Table Of ContentMore 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.
