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More trouble with maths : a complete manual to identifying and diagnosing mathematical difficulties PDF

225 Pages·2020·16.745 MB·English
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More Trouble with Maths Now in an updated third edition, this invaluable resource takes a practical and accessible approach to identifying and diagnosing many of the factors that contribute to mathemati­ cal learning difficulties and dyscalculia. Using a combination of formative and summative approaches, it provides a range of norm-referenced, standardised tests and diagnostic activities, each designed to reveal common error patterns and misconceptions in order to form a basis for intervention. Revised to reflect developments in the understanding of learning difficulties in mathematics, the book gives a diagnostic overview of a range of challenges to mathematical learning, including difficulties in grasping and retaining facts, problems with mathematics vocabulary and maths anxiety. Key features of this book include: ●● Photocopiable tests and activities designed to be presented in a low-stress way ●● Guidance on the interpretation of data, allowing diagnosis and assessment to become integrated into everyday teaching ●● Sample reports, showing the diagnostic tests in practice Drawing on tried and tested methods, as well as the author’s extensive experience and expertise, this book is written in an engaging and user-friendly style. It is a vital resource for anyone who wants to accurately identify the depth and nature of mathematical learn­ ing difficulties and dyscalculia. Steve Chinn was principal of two schools for dyslexic students before founding his own school which received Beacon School status from the government and the Independent Schools ‘Award for Excellence’. He designed and delivered the UK’s first Post Graduate course on dyslexia and maths difficulties. Steve’s research papers, articles and books include the award-winning The Trouble with Maths. He compiled and edited The International Handbook of Dyscalculia and Mathematical Learning Difficulties (2015). The fourth edition of his seminal book Mathematics for Dyslexics was published in 2017. He has recently written catch-up mate­ rials for Numicon. Steve has lectured in 30 countries, including consultation work for the Singapore MoE. He is Visiting Professor at the University of Derby. More Trouble with Maths A Complete Manual to Identifying and Diagnosing Mathematical Difficulties Third edition Steve Chinn Third edition published 2020 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN and by Routledge 52 Vanderbilt Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2020 Steve Chinn The right of Steve Chinn to be identified as author of this work has been asserted by him in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. The purchase of this copyright material confers the right on the purchasing institution to photocopy pages which bear the photocopy icon and copyright line at the bottom of the page. No other 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 prior permission in writing from the publisher. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. First edition published by Routledge 2012 Second edition published by Routledge 2017 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Names: Chinn, Stephen J., author. Title: More trouble with maths: a complete manual to identifying and diagnosing mathematical difficulties / Steve Chinn. Description: 3rd edition. | Abingdon, Oxon; New York, NY: Routledge, 2020. | Series: NASEN spotlight | Includes bibliographical references and index. Identifiers: LCCN 2019054156 (print) | LCCN 2019054157 (ebook) | ISBN 9780367862152 (hardback) | ISBN 9780367862169 (paperback) | ISBN 9781003017721 (ebook) Subjects: LCSH: Mathematics–Study and teaching. | Math anxiety. | Mathematical ability–Testing. | Acalculia. | Dyslexia. Classification: LCC QA11.2 .C475 2020 (print) | LCC QA11.2 (ebook) | DDC 510.71–dc23 LC record available at https://lccn.loc.gov/2019054156 LC ebook record available at https://lccn.loc.gov/2019054157 ISBN: 978-0-367-86215-2 (hbk) ISBN: 978-0-367-86216-9 (pbk) ISBN: 978-1-003-01772-1 (ebk) Typeset in Helvetica by Deanta Global Publishing Services, Chennai, India Contents Foreword by Professor Maggie Snowling vii 1 Introduction: Dyscalculia and mathematical learning difficulties: The test protocol 1 2 Diagnosis, assessment and teaching: The benefits of linking 14 3 The Dyscalculia Checklist: Thirty-one characteristics that can contribute to maths failure 23 4 Starting the assessment/diagnosis: Getting to know the person through informal activities 38 5 Short-term memory and working memory: Two key underlying skills that influence learning 53 6 Tests of basic facts - addition, subtraction, multiplication and division: Their role in mathematical learning difficulties and