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Mathematics for Dyslexics Including Dyscalculia Mathematics for Dyslexics Including Dyscalculia Third Edition Mathematics for Dyslexics Including Dyscalculia Third Edition STEVE CHINN AND RICHARD ASHCROFT John Wiley & Sons, Ltd Copyright 2007 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxed to (+44) 1243 770620. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 6045 Freemont Blvd, Mississauga, ONT, L5R 4J3, Canada Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data: Chinn, Stephen J. Mathematics for dyslexics : Including dyscalculia, Third Edition / Steve Chinn, Richard Ashcroft. p. cm. ISBN 0-470-02692-8 1. Mathematics—Study and teaching. 2. Dyslexic children—Education. I. Ashcroft, J. Richard. II. Title. QA11.2.C47 2006 371.91 44—dc22 2006011783 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-13: 978-0-470-02692-2 ISBN-10: 0-470-02692-8 Typeset in 10/12 Sabon by Laserwords Private Limited, Chennai, India Printed and bound in Great Britain by TJ International, Padstow, Cornwall This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production. This third edition is especially dedicated to the memory of Dorian Yeo Contents Foreword to Second Edition xiii Chapter 1 1 Dyscalculia, Dyslexia and Mathematics Introduction 1 Definitions of Dyslexia 2 Dyscalculia 5 The Nature of Mathematics 13 Chapter 2 17 Factors that may Contribute to Learning Difficulties in Mathematics Potential Areas of Difficulty in Learning Mathematics 17 General Principles of Intervention 33 Summary 35 Chapter 3 37 Cognitive (Thinking) Style in Mathematics Introduction 37 Qualitative and Quantitative Style 38 Cognitive (Thinking) Style in the Classroom Grasshoppers (Intuitive/Answer Oriented) and Inchworms (Step by Step/Formula Oriented) 40 Examples 42 Summary 48 vii viii Contents Chapter 4 49 Testing and Diagnosis A Diagnostic Test Protocol 51 Structure of the Diagnostic Protocol 52 Attitude and Anxiety 59 Thinking Style or Cognitive Style 60 Summary of the Test Protocol 60 Testing for Dyscalculia 60 Chapter 5 61 Concept of Number Introduction 61 Early Recognition of Numbers and Their Values 62 The Language of Mathematics 63 Early Number Work 63 Visual Sense of Number 66 Visual Clues to the Number Concept 67 Number Bonds 68 Place Value 69 Number Bonds for 10 76 Numbers near 10, 100 or 1000 77 Summary 80 Chapter 6 81 Addition and Subtraction: Basic Facts Introduction 81 Strategies for Learning/Remembering the Addition and Subtraction Facts 83 Summary 89 Subtraction Facts 89 Extension 90 Chapter 7 91 Times Tables Introduction 91 Rote Learning with Audio Recorders and Computers 92 Learning by Understanding 93 The Commutative Property 96 Learning the Table Square 98 Summary 115 Contents ix Chapter 8 117 Computational Procedures for Addition and Subtraction Estimation 118 Addition 118 Teaching Subtraction as a Separate Exercise 127 Chapter 9 133 Multiplication Introduction 133 The Special Case of Multiplying by 10 and Powers of 10 133 Multiplication 136 Estimation 142 Extension 143 Chapter 10 145 Division Introduction 145 Introduction to Division 146 Estimating 152 Division by Powers of 10 154 Division by Multiples of Powers of ten 154 Conclusion 155 Chapter 11 157 Fractions, Decimals and Percentages: An Introduction Introduction 157 Fractions 157 Decimals 167 Percentages 176 A Global Model for Percentages, Fractions and Decimals 176 A Global Exercise with Fractions, Percentages and Decimals 184 Chapter 12 185 Operating with Fractions Introduction 185 Making Segment Sizes the Same 185 Comparing Fractions 188 Combining Fractions 191 Adding Fractions 192 Subtracting Fractions 197 x Contents Combined Additions and Subtractions 201 Multiplying by Fractions 202 Multiplying Mixed Fractions 205 Dividing with Fractions 207 Chapter 13 213 Decimals Introduction 213 Addition and Subtraction 213 Multiplication and Division by Powers of 10 216 Division of Decimals 223 Summary 229 Chapter 14 231 Percentages Introduction 231 An Image of Percentage 231 Summary 236 Chapter 15 237 Time What are the Potential Problems with Time? 237 Reading the Time 239 Time Problems 243 Summary 247 Chapter 16 249 Teaching the Full Curriculum Introduction 249 Some General Principles 250 Teaching the Other Parts of the Curriculum 256 Combining the Parts of the Curriculum 261 Summary 264 Chapter 17 265 Attacking and Checking Questions Practice Examples 265 Preliminary Checks 266 Attacking Questions 268 Methods of attacking questions 268 Checking 276 Contents xi Chapter 18 281 Important Elements of a Teaching Programme Introduction 281 Consider the Pupils’ Needs 281 The Structure of the Course 282 Classroom Management: Making the Lessons Suit the Pupils 286 Evolving Expectations and Emphases 287 Internal Assessment 291 GCSE Examinations 293 Summary 294 Appendices 295 Appendix 1: Books, Journals, Tests and Games 296 Appendix 2: Teaching Materials 301 References 303 Index 311 Foreword to Second Edition The first edition of ‘Mathematics for Dyslexics: A Teaching Handbook’ by Steve Chinn and Richard Ashcroft put a previously neglected area of education on the map for those concerned with dyslexia. Teachers have found much support and inspiration from the guidelines set out by the authors. This second edition, updated and expanded will again be welcomed by both teachers and learners. The mysteries of mathematics have always posed some problems for me and therefore I add my personal welcome to this edition and would like to wish both authors and users achievement and success. Marion Welchman, MBE. xiii Chapter 1 Dyscalculia, Dyslexia and Mathematics Introduction In 1981, when we moved from working in mainstream schools and began teaching in schools for dyslexic learners, our initial expectation was that teaching mathematics would be much the same as before. At that time, we could not find any source of guidance to confirm or contradict this expectation. We thought dyslexia meant difficulties with languages, not mathematics. Experience would change this impression! Over the last 25 years, we have accumulated experience, tried out new (and old) ideas, researched, read what little appropriate material was available (there is still far less published on learning difficulties in mathematics than on languages), learned from our learners and have become convinced that difficulties in mathematics go hand in hand with difficulties in language and that a different teaching attitude and approach is needed. The first four chapters of this book look at some of the background that influenced the evolution of these teaching methods and continues to underpin their ongoing evolution. This necessitates a look at the learner, the subject (mathematics) and the teacher. The main mathematical focus of this book is number, primarily because this is the first area of mathematics studied by children and thus provides the first opportunity to fail. Our experience suggests that number remains the main source of difficulty for most learners, even in secondary education. We also know that the foundations for all studies leading to General Certificate of Secondary Education (GCSE), and beyond, are based in these early learning experiences. The evaluations and expectations of a child’s mathematical potential are often based, not always correctly, on performance in early work on number. The remaining chapters describe some of the methods we use to teach our dyslexic learners, with the ever-present caveat
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