Table Of ContentThe Trouble with Maths
Now in its fourth edition, with updates to reflect developments in our understanding
of learning difficulties in maths, this award-winning text provides vital, pragmatic
insights into the often-confusing world of numeracy. By looking at learning difficulties
in maths and dyscalculia from several perspectives, for example, the vocabulary and
language of maths, cognitive style and the demands of individual procedures, this
book provides a complete overview of the most frequently occurring problems asso-
ciated with maths teaching and learning. Drawing on tried-and-tested methods based
on research and Steve Chinn’s decades of classroom experience, it provides an
authoritative yet accessible one-stop classroom resource.
Combining advice, guidance and practical activities, this user-friendly guide will
help you to:
(cid:129) develop flexible cognitive styles
(cid:129)
use alternative strategies to replace an over-reliance on rote-learning for pupils
trying to access basic facts
(cid:129)
understand the implications of underlying skills, such as working memory, on
learning
(cid:129)
implement effective pre-emptive measures before demotivation sets in
(cid:129)
recognise the manifestations of maths anxiety and tackle affective domain
problems
(cid:129)
find approaches to solve word problems
(cid:129)
select appropriate materials and visual images to enhance understanding.
With useful features such as checklists for the evaluation of books and an overview
of resources, this book will equip you with essential skills to help you tackle your
pupils’ maths difficulties and improve standards for all learners. This book will be
useful for all teachers, classroom assistants, learning support assistants and parents.
Steve Chinn is a Visiting Professor at the University of Derby. He is also the author
of More Trouble with Maths: A Complete Guide to Identifying and Diagnosing Math-
ematical Difficulties, 3rd edition and editor of The Routledge International Handbook
of Dyscalculia and Mathematical Learning Difficulties. He has lectured and trained
teachers in over 30 countries.
[This book] focuses on the individual student and shows how to equip them with
both an understanding of the problem and appropriate strategies to deal with the dif-
ficulties experienced. It draws on practical experience and evidence-based methods
as well as current research […] This will be seen as an essential resource.
Dr.GavinReid,PsychologistandauthorofDyslexiaandInclusion:Classroom
ApproachesforAssessing,TeachingandLearning
Steve Chinn’s book The Trouble with Maths has long been an essential part of any
special needs teacher’s toolkit.
PatriciaBabtieandJaneEmerson
Steve’s books are very well respected and well known and are generally the first port
of call for someone looking for information on dyscalculia and maths difficulties.
JudyHornigold,InternationalLecturerinDyscalculia
The Trouble with Maths
A Practical Guide to Helping
fi
Learners with Numeracy Dif culties
Fourth edition
Steve Chinn
Fourtheditionpublished2021
byRoutledge
2ParkSquare,MiltonPark,Abingdon,Oxon,OX144RN
andbyRoutledge
52VanderbiltAvenue,New York,NY10017
RoutledgeisanimprintoftheTaylor&FrancisGroup,aninformabusiness
©2021SteveChinn
TherightofSteveChinntobeidentifiedasauthor ofthisworkhasbeenasserted
byhiminaccordancewithsections77and78oftheCopyright,Designsand
PatentsAct1988.
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FirsteditionpublishedbyRoutledge2004
ThirdeditionpublishedbyRoutledge2016
BritishLibraryCataloguing-in-PublicationData
Acataloguerecordforthis bookisavailablefromtheBritishLibrary
LibraryofCongressCataloging-in-PublicationData
Names:Chinn,StephenJ., author.
Title:Thetroublewithmaths:apracticalguidetohelpinglearnerswith
numeracydifficulties/SteveChinn.
Description:Fourthedition.|Abingdon,Oxon; NewYork,NY:Routledge,[2021]|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2020015508(print)|LCCN2020015509(ebook)|
ISBN9780367862138(hardback)|ISBN9780367862145(paperback)|
ISBN9781003017714(ebook)
Subjects:LCSH:Mathematics–Studyandteaching.|Specialeducation.|
Underachievers–Education.|Mathematicalability.|Acalculia|Dyslexia.
