out the implications of their suggestions through reasoning and conceptual exploration, and 4 comparing and evaluating various alternatives in order to form reasoned judgements or resolutions. While this is the basic pattern, actual inquiries will naturally vary in emphasis and detail. No matter what actual shape an inquiry takes, it is vital to keep track of the proceedings. It is all too easy to forget where a discussion has come from or where it was supposed to be going. We can lose sight of the fact that we were discussing a particular question, and be left wondering how we got onto some topic that seems only distantly related to the matter with which we began. We may become so involved in a dispute over a suggestion that we omit to think about significant alternative possibilities that were raised. In fact, the danger of becoming entangled in our subject matter in ways that thwart the inquiry is ever-present. One tool that can assist us to avoid such problems is a Discussion Map. While there is no rigid formula for mapping a discussion, and the details will vary with the intellectual terrain, a Discussion Map should always reflect the pattern of inquiry. Thus we need only consider the basic pattern of inquiry in order to construct the outline of a general Discussion Map. It will follow the same sequence of initiating, suggesting, reasoning, analysis, evaluating, and concluding. More concretely, it will lead from a question to suggestions, to indications of their relevant implications and meanings, coupled with evaluations based on relevant criteria, with the whole affair culminating in a judgement or conclusion.

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QUESTION SUGGESTIONS REASONING AS TO CONSEQUENCES, MEANINGS, ETC. EVALUATION OF ALTERNATIVES CONCLUSION

The map of a particular session might deal with only a part of this process, of course, and it may also ignore all sorts of details and subsidiary inquiries within the overall inquiry process, recording only its larger results. Earlier I gave the example of a group of secondary students who decided to inquire into the question, ‘What makes an action fair?’ On that occasion, after some preliminary discussion, the class broke into small groups, and each group was asked to come up with a brief written response to that question in the form ‘An action is fair if …’ There was considerable discussion in most of the groups about what their short statement should contain, with various suggestions being made and then discarded as seemingly better alternatives presented themselves. Because this activity asked for an answer to the question, in effect it invited each group to hold a rapid-fire mini-inquiry and to come up with at least a somewhat considered conclusion. Yet the details of those mini-inquiries were not recorded, even though some of the deliberations that occurred undoubtedly informed later discussion. At this stage the class’s Discussion Map included only the question and the students’ preliminary answers. These partially considered conclusions then became suggestions requiring further examination when the group next met.

What makes an action fair?

An action is fair if it treats people as they deserve to be treated.

An action is fair only if it treats everyone equally.

An action is fair enough if it does no one any harm.

An action is fair if everyone’s interests are taken into account.

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In another small group case illustrated earlier, middle primary school students had raised the question, ‘Do bunyips exist?’, and a small group was working on the suggestion that they do not exist by assembling reasons in its support. In this case the students effectively reasoned that if there were bunyips, then: 1 we would expect there to be photographs of them 2 there should be reported sightings of them 3 they would not be depicted as such different kinds of animals in different books 4 they wouldn’t have a ‘made-up’ name. Therefore, the lack of photographs and reports, the different depictions and the curious name are all reasons to suppose that there are no bunyips. What this group of students actually recorded, however, was just the list of reasons that they presented to the class. This written record should be seen as part of a Discussion Map that will also include the reasons that other groups of students have given as to whether bunyips exist or not. If the inquiry is to be really thoroughgoing, no final conclusion can be reached until all of these reasons have been assembled and conjointly evaluated; and even then we may come to only a broad consensus, with universal agreement being hard to attain.

Do bunyips exist? Bunyips do not exist • • • •

no photographs of bunyips no reports of bunyips bunyip pictures are different in different books ‘bunyip’ sounds like a vegetable

Sometimes subsidiary inquiries must of course be mapped. An obvious instance is when a concept is examined in preparation for answering a question that employs it. Let us look at this as a final illustration. In the following case, the students began with the question, ‘How can stealing ever be all right?’ but almost immediately moved to the subsidiary question, ‘What is stealing?’ They explored this subsidiary question as a whole class using the exercise on stealing that I included in the section on Criteria, with the teacher scribing the main points on the board. (In more advanced classes, by the way, students can become quite proficient transcribers of class discussion.) This transcription formed a significant part of the class’s Discussion Map, with further reference being made to it when discussion returned to their initial question.

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How can stealing ever be all right? What is stealing? Suggestions: • knowingly taking something that isn’t yours • taking someone’s things without permission • taking someone’s things without their knowledge • to take something dishonestly Criteria: is deliberate, involves property, lack of permission, secrecy (usually), dishonesty Conclusion: Stealing is deliberately and dishonestly taking property that isn’t yours, without permission and usually without the owner’s knowledge.

Twenty Thinking Tools Copyright © Philip Cam 2006

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Notes

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Intermediate Toolkit—Notes

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Inquiry questions are of various kinds. Some concern matters of fact about which there is either total ignorance or dispute; others concern matters of value, particularly where there is uncertainty or disagreement regarding proper conduct; and yet others are questions about the adequacy of our reasoning and the connections between ideas. Inquiry questions may also involve a mixture of the above, and cannot be adequately addressed without first sorting them out. Before proceeding to such complexities and suggestions for dealing with them, let us first review these different kinds of questions in a little more detail.

