Brian Butterworth - Forest Way Alliance

Brian Butterworth Institute of Cognitive Neuroscience, UCL

Centre for Educational Neuroscience

Consequences of poor maths ability and poor reading ability for life chances

•  More of a handicap in the workplace than poor literacy (Bynner & Parsons, 1997, Does Numeracy Matter? )

•  Men and women with poor numeracy, have poorer educational prospects, earn less, and are more likely to be unemployed, in trouble with the law, and be sick (Parsons & Bynner, 2005, Does Numeracