K Y Thinking Skills M Thinking Skills C Critical Thinking and Problem Solving John Butterworth and Geoff Thwaites Second edition John Butterworth and Geoff Thwaites Cover This lively coursebook encourages students to develop more sophisticated and mature thinking processes by learning speci c, transferable skills independent of subject content which assist con dent Thinking Skills engagement in argument and reasoning. As well as giving a thorough grounding in critical thinking and problem solving, the book discusses how to analyse and evaluate arguments, Critical Thinking and Problem Solving manipulate numerical and graphical information and develop a range of Second edition skills including data handling, logic and reasoning. The second edition of the book has been substantially updated with new and revised content throughout. The only endorsed coursebook offering complete coverage of the Cambridge AS and A Level Thinking Skills syllabus, this resource also contains extensive extra material to cover a wide range of related awards. Features include: • clearly focused and differentiated critical thinking and problem solving Thinking Skills units that provide complete coverage of the Thinking Skills syllabus and beyond • a range of stimulating student activities with commentaries to develop analytical skills • summary of key concepts at the end of each chapter to review learning Butterworth and Thwaites • end-of-chapter assignments to reinforce knowledge and skills, with answers at the back for self-assessment • a mapping grid to demonstrate the applicability of each unit to awards including Critical Thinking, BMAT and TSA. Thinking Skills is written by two experienced examiners, who have produced a lively and accessible text which all students of Thinking Skills will nd invaluable. Visit education.cambridge.org/cie for information on our full range of Cambridge International A Level titles including e-book versions and mobile apps. John Butterworth and Geoff Thwait John Butterworth and Geoff ISBN 978-1-107-66996-3 9781107606302 Second edition John Butterworth and Geoff Thwaites Thinking Skills Critical Thinking and Problem Solving Second edition CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK www.cambridge.org Information on this title: www.cambridge.org/9781107606302 © Cambridge University Press 2005, 2013 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2005 Second edition 2013 Printed in Italy by L.E.G.O. S.p.A. 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Contents Unit 1 Thinking and reasoning 1.1 Thinking as a skill 1 1.2 An introduction to critical thinking 7 1.3 Solutions not problems 13 Unit 2 Critical thinking: the basics 2.1 Claims, assertions, statements 16 2.2 Judging claims 21 2.3 Argument 28 2.4 Identifying arguments 33 2.5 Analysing arguments 38 2.6 Complex arguments 43 2.7 Conclusions 50 2.8 Reasons 58 2.9 Assumptions 63 2.10 Flaws and fallacies 70 Unit 3 Problem solving: basic skills 3.1 What do we mean by a ‘problem’? 79 3.2 How do we solve problems? 82 3.3 Selecting and using information 86 3.4 Processing data 90 3.5 Finding methods of solution 93 3.6 Solving problems by searching 98 3.7 Recognising patterns 102 3.8 Hypotheses, reasons, explanations and inference 106 3.9 Spatial reasoning 112 3.10 Necessity and sufficiency 116 3.11 Choosing and using models 119 3.12 Making choices and decisions 123 Unit 4 Applied critical thinking 4.1 Inference 126 4.2 Explanation 137 4.3 Evidence 144 4.4 Credibility 150 4.5 Two case studies 156 4.6 Critical thinking and science 163 Contents iii 4.7 Introducing longer arguments 170 4.8 Applying analysis skills 177 4.9 Critical evaluation 183 4.10 Responding with further argument 191 4.11 A self-assessment 195 Unit 5 Advanced problem solving 5.1 Combining skills – using imagination 205 5.2 Developing models 211 5.3 Carrying out investigations 220 5.4 Data analysis and inference 225 Unit 6 Problem solving: further techniques 6.1 Using other mathematical methods 231 6.2 Graphical methods of solution 235 6.3 Probability, tree diagrams and decision trees 240 6.4 Have you solved it? 246 Unit 7 Critical reasoning: Advanced Level 7.1 Conditions and conditionals 249 7.2 Soundness and validity: a taste of logic 254 7.3 Non-deductive reasoning 262 7.4 Reasoning with statistics 269 7.5 Decision making 279 7.6 Principles 287 7.7 An argument under the microscope 295 7.8 Critical writing 301 Answers to assignments 311 Appendix 342 Acknowledgements 344 Index 345 iv Contents Unit 1 Thinking and reasoning 1.1 Thinking as a skill This book is about thinking. But it is not about there are advanced skills like gymnastics or any thinking. It is about those kinds of woodwork or piano playing. It doesn’t make thinking that take conscious effort, and which much sense to talk about jumping ‘well’ can be done well or badly. Most of our unless you mean jumping a significant thinking takes little or no conscious effort. We distance, or clearing a high bar, or just do it. You could almost say that we think somersaulting in mid-air and landing on without thinking! If I am asked whether I your feet. There has to be a degree of would like coffee or tea, I don’t have to challenge in the task. But even when the exercise skill to reply appropriately. Similarly if challenge is met, there is still more to be said I am asked a factual question, and I know the about the quality of the performance. One answer, it takes no skill to give it. Expressing a gymnast may look clumsy and untidy, preference or stating a fact are not in another perfectly controlled and balanced. themselves thinking skills. There are language Both have performed the somersault, but one and communication skills involved, of course, has done it better than the other: with more and these are very considerable skills in their economy of effort, and more skilfully. own right. But they are contributory skills to The first of these two criteria also applies to the activities which we are calling ‘thinking’. thinking. Once we have learned to count and This distinction is often made by assigning add, tell the time, read and understand a text, some skills a ‘higher order’ than others. Much recognise shapes, and so on, we do these work has been done by psychologists, things without further thought, and we don’t educationalists, philosophers and others to really regard them as skilled. You don’t have classify and even rank different kinds of to think ‘hard’ unless there is a hard problem thinking. Most would agree that activities to solve, a decision to make, or a difficult such as analysis, evaluation, problem solving concept to understand. So, as with physical and decision making present a higher order of performance, we judge thinking partly by the challenge than simply knowing or recalling or degree of challenge posed by the task. If a understanding facts. What distinguishes student can solve a difficult problem, within higher orders of thinking is that they apply a set time, that is usually judged as a sign of knowledge, and adapt it to different purposes. greater skill than solving an easier one. They require initiative and independence on However, when it comes to assessing the the part of the thinker. It is skills of this order quality of someone’s thinking, matters are that form the content of this book. more complicated. Mental performance is Skills are acquired, improved, and judged largely hidden inside a person’s head, unlike by performance. In judging any skill, there physical performance which is very visible. If are two key criteria: (1) the expertise with two students give the same right answer to a which a task is carried out; (2) the difficulty of question, there is no telling from the answer the task. We are very familiar with this in the alone how it was reached. One of the two case of physical skills. There are basic skills may simply have known the answer, or have like walking and running and jumping; and learned a mechanical way to obtain it – or 1.1 Thinking as a skill 1 even just guessed it. The other may have to suggest that there are two distinct ways of worked it out independently, by reasoning thinking: cold hard reason on one hand and and persistence and imagination. Although free-ranging creativity on the other. In fact, the difference may not show from the answer there is so much overlap and interdependence given, the second student scores over the first between the two that it is very difficult to say in the long term, because he or she has the where one begins and the other ends. Clearly ability to adapt to different challenges.