Factual questions Science provides us with the most successful procedures that we have for inquiry into matters of fact. Procedures for systematic observation and recording, laboratory techniques, experimental method, mathematical modelling, statistical analysis and all the trappings of quantitative method provide scientific inquiry with enormous predictive and explanatory power. In this book, however, we are not concerned with scientific inquiry, but with trying to develop an inquiring outlook in social and intellectual contexts away from science, and attempting to bring at least a modicum of resourcefulness and rigour to everyday judgement and decision-making. This does not mean that these other endeavours have little to learn from science. On the contrary, our generalisation of the inquiry process is modelled on science in many respects. Yet insofar as questions that arise in the kind of classroom inquiry with which we are presently concerned turn out to be about matters of fact, they are unlikely to be settled by students using sophisticated empirical methods. The more usual resources for settling such questions are factual information that is presented in the curriculum, general knowledge brought into the classroom, and students’ personal experience. These are the ready sources of evidence for your students, albeit ones that they need to use with appropriate caveats and caution. It is important for students to distinguish between the kinds of factual questions that they can answer with some assurance and those that they cannot. Partly this has to do with learning to judge the worth of evidence and learning to be careful in drawing conclusions from it. In addition, however, many students are prepared to argue endlessly over questions about matters of fact

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that they obviously cannot settle, and may need to be reminded of the need to avoid such lengthy and fruitless disputes. Even so, we should not entirely abandon speculation. For example, the domain of metaphysics appears to deal with speculative questions concerning matters of fact about which there is endless dispute. Traditional questions about the existence of God, the relations of mind to body, and the existence of freedom in a deterministic world, for example, look to be about matters of fact, even though philosophers and theologians seem unable to settle them. Such questions are important to many people and may arise in the minds of students. That students are unable to arrive at definitive answers to such questions does not mean that they are not worth discussing. Given the perennial nature of these questions, we should value reasoned disagreement and the development of a thoughtful attitude towards such matters above mere conviction.

Questions about values Questions about values are of various kinds, which include those of an ethical nature as well as those that belong to aesthetics, but extend to all matters of preference and what we may call ‘pro’ and ‘con’ attitudes. Some values are not subjects for inquiry because it is unproblematic whether a person has one preference rather than another. One child prefers vanilla ice cream and another prefers chocolate, one person likes colourful attire while another prefers muted tones, and so on. Even so, there is such a thing as having good taste or poor taste, and tastes can be relatively untutored or more educated. So we need to distinguish matters of preference that require no justification from those that call for deliberation and reflective judgement. The latter are amenable to inquiry, and the development of good taste and more mature aesthetic judgement can be aided by such means. Ethical questions are a major stimulus for values inquiry in the classroom and, indeed, collaborative inquiry can be a vehicle for moral education. To have students inquire together into ethical issues—to think together about all kinds of matters concerning character and conduct—is to enrich their ethical understanding. They learn to apply their intelligence to ethical predicaments, to think about the role of both principles and consequences in ethical debate, and to make more considered ethical judgements. Given its collaborative nature, such an activity also develops and strengthens ethical behaviour more directly. For example, students who are learning to listen to one another, to develop the trust and respect that enables them to say what they think, and to explore points of view with which they may not agree, are developing social dispositions and interpersonal abilities that we may call ethical. So engaging students in collaborative ethical inquiry combines a reasoned approach to ethical subject matter with the development of abilities and dispositions that build moral character.

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Conceptual questions Just as factual questions are concerned with how things actually stand, and questions of value are concerned with how we should stand towards things, logical and conceptual questions deal with relations between propositions and distinctions and connections among ideas. Relations in the latter domain are, of course, in many ways answerable to those in the former. Erroneous conceptions can misrepresent how things actually stand, faulty reasoning can suggest that things must be thus-and-so when they may not, and we can both fail to distinguish things that are actually distinct and make distinctions where none exist. However, logical and conceptual relations may also govern how things otherwise stand. We reason in order to control or reconstruct our world. We arrange our affairs according to how we conceive of them. And we behave as we think proper according to our understanding. The interdependence of objective relations, our agency, and our reasoning and conceptions lies at the heart of inquiry. We ultimately rely on our reasoning to run true and our conceptions to be both fitting and productive in regard to the ends that we are trying to achieve. So questions about whether certain things should be held distinct for particular purposes, or by what criteria we should judge something to fall in a certain category, or whether we can assert a given proposition on the basis of certain reasons or evidence, are among the most common in inquiry and a great deal of attention needs to be paid to them.

Sorting out the questions Two basic steps are required to sort out inquiry questions once we have identified them as such. First, we need to determine whether a given question is primarily a question about a matter of fact, one that concerns values, or whether it is a logical or conceptual question. I say ‘primarily’ because, as I remarked above, questions may be mixed; and that is something we will come to in a moment. To ask into which of these three categories a given inquiry question at least initially falls, may seem to be a bit like asking whether something is animal, vegetable or mineral in the old parlour game. What happens in the parlour game if I am thinking of, say, a number? Numbers do not fit into any category on offer. So can we be sure that all inquiry questions will fall into one (or more) of my three categories? Well, insofar as a question can be answered by reference to actual or possible experience, by gathering evidence, conducting an experiment, employing principles, standards, norms or criteria, or by thinking about reasoning, it can be so classified. And if nothing of this sort can help us to answer the question, it is unclear how any kind of inquiry could answer it at all. Again, to ask whether a question is about matters of fact or of value may appear to be philosophically presumptuous, in assuming that values are not facts and that there is a clear divide between the two. Nothing of the kind is being presupposed, however. We can distinguish between these different kinds of

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questions without worrying about whether we are dealing with different classes of facts or different kinds of things altogether, or indeed whether the distinction is always clear-cut. Secondly, having decided that a given question is first and foremost of one kind, we need to determine whether it also involves or gives rise to questions of other kinds. Suppose that we were addressing the question, ‘Do animals think?’ While we may suppose that this is primarily a question about a matter of fact, we could hardly begin to answer it without first discussing the conceptual issue of what we are to understand by ‘think’. If we want to know whether animals can do something, then first we must be clear about what that something is. So there is a subsidiary question of concept here, which we might express as ‘What do we mean by think?’ or just ‘What is it to think?’ And as I suggested, there is a logical ordering here. We had better have at least a crack at answering this question first. Sometimes questions about concepts do not require us to engage in an indepth exploration of big ideas. They may be merely requests for clarification that can be satisfied by a more careful wording or appropriate qualification. On the question whether animals think, for instance, someone might suggest that we had better be clear about what we mean by ‘animals’, too. After all, what is to stop us from straightforwardly saying that some animals think because humans are animals and we think? Presumably, though, the questioner meant to ask whether non-human animals think, and would be prepared to amend the formulation accordingly. Even then, further clarification may be needed. And is the question asking whether non-human animals in general think, or whether any of them do? In any event, clarification should always be carried out as soon as the need arises. It can be useful to keep track of question types and any amendments or subsidiary questions on the board. With the sample question, for instance, I might end up with the following, where ‘F’ means that the question is factual and ‘C’ means that the question is conceptual: any non-human Do animals think? (F) What do we mean by ‘think’? (C)

The following is an exercise in sorting out inquiry questions that I might give to a group of senior secondary students. You might find it useful to try some of the questions for yourself.

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Sorting out inquiry questions We can generally divide inquiry questions into three categories: • factual • evaluative, and • conceptual. Simply put, • a factual question is one that can be answered by uncovering or mustering the appropriate facts; • an evaluative question requires us to consider what would justify certain values or preferences; • a conceptual question asks what we are to understand by certain words or concepts. Sometimes questions that are primarily of one kind involve or imply questions of another kind. For example, even though the question, ‘Can animals think?’ is primarily a factual one, we cannot answer it without first addressing the question ‘What do we mean by think?’, and that is a conceptual question. Sometimes, too, we need to clarify a question before we can answer it, because we are not sure precisely what the question is asking. In the above example, does ‘animals’ refer only to non-human animals? And are we being asked whether animals in general can think or only whether some of them can think? Can you say whether each of the following questions is primarily factual (F), evaluative (V) or conceptual (C)? Where appropriate, identify any matters that require clarification and any implied subsidiary questions of the above three kinds that would also need to be addressed. 1 2 3 4 5 6 7 8 9

Do animals think? Should we never tell a lie? What do we mean by a ‘true friend’? Is the universe infinite? Is euthanasia sometimes justified? Are apples alive? Are bananas still yellow in the dark? What would it mean to say that history is fiction? Is the world in reality nothing like the way it appears?

Answers: (1) F, (2) V, (3) C, (4) F, (5) V, (6) F, (7) F, (8) C, (9) F

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Copyright © Philip Cam 2006

Deductive reasoning is fuelled by the desire to preserve truth when we reason. If we start from some statement or proposition of which we can be certain, then deductive reasoning provides us with a tool that can guarantee that what we conclude will also be true. Provided we stick to the paths it marks out, deduction provides a surefooted way of moving ahead. In these respects, the deductive method is very different from the inquiry method. Inquiry does not make headway by supposing that we have a stock of certain knowledge from which we can derive other truths in turn. Rather, it employs suggestions or hypotheses that can be put to the test, providing us only with a means of ensuring that our conclusions will be more defensible as we move along. Even so, deductive reasoning is a valuable tool in the inquirer’s kit. Implicitly, we use deductive reasoning when we argue that a hypothesis should be rejected because it is not consistent with the evidence, for example, and we use it to explain something when we argue that, given the observed conditions, it follows from our hypothesis. While deductive reasoning has been the mainstay of the discipline known as ‘formal logic’ since the days of Aristotle, modern systems of deduction began to develop only in the late nineteenth century. Aristotelian or syllogistic logic deals with relations between what are known as categorical statements—statements such as ‘All rabbits are furry creatures’ and ‘No furry creatures are things that can fly’. (This is a logician’s somewhat cumbersome way of stating what would more naturally be expressed as ‘No furry creatures can fly’. As we will see shortly, such awkwardness has its uses.) Modern logic starts with logical approximations of words such as ‘not’, ‘and’, ‘or’ and conditional expressions such as ‘if … then …’ and ‘if and only if’, which it defines in terms of patterns of truth and falsehood that arise when they operate on statements. For example, if we conjoin two statements together with ‘and’, we get a conjunction; and a conjunction will be true if both of its conjuncts are true, otherwise it will be false. From such humble beginnings very powerful systems of deduction can be built. You may be relieved to know that I am not about to offer you a systematic introduction to either ancient or modern formal logic. When it comes to discursive classroom inquiry, these systems do not offer sufficient pay-off for all the work required to master them in even an elementary form. Yet it is worthwhile for students to acquire some of the fundamental ideas in formal deductive logic, as well as logical competence in elementary forms of deductive reasoning, by the time they begin secondary school. It is worth understanding Advanced Toolkit—Deductive Reasoning

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that the validity of such reasoning depends on its form rather than its content, for example, and it is certainly worthwhile for students to be able to distinguish between the most basic forms of valid and fallacious reasoning. We can give students an elementary competence with deductive reasoning by paying attention to just a few common forms of reasoning when they occur in discussion, and by making students familiar with these patterns through exercises. I prefer to do this through the most basic and easily discernible forms of what is known as conditional reasoning. First, however, I want to explain the idea that the validity of a deductive argument depends on its form rather than its content. So let us go back to the categorical statements with which I began:

All rabbits are furry creatures. No furry creatures are things that can fly.

At the moment we are not concerned with whether these statements are true, but only with what could be said to follow from them. If the statements are or were true, is there any other statement that would have to be true as well? Once we put it this way, there is an intuitively obvious conclusion that we can draw: No rabbits are things that can fly. Now the deduction of this conclusion from what we may call the above two ‘premises’ can easily be shown, intuitively, to depend not at all on the fact that these statements are about rabbits, furry creatures and things that can fly. They may just as well have been about planets, balls and pyramids, or indeed about anything at all. In order to see this, we only need to replace the relevant words systematically with letters. So let us replace ‘rabbits’ with the letter ‘A’, ‘furry creatures’ with the letter ‘B’ and ‘things that can fly’ with the letter ‘C’. This time we will also put the conclusion under the other two statements and separate it by a line—the equivalent of saying ‘therefore’—to indicate that it has been deduced from them. We may call the resulting schema the ‘form’ of the argument. All A are B. No B are C. No A are C.

I might have demonstrated this with a Venn diagram or some other convention, but I take it that within a few moments nearly everyone can see that the third line follows from the other two just as surely as in the original argument. Yet the choice of letters was arbitrary, even though they were substituted systematically. And since that choice was arbitrary, I may now substitute new words for the

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letters in turn. By substituting, say, ‘whales’, ‘toffee-apples’ and ‘diamonds’, we can derive the following argument: All whales are toffee-apples. No toffee-apples are diamonds. No whales are diamonds.

Once again, it is intuitively easy to see that the conclusion follows from the premises. Any systematic substitution of common nouns for the letters ‘A’, ‘B’ and ‘C’ would have had the same result. So the connection between the premises and the conclusion of the argument does not depend on what the statements are about, but rather on the form of the argument itself. Let me clarify what is meant by saying that the conclusion ‘follows’. In deduction, when we say that the conclusion follows, we mean that it is impossible for the premises to be true and the conclusion to be false. This also allows me to explain the use of the word ‘valid’ when used in deduction. A valid argument is one that gives this guarantee: An argument is said to be valid if and only if it is impossible for all of the premises to be true and the conclusion to be false. Finally, then, we may say that an argument is valid in virtue of its form. Having introduced the idea of the form of an argument and the concept of validity, let us now return to the topic of conditional reasoning. Like the rest of us, children are forever using the conditional, which is commonly expressed in English by ‘if … then …’: • ‘If I am kept in after school, then my mum will throw a fit.’ • ‘Well, if I were you, then I would apologise to Mrs McDonald. Otherwise she’s sure to keep you in.’ There are many variations of this so-called conditional form, including: • implicit terms (‘If she tries to keeps me in, [then] I’ll just leave.’) • implicit conditions (‘Then you’ll get into even more trouble.’) • the substitution for ‘if ’ or ‘then’ of logically equivalent expressions (‘Whenever I get into trouble, my mum throws a fit.’), and • reversal in the order of the clauses (‘My dad throws a fit, if I get into trouble.’) In all of its variations, the conditional consists of an antecedent or ‘if ’ clause and a consequent or ‘then’ clause. A wide array of relationships may be expressed by this means—including conceptual and logical relationships, causal relationships, correlations, temporal sequences and mathematical relationships—and conditional expressions commonly feature in an extensive range of human acts, such as prediction, promising, warning and bargaining. Conditionals express a movement in thought from one condition to another, where one condition is taken to be dependent on the other. Therefore it is the natural form with which to begin reasoning. Not only that, the conditional also lends itself to deductive inference, because in deduction we are saying, in effect, that if the premises are (or were) true, then the conclusion must be (would have to be) true, too. So the conditional is a good vehicle for introducing students to deductive forms of argument. Advanced Toolkit—Deductive Reasoning

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There are two basic forms of valid deductive argument that begin with the conditional. One involves affirming the antecedent and the other denying the consequent. These forms are of great antiquity and traditionally go by their Latin names, which I may as well introduce.

Modus ponens

Modus tollens

If P, then Q P Q

If P, then Q Not Q Not P

Modus ponens Modus ponens provides us with a simple form of reasoning for both prediction and explanation. In prediction, we argue from 1 the supposition that if a given condition obtains, then a certain result can be expected, and 2 the fact that the condition is found to obtain (is observed, or whatever), to the conclusion that the result can be expected. Here is an example: If the pea is not under this cup, then it will be under that one. Ah, huh! The pea is not under this cup. The pea will be under that one.

In explanations using modus ponens, we deduce a statement of the circumstances to be explained from what we already know (have observed, or whatever), together with an explanatory hypothesis. For example: If you eat green bananas, then you’ll have a stomach-ache. You ate green bananas. You have a stomach-ache.

Of course, we usually do not bother to spell things out in this way. If a boy suffered a stomach-ache after he had eaten green bananas, we might explain it simply by saying that it was because he had eaten the bananas. By making the underlying conditional explicit, however, we have drawn attention to the generalisation on which the explanation depends. This can be important because, just as in science, the generalisations that people rely on in everyday explanation are often in need of scrutiny. This is particularly true when it comes to explanations that rely on questionable attitudes and values. Explanations that appeal to racist and other prejudices provide all too many examples. For example, for a child to say that some newly arrived immigrants did something ‘stupid’ because they are migrants, might well rest on the prejudicial assumption that migrants are by nature stupid. (By the way, the generalisation that ‘All migrants are stupid’ is logically equivalent to ‘If someone is a migrant, then they are stupid.’)

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Modus tollens Now let us look at some examples of modus tollens. We all know the story of the princess and the frog. Having been turned into a frog by an evil spell, the prince can be changed back again only by the kiss of a beautiful young princess. We may imagine the following exchange between the prince and the princess: Princess: You’re not a handsome young prince. You’re just a slimy old frog. Prince: But I am a prince, I tell you. Princess: If you’re a prince, then I’m a roast duck.

Here the princess is claiming that the frog is obviously not a prince, and she implicitly appeals to modus tollens. That is to say, she reasons as follows: If you’re a prince, then I’m a roast duck. Obviously, I’m not a roast duck. You’re not a prince.

Young children would have no difficulty in following the princess’s reasoning, and therefore in understanding modus tollens. In fact, they are probably already familiar with some version of the princess’s argument. My father used to say to me, ‘If that’s true, then I’m a monkey’s uncle.’ He obviously expected me to draw the intended conclusion, and therefore to follow his reasoning. For a second example, we may turn to hypothesis-testing in science. We test an experimental hypothesis by arguing that if the hypothesis is true, then we should obtain certain observable results. And if we do not obtain those results, then doubt is cast on the hypothesis. The example is drawn from primary school students who are testing the hypothesis that it is after mid-day by observing changes in the length of shadows: If it is after mid-day, then the shadows should be lengthening. The shadows are not lengthening, but shortening. It is not after mid-day.

Associated fallacies These two forms of valid reasoning have invalid counterparts. To say that they are invalid is simply to say that they are not valid, or in other words that the truth of the conclusion is not guaranteed by the truth of the premises. These ‘fallacies’, as they are known, have the following forms: Fallacy of denying the antecedent

Fallacy of affirming the consequent

If P, then Q Not P Not Q

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The problem with the ‘Fallacy of denying the antecedent’ is that conditions other than those stated by the antecedent may be sufficient for the fulfilment of the consequent. Thus, suppose that one were to argue as follows: If you build your house of sticks, then the wolf will be able to blow it down. You do not build your house of sticks. The wolf will not be able to blow it down.

The conclusion does not follow, of course, because it is possible for the premises to be true and the conclusion to be false, which is, of course, what happens in the story when you build your house of straw. Fallacious reasoning can be very dangerous. The problem with the ‘Fallacy of affirming the consequent’ is, once again, that conditions other than those stated by the antecedent might be sufficient to ensure the consequent. Here is an example: If the miller’s daughter can spin straw into gold, then there’ll be gold in the morning. There is gold in the morning. The miller’s daughter can spin straw into gold.

Once again, we can see that the argument is clearly invalid. The premises can be true while the conclusion is false—which is exactly what happens when it turns out to be Rumplestiltskin rather than the miller’s daughter who can perform the trick. We fall for the fallacy of affirming the consequent whenever we fail to consider possibilities other than the one we had in mind for explaining the known condition. The danger in doing so is that we will think that what we know or can observe confirms our theories, when those facts are really subject to a quite different explanation. Like the miller’s daughter, we can be in for a long, rough ride when this happens. I have set out these rudiments of deductive reasoning in the hope that you will consider it worthwhile introducing them to students. As mentioned earlier, by paying attention to such reasoning when it occurs in discussion and giving students associated exercises, you will be helping them to learn to reason well, and to avoid at least some invalid forms of reasoning that can prove to be both expensive and dangerous. In the concluding exercise you are asked to decide whether a given argument is valid or not. It is the kind of exercise that might be given to Year 6 or 7 students. I have included answers at the bottom of the page, but do avoid looking at them until you have satisfied yourself. If you manage to get all of the answers right, I can assure you that you have learnt something. When these examples have been presented to groups of untutored teachers, the results have been close to what one might expect by chance.

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Which of the following arguments are valid and which are not? 1

If there is a red sky tonight, then tomorrow will be a shepherd’s delight. There is a red sky tonight. Tomorrow will be a shepherd’s delight.

2

If you eat an apple a day, then you will keep the doctor away. You do not eat an apple a day. You will not keep the doctor away.

3

If it is good for the goose, then it is good for the gander. It is good for the gander. It is good for the goose.

4

If people were meant to fly, then they would be born with wings. People are not born with wings. People were not meant to fly.

Answers: 1 Valid (modus ponens) 2 Invalid (denying the antecedent) 3 Invalid (affirming the consequent) 4 Valid (modus tollens) Twenty Thinking Tools Copyright © Philip Cam 2006 Advanced Toolkit—Deductive Reasoning

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Whenever someone argues for a claim by offering a number of reasons for it or by engaging in a chain of reasoning, we need to be clear about the form of support that is being presented. If the relationship between a claim and the reasons being offered in support of it is not clear to us, then we are not able to properly assess the case that is being made. A Reasoning Diagram is a simple tool for inspecting someone’s reasoning in order to become clear about the relation between claims and supporting reasons. It is therefore a tool that often comes in handy when reasoning occurs in the conduct of inquiry. I particularly recommend its use in the senior secondary school. The basic convention of a Reasoning Diagram is an arrow that leads from a reason given in support of some claim to the claim that it supports. In the simplest case, a Reasoning Diagram consists of just one such arrow connecting a reason to the claim that it supports. supporting reason

claim supported

If arguments were always so simple there would be no need for Reasoning Diagrams. The need may arise, however, when two or more reasons are offered in support of a claim. In that case we need to be clear as to whether each reason offers independent support for the claim or whether it is only their combined force that offers the support. This may turn out to be important in assessing the argument that is being put, because in one case we may still have been given some good reasons for accepting the claim even if others do not stand up to scrutiny, but in another case the whole argument may fall with the dismissal of any one of its supporting reasons. Let us examine a couple of examples. To keep things simple, I have focused on arguments where just two reasons are given in support of some claim. First, suppose someone were to argue that where asylum-seekers enter the country unannounced, it is right for the government to apply a policy of

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mandatory detention. The reasons given for this might be that it is easier to deport them if their application for refugee status fails, and that it serves as a deterrent to others who might contemplate similar action. These two reasons are clearly independent of one another. If one reason collapses, the argument can still rest on the other. The overall argument will be weaker, of course, but this is only to say that the total weight of such an argument is the sum of the weights of each of the reasons that are given. In a Reasoning Diagram, each independent reason is presented with an arrow showing its support for the claim.

acts as a deterrent to others

allows ease of deportation

A government policy of mandatory detention is right.

As the diagram indicates, it is generally not necessary to fully transcribe statements of the reasons given during classroom discussion. Provided that we are clear about what statements are being made, phrases will usually suffice. The statements do need to be clear, of course. In the present case, we may want to know whether ‘a policy of mandatory detention’ refers to a specific government policy or to a general conception, for example, and it may not be clear what is meant by saying that such a policy is ‘right’. Now suppose that someone were to argue that a government policy of mandatory detention is wrong, because it is inconsistent with international conventions on human rights, which the government has a duty to uphold. We may need considerable clarification here. For instance, to what international conventions on human rights is the speaker referring? And is the duty they are supposed to imply a legal responsibility or a moral one? Such clarifications aside, however, it is important to note that the word ‘which’ does not qualify the conventions spoken of, but rather acts as a conjunction. It is being argued that mandatory detention is inconsistent with certain international conventions and that governments have a duty to uphold those conventions. The statement about government duty is not an independent reason for objecting to a policy of mandatory detention, however, but is meant to make its alleged inconsistency with international conventions something that the government should not ignore. In order to distinguish the form of this argument from that of the previous one, we may adopt the convention of using the plus sign (+) together with a bar and a single arrow to indicate the interdependence of the reasons that are offered in support of the claim. We will call these reasons ‘dependent’ reasons as opposed to the ‘independent’ reasons in the first example.

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inconsistent with international conventions on human rights

+

governmental duty to uphold those conventions

A government policy of mandatory detention is wrong.