dyscalculia 60 7 Mathematics anxiety: Which topics and activities create anxiety 74 8 The 15-Minute norm-referenced Mathematics Test: Basic computations and algebra designed to compare performances 84 9 Errors and the 15-Minute Mathematics Test: Recognising and understanding common error patterns 108 10 Cognitive (thinking) style: How learners think about and solve mathematics problems 127 11 Estimation: A key life skill used to develop more confidence with mathematics 148 12 Mathematics vocabulary, symbols and word problems: Exploring how they contribute to mathematics learning difficulties 152 13 Criterion-referenced (formative) tests: Focusing on identified problems and showing how to build ongoing diagnosis into teaching 162 vi Contents 14 Speed of working: The implications of ‘doing mathematics’ quickly 171 15 Two sample reports 174 Appendix 1 A sample ‘teacher observations’ pro-forma 203 Appendix 2 A pre-assessment pro-forma for parents/carers 205 Appendix 3 Schools, colleges, institutions and individuals who provided data for the norm-referenced tests in Chapters 6 and 8 206 References 208 Index 213 Foreword This is an astonishing book! ‘Troubles with maths’ are both varied and widespread; difficulties with maths in school cause anxiety and not only affect educational achieve­ ment but also limit career prospects. It follows that the early identification of problems with numbers, followed by appropriate intervention, should be a priority for all indus­ trialised societies. But knowledge of how to assess mathematical difficulties is poor despite a growing evidence base on the nature and causes of ‘dyscalculia’. In this book, Steve Chinn shares many years of expertise with extreme clarity; assessment needs to be the first step to intervention, and the book provides a comprehensive explanation for the practitioner of what is needed in order to properly understand mathematical learning difficulties. At the core of the book is a test protocol that goes well beyond a screening instrument. The assessment incorporates background infor­ mation, teacher observations and a questionnaire probing maths anxiety as well as more conventional tasks tapping basic number knowledge, number facts, numerical operations and reasoning skills. It also includes standardised assessment procedures that have been developed by the author, together with sample diagnostic reports, generously shared. This book should be on the shelves of all professionals in the field of maths education and educational assessment, and I am confident that it will spearhead a much-needed increase in proficiency in the assessment of numeracy skills in the field. Maggie Snowling, St. John’s College, University of Oxford 1 1 Introduction Dyscalculia and mathematical learning difficulties: The test protocol This book was written to complement The Trouble with Mathematics: A Practical Guide to Helping Learners with Numeracy Difficulties. It looks at assessing and diagnosing and learning difficulties in mathematics and dyscalculia and links those processes to the teaching philosophies and pragmatics in The Trouble with Mathematics: A Practical Guide to Helping Learners with Numerical Difficulties (now in 4th edition). It contains: OO A suggested diagnostic protocol and the reasons for selecting the components OO A norm-referenced (UK sample*) 15-minute Mathematics Test for ages 7 to 59 years old OO Norm-referenced (UK sample*) tests for the four sets of basic facts (+ − × ÷) for ages 7 to 15 years old OO A norm-referenced (English sample*) anxiety, ‘How I feel about mathematics’, test of mathematics anxiety for ages 11 to 16 years old (a version for adults is available on my website, www.stevechinn.co.uk) OO A test of thinking cognitive (thinking) style in mathematics OO A Dyscalculia Checklist OO Informal tests for vocabulary, symbols, place value, estimation OO A structured, exemplar test of word problems OO Informal tests of short-term memory and working memory OO Guidance on how to appraise the ability to estimate OO Guidance on how to use errors and error patterns in diagnosis and intervention OO Guidance on how to construct criterion referenced tests and how to integrate them into day-to-day teaching OO Case studies *Samples for each test were over 2000 Many of the factors from the protocol interact. The tests and procedures in this book should enable teachers and tutors to diag­ nose and identify the key factors that contribute to learning difficulties in mathematics and dyscalculia. There are many examples where the relationships between topics reinforce the need to take a broad and flexible approach to diagnosis and assessment. None of the tests are restricted. Dyscalculia This book is about assessing and diagnosing mathematics learning difficulties and dyscalculia. It takes the view that mathematics learning difficulties are on a spectrum.

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