Classification:LCCQA11.2.C482021(print)|LCCQA11.2(ebook)|
DDC510.71–dc23
LCrecordavailableathttps://lccn.loc.gov/2020015508
LCebookrecordavailableathttps://lccn.loc.gov/2020015509
ISBN:978-0-367-86213-8(hbk)
ISBN:978-0-367-86214-5(pbk)
ISBN:978-1-003-01771-4(ebk)
TypesetinHelvetica
bySwales&Willis, Exeter,Devon,UK
Contents
Listofillustrations vi
1 Introduction:mathematicslearningdifficultiesanddyscalculia 1
2 Factorsthataffectlearning 24
3 Whatthecurriculumaskspupilstodoandwheredifficultiesmayoccur 47
4 Cognitivestyleinmathematics 71
5 Developmentalperspectives:apragmaticapproach 90
6 Thevocabularyandlanguageofmathematics 110
7 Anxiety,attributionsandcommunication 123
8 Theinconsistenciesofmathematics 136
9 Manipulatives,materialsandvisualimages:multisensorylearning 143
10 Thenasties:longdivisionandfractions 162
Appendix1Furtherreading 178
Appendix2Checklists 179
Appendix3Resources 181
Referencesandnotes 183
Index 187
Illustrations
Figures
2.1 Placevaluecards 43
2.2 Ablanktaskanalysisform 45
2.3 Anexampleofataskanalysis 46
3.1 Numberline 51
3.2 Using10pcoinsasimagesfornumberbondsfor100 53
3.3 Coinstoshow62+38 53
3.4 Cuisenairerodsfor6×7 59
3.5 Numicon/Sternmaterials:5(odd)plus3(odd)=8(even) 61
3.6 Areamodelfor31×17 64
3.7 28×39comparedto30×40 64
3.8 Divisionbysubtractionofchunks:713÷23 65
4.1 Subtractiontheinchwormway 74
4.2 Whatistheareaoftheshadedfigure? 76
5.1 Thesheepcounters 93
5.2 Imagesfornumberbonds10 95
5.3 Numberbondsfor100withbasetenblocks 96
5.4 Areamodelformultiplication:trackingback 99
5.5 Theblanktablesquare 103
5.6 Thetablesquarewiththeeasyfacts 103
5.7 6×10comparedto6×9 104
6.1 Placevaluearrowcards 112
6.2 Twolinesofsymmetryortwolinesinacemetery 115
7.1 Expectations 133
9.1 Subtractionandlanguage 146
9.2 Patternsfor1to10 147
9.3 Basetenblocks:45 148
9.4 Basetenblocks:405 149
9.5 Countingoninones,tensandhundreds 149
9.6 Beadstring:13and23 150
9.7 Stern/Numiconblocks:13and23 150
9.8 Coinsanddecimals 151
9.9 Beadstringfornumberbondsfor10 152
9.10 Imagesfornumberbondsfor1,10,100,1000 153
9.11 Counters(orcoins)inaconsistentandinterrelatingpattern 153
9.12 Cuisenairerodsfor5×5and(2×5)+(2×5)+(2×5)and(5×5)+(1×5) 155
9.13 Cuisenairerodsandthecommutativeproperty 155
9.14 Cuisenairerodsandbuildingfacts 156
9.15 Numberlinesfordifferentpowersoften 157
9.16 Foldingtomakeahalf 158
9.17 Foldingtomakeathird 158
Illustrations vii
9.18 The‘half’paperfoldedintothirds.The‘third’paperfoldedintohalves.
Bothcreatesixths 158
9.19 Threetoycars 159
9.20 Oddplusoddmakeseven:5+3=8andoddplusevenmakes
odd:5+4=9 161
10.1 Traditionallongdivision 163
10.2 Thehiddendivisionsign 167
10.3 Thefractionnumberline 168
10.4 Theanalogueclockfaceandfractions 168
10.5 Criss-cross,timesforaddingfractions 170
10.6 Criss-cross,timesasabutterfly! 170
1 þ 2
10.7 Thecircleand 175
4 3
10.8 Fractionsandclocks 175
10.9 Comparingfractionsizes 176
10.10 Renamingfractionstomakethemhavethesamename 176
1 (cid:2) 2 ¼ 2 ¼ 1
10.11 Foldingpapertoshow 177
4 3 12 6
Tables
4.1 Cognitivestylesoftheinchwormandthegrasshopper 73
4.2 Trialandadjusttheinchwormway 80
1 Introduction
fi
Mathematics learning dif culties
and dyscalculia
This book was written to help teachers, classroom assistants, learning support
assistants and parents who are dealing with pupils who are underachieving in
mathematics. The level of underachievement might be significant enough to be rec-
ognised as a mathematical learning difficulty or severe enough to be considered as
dyscalculia.
The book looks at the problems from several perspectives, from preventative meas-
ures to use in the classroom, to cognitive styles, to practical ideas for intervention. It
works like a repair manual in some respects and like a care awareness manual (looking
after your students) in other respects.
It is a book which can be accessed in different ways. It can provide an overview of
where and how problems may arise. It offers insights for teachers into areas of poten-
tial difficulty for learners. It can focus on a specific problem and suggest approaches
which can help the pupil overcome the problem.
It would be an impossible task to attempt to provide an answer for every problem
for every child. One way of being as comprehensive as is practical within one book is
to focus as much on prevention as on intervention. A pro-active awareness of learn-
ing issues can help in reducing their impact on learners.
In many respects then, the key purpose of this book is to provide a context with
which to design and appraise any intervention, be it major or minor.
The Trouble with Maths can be used to:
(cid:129)
understand some of the reasons problems may arise in learning mathematics
(cid:129)
understand that many problems track back to the very early experiences and thus
that these basics need to be addressed within any intervention
(cid:129)
pre-empt learning problems
(cid:129) develop flexible cognitive skills and encourage metacognition
(cid:129)
circumvent problems in basic numeracy by developing understanding, rather than
an over-dependency on rote learning
(cid:129)
address the difficulties pupils have with word problems
(cid:129)
teach alternative strategies for accessing basic facts
(cid:129)
recognise affective domain issues and suggest strategies for addressing maths
anxiety, attributional style, self-efficacy and self-esteem problems
(cid:129)
stimulate the ability to create effective ideas for teaching maths to all pupils, but
especially those who are facing difficulties with the subject
(cid:129)
select appropriate materials, manipulatives and visual images for teaching maths
topics
(cid:129)
encourage students to develop an understanding of maths.