It is obvious that many other patterns are possible, including using the same reason in support of different claims, and using claims for which support has been given as support for yet other claims, in turn. The following looks at an example of the latter kind. Suppose that the person who was arguing in favour of a mandatory detention policy was challenged about whether such a policy is in fact an effective deterrent. That person might then claim that the number of unannounced arrivals has fallen in countries where such a policy has been adopted, which has not been the case elsewhere. Right now we are not concerned with the truth of these claims or how they might be verified, but only with the structure of the argument given. Two points need to be made. First, support is being provided for one of the reasons previously given. That is to say, we have buttressing of an existing reason. Secondly, this further support consists of two claims that depend on each other to provide a reason for accepting that the policy acts as a deterrent. The entire argumentative structure can therefore be represented as follows: reduction of arrivals where the policy is in place

+

no reduction of arrivals where the policy is not in place

acts as a deterrent to others

allows ease of deportation

A government policy of mandatory detention is right.

Reasoning Diagrams are not necessary when the relations between supporting and supported claims is evident to those engaged in the discussion, and to habitually set them out in this way would be unduly laborious. However, they can be an invaluable tool for helping those putting the argument to become clear about just what argument they are advancing, as well as an aid to clear-headed critical discussion of the actual argument put forward.

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In conducting inquiry we investigate assumptions in two different contexts. On the one hand, we attend to assumptions that appear to be mistaken or questionable. This is a process of exposing things that have been taken for granted and probing them to see whether our concerns are justified. On the other hand, we also sometimes tentatively make an assumption for the sake of argument. This is to use an assumption as a tool. We deliberately make an assumption in order to see what follows. This is usually because we are attempting to find our way between rival suppositions or hypotheses. If we were to suppose this, then certain consequences would follow; whereas were we to suppose that, then things would be different. Or when considering some particular matter, we might make an additional assumption and then check to see whether that would make a significant difference to how things turn out.

Uncovering assumptions While the assumptions that we uncover are not themselves tools of inquiry, we can use our tools to help uncover them. In particular, we can use Reasoning Diagrams to help reveal what is being assumed when someone argues for a conclusion that does not seem to follow automatically from their premises. Since that is common in everyday reasoning, this move has the potential for wide application. Let us see what is involved by working our way through an example. Suppose someone were to argue that democratic government is the best form of government because it maximises freedom. We may set this out as a Reasoning Diagram. Democratic government maximises freedom. Democratic government is the best form of government.

Many questions arise here, including: What is meant by ‘freedom’? By what means can we make relative judgements about its measure? Is it true that, of all forms of government, democracy promotes freedom more than any other? Does the person who put this argument mean to refer to all possible forms of government or only to actual forms of government? We would obviously have a lot of work to do in order to evaluate this argument. Advanced Toolkit—Assumptions

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Aside from these things, however, we can also sense that the conclusion does not follow from the speaker’s premise in the way that the conclusion does follow from the premises of a valid deductive argument. There is, we might say, a ‘gap’ between the reason given and the claim it is meant to support. This indicates that something is being assumed. The most plausible assumption is the thing that best plugs the gap. What we are looking for, of course, is not just any means of plugging the gap. The presenter might come up with additional independent premises, for instance. But that would be to present further argument. We need to stick to the argument given, if we wish to see what it assumes. In fact, we need to look for some dependent reason that is already implicitly assumed. That is to say, we are looking to replace the question mark in the following Reasoning Diagram:

Democratic government maximises freedom.

+

?

Democratic government is the best form of government.

There are various ways of plugging this gap. For example, we could always make the argument deductively valid by converting it to modus ponens. This involves merely the addition of a conditional statement that allows us to validly deduce the conclusion. Democratic government maximises freedom.

+

If a form of government maximises freedom, then it is the best form of government.

Democratic government is the best form of government.

This manoeuvre is not very informative. In effect, all it tells us is that the original argument depends on the assumption that the best form of government is one which maximises freedom. But we don’t need to complete a Reasoning Diagram in order to work that out. We know it already. In order to see more deeply into what is being assumed, we need to plug the gap in the original argument with something more informative. For example, consider a couple of alternative suggestions for plugging the gap:

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Nothing else matters beside freedom when it comes to good government. Freedom is to be prized above all other things that government can deliver.

These statements are equally good at plugging the gap that originally existed between the premise and the conclusion. When added to the Reasoning Diagram, either one would allow us to deduce the conclusion. Both of them are also more informative than our first attempt to plug the gap, because they tell us why the best form of government is one that maximises freedom. They supply explanations as to why the claim that democratic government maximises freedom may be supposed to imply the conclusion that it is the best form of government. One statement says that this is because, when it comes to good government, nothing else matters beside freedom. The other says that it is the best form because freedom is the most valuable thing that government can deliver. These are substantial claims and they are obviously not equivalent. It would make a difference to suppose that the argument depended on one statement rather than the other. Finally, we need to acknowledge that some explanations are more plausible than others. By saddling the argument with the claim that nothing beside freedom is of value, we would be making it depend on an obviously false assumption. If this were what the presenter had in mind, the argument would not be worthy of further consideration. Our second suggestion fares much better in this respect. While it is certainly debatable whether freedom is to be prized above all other things that governments can deliver, it is not an altogether implausible suggestion. With further investigation, it might even turn out to be an acceptable one. So plausibility provides a third criterion for fixing on a given assumption. We may now summarise the things to be taken into account when attempting to uncover a premise that is implicit in the presentation of an argument. If we are going to stick with the original argument and make the most of it, we need to look for a claim that could plug the gap between the premises and the conclusion of a Reasoning Diagram that is: • a dependent premise • explanatory or informative • the most plausible alternative.

Making and testing assumptions Let us return now to assumptions as tools. To tentatively assume something in an inquiry is to make a supposition for the purposes of testing out an idea. It is equivalent to suggesting a hypothesis. We temporarily take the supposition on board in order to see whether it can illuminate or resolve a problem or difficulty. Given this, nothing in particular needs to be said about making assumptions that does not apply to hypotheses in general. An assumption is an investigative tool the value of which lies in what it can help us to predict and explain.

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In testing an assumption, we look to its implications. We want to know what it implies and whether those implications are acceptable in one way or another. This means that testing an assumption involves hypothetical reasoning: If the assumption is correct, then things should be thus-andso. From a logical point of view, the rejection of an assumption involves reasoning by modus tollens: If the assumption were correct, then things would have been thus-and-so. But things turned out not to be thus-and-so. So the assumption was not correct. Things are a little more complicated when an assumption turns out to be justified. An assumption may straightforwardly be proved to be correct, or it may only be justified to the extent that it conforms to the evidence we have so far and we have no other cause for rejection. ‘We assumed that it would rain, and so it did.’ Here our assumption proved to be correct and that is the end of the matter. ‘Mr Treasurer, are we justified in assuming that the economy will improve?’ ‘Yes, all the signs are there.’ Here the assumption is justified only to the extent that those signs have been predictive in the past, and provided that what the treasurer says about the signs is true. Even if justified in the context, our assumption might not be correct. To think that it must, is to fall for the fallacy of affirming the consequent: ‘If the economy is about to improve, then there should be such-and-such signs. All the signs are there. So the economy is about to improve.’ This argument is not deductively valid, as we saw. It is possible for the premises to be true and the conclusion false. Note: See Deductive Reasoning (pp. 95–101) for more about modus ponens, modus tollens and the fallacy of affirming the consequent.

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Strictly speaking, a disagreement involves a difference of opinion. It always involves some proposition that one party affirms but another denies. If one student or group of students is merely inclined to support a given view, while another student or group is leaning towards a contrary view, then there is only a potential disagreement; and if students are merely exploring the pros and cons of some claim, then we do not even have that. However, the technique introduced below for exploring disagreements can be used in these contexts as well. All it requires is a claim that someone might argue either for or against, and reasons that might be given in support of either stance. This tool is a variant of the Reasoning Diagram introduced earlier. Just as Reasoning Diagrams are based on the relation between a claim and a reason given in support, a Disagreement Diagram is based on reasons that are given both for and against some claim. We already have the convention of using an arrow to indicate a relation of support between a reason and a claim, and we may adopt the further convention of using a ‘bow and arrow’ to indicate a reason given to reject that claim. Hence the simplest case of a Disagreement Diagram would consist of just one arrow and one bow and arrow pointing at a claim that is in dispute.

supporting reason

reason for rejection

claim

When people express a difference of opinion, however, they are more often not only disputing some claim, but also arguing in favour of incompatible claims. This would be the case if, for example, I am arguing that we should go away for the weekend, while you are arguing that we should stay at home. Given that we can’t both stay at home for the weekend and go away, we are arguing in favour of incompatible propositions, each of which excludes the other. We may represent the situation as follows:

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supporting reason

We should go away.

supporting reason

We should stay at home.

In such cases we need to be sure that we really do have a disagreement on our hands. If I were arguing that we should go to the mountains and you were arguing that we should go to the beach, then it may be that we are not actually making incompatible suggestions. Depending on the circumstances, we might be able to do both. So we did not really have a disagreement to begin with, but only confusion as to the implications of our proposals. So before launching into a Disagreement Diagram, do check to see that the ‘disagreement’ really does conform to one or other of the above patterns. There are two basic steps in beginning to construct a Disagreement Diagram: 1 Identify the claim or pair of incompatible claims on which the disagreement rests. In the case of a single claim, it will form the conclusion of the proponent’s argument, just as its denial will be the conclusion of the opponent’s argument. In the example given to illustrate how to use Reasoning Diagrams to uncover Assumptions, we would begin with the following single claim: Democratic government is the best form of government.

In the case of incompatible claims, the arguments will have the respective claims as their conclusions. Going back to the example used to introduce Reasoning Diagrams, we would begin to construct a Disagreement Diagram as follows:

A government policy of mandatory detention is right.

A government policy of mandatory detention is wrong.

This seems to be the natural way to represent the disagreement, as arising from support for incompatible claims rather than being directly a dispute about the acceptability of a single claim. 2 Next we build the supporting arguments for both sides of the argument, using the tool of Reasoning Diagrams. In other words, the Disagreement Diagram will be a combination of the relevant Reasoning Diagrams. In terms of the earlier disagreement about mandatory detention, in the first round of discussion we would have produced the following Disagreement Diagram.

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acts as a deterrent

allows ease of deportation

A government policy of mandatory detention is right.

inconsistent with human rights conventions

+

governmental duty to uphold the conventions

A government policy of mandatory detention is wrong.

Actual disagreements are often more complex than my simple sketch suggests. It is very common for people who disagree with one another about some claim to also disagree about the relevance, strength, truth or acceptability of one or more of the reasons given in support of the opposing view. While this adds further complexity to a diagram, it does not introduce anything other than further layers of argument that end with a bow and arrow pointed at the claim that is an additional source of dispute. In the example above, if someone were to argue that the kind of policy under discussion was not actually inconsistent with international conventions on human rights, for instance, then the reasons or evidence they assembled would constitute a counterargument whose bow and arrow would be directed at the premise claiming that the policy is inconsistent. further counterargument

acts as a deterrent

allows ease of deportation

A government policy of mandatory detention is right.

inconsistent with human rights conventions

+

governmental duty to uphold the conventions

A government policy of mandatory detention is wrong.

Finally, when constructing a Disagreement Diagram, students may disagree about whether various inferences really can be drawn from reasons that are given. Unless it is being claimed that a piece of reasoning is simply fallacious (see Deductive Reasoning, pp. 95–101), such disagreements are about whether Advanced Toolkit—Disagreement Diagrams

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some reason given in support of a claim rests on one or more ungrounded assumptions. In that case, first of all we need to uncover those assumptions (see Assumptions, pp. 105–08) and add them to the diagram. Then we can see whether they are subject to objection by further counterargument. While such diagrams can become quite complex, they will be no more complicated than the arguments actually being put, and they will actually assist students to reason more carefully and constructively when they explore their disagreements.

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Notes

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Further reading Baron, Joan Boykoff & Sternberg, Robert J (eds) 1987, Teaching Thinking Skills: Theory and Practice, WH Freeman and Company, New York. Bennett, Deborah J 2004, Logic Made Easy, WW Norton & Company, New York. Cam, Philip 1995, Thinking Together: Philosophical Inquiry for the Classroom, Hale & Iremonger/PETA, Sydney. Dewey, John 1966, Democracy and Education, The Free Press, New York. Dewey, John 1997, How We Think, Minolta, Dover Publications Inc, New York. Fisher, Robert 1993, Teaching Children to Think, Simon and Schuster Education, Hemel Hempstead. Haynes, Joanna 2002, Children as Philosophers, Routledge Falmer, London. Kelley, David 1988, The Art of Reasoning, Norton and Company, New York. Lipman, Matthew 1988a, Philosophy Goes to School, Temple University Press, Philadelphia. Lipman, Matthew 2003, Thinking in Education, 2nd edition, Cambridge University Press, New York. Lipman, Matthew, Sharp, Ann M & Oscanyan, Frederick S 1980, Philosophy in the Classroom, Temple University Press, Philadelphia. Matthews, Gareth B 1980, Philosophy and the Young Child, Harvard University Press, Cambridge, Mass. Matthews, Gareth B 1984, Dialogues with Children, Harvard University Press, Cambridge, Mass. Paul, Richard 1994, Critical Thinking, Hawker Brownlow Education, Highett, Victoria. Pritchard, Michael S 1985, Philosophical Adventures with Children, University Press of America, Lanham, MD. Splitter, Laurance J & Sharp, Ann M 1995, Teaching for Better Thinking: The Classroom Community of Inquiry, Australian Council for Educational Research, Camberwell, Victoria. Thouless, Robert H 1974, Straight and Crooked Thinking, Pan Books, London. Vygotsky, Lev 1978, Mind in Society: The Development of Higher Psychological Processes, Harvard University Press, Boston. Vygotsky, Lev 1986, Thought and Language, Revised edition, MIT Press, Boston. Wilks, Sue 1995, Critical and Creative Thinking: Strategies for Classroom Inquiry, Eleanor Curtain, Armadale, Victoria. Wilson, John 1971, Thinking with Concepts, Cambridge University Press.

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Classroom resources Cam, Philip 1993a, Thinking Stories 1: Philosophical Inquiry for Children, Hale & Iremonger, Sydney. Cam, Philip 1993b, Thinking Stories 1: Teacher Resource/Activity Book, Hale & Iremonger, Sydney. Cam, Philip 1994a, Thinking Stories 2: Philosophical Inquiry for Children, Hale & Iremonger, Sydney. Cam, Philip 1994b, Thinking Stories 2: Teacher Resource/Activity Book, Hale & Iremonger, Sydney. Cam, Philip 1997a, Thinking Stories 3: Philosophical Inquiry for Children, Hale & Iremonger, Sydney. Cam, Philip 1997b, Thinking Stories 3: Teacher Resource/Activity Book, Hale & Iremonger, Sydney. Cam, Philip 1998, Twister, Quibbler, Puzzler, Cheat, Hale & Iremonger, Sydney. de Hann, Chris, MacColl, San & McCutcheon, Lucy 1995, Philosophy with Kids, Longman, South Melbourne, Victoria. Golding, Clinton 2002, Connecting Concepts, Australian Council for Educational Research, Camberwell, Victoria. Lipman, Matthew 1981, Pixie, Institute for the Advancement of Philosophy for Children, Montclair State College, Montclair, NJ. Lipman, Matthew 1983, Lisa, University Press of America, Lanham, MD. Lipman, Matthew 1986, Kio & Gus, Revised edition, Institute for the Advancement of Philosophy for Children, Montclair State College, Upper Montclair, NJ. Lipman, Matthew 1988b, Elfie, Institute for the Advancement of Philosophy for Children, Montclair State College, Upper Montclair, NJ. Lipman, Matthew 1992, Harry Stottlemeier’s Discovery, Australian adaptation prepared by Laurance Splitter, Australian Council for Educational Research, Camberwell, Victoria. Lipman, Matthew & Gazzard, Ann 1988, Getting Our Thoughts Together: instructional manual to accompany Elfie, Institute for the Advancement of Philosophy for Children, Montclair State College, Upper Montclair, NJ. Lipman, Matthew & Sharp, Ann Margaret 1983, Ethical Inquiry: instructional manual to accompany Lisa, University Press of America, Lanham, MD. Lipman, Matthew & Sharp, Ann Margaret 1984, Looking for Meaning: instructional manual to accompany Pixie, University Press of America, Lanham, MD. Lipman, Matthew & Sharp, Ann Margaret 1986, Wondering at the World: instructional manual to accompany Kio & Gus, University Press of America, Lanham, MD. Lipman, Matthew, Sharp, Ann Margaret & Oscanyan, Frederick S 1984, Philosophical Inquiry: an instructional manual to accompany Harry Stottlemeier’s Discovery, 2nd edition, University Press of America, Lanham, MD. Bibliography

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Murris, Karen & Haynes, Joanna 2000, Storywise, www.dialogueworks.co.uk Sharp, Ann M 2000, Geraldo, Australian Council for Educational Research, Camberwell, Victoria. Sharp, Ann M & Splitter, Laurance 2000, The Doll Hospital, Australian Council for Educational Research, Camberwell, Victoria. Sharp, Ann M & Splitter, Laurance 2000, Making Sense of My World: a teachers companion to The Doll Hospital, Australian Council for Educational Research, Camberwell, Victoria. Sharp, Ann M & Splitter, Laurance 2000, Discovering Our Voice: a teachers companion to Geraldo, Australian Council for Educational Research, Camberwell, Victoria. Sprod, Tim 1993, Books into Ideas, Hawker Brownlow Education. Sutcliffe, Roger, Newswise. www.dialogueworks.co.uk/newswise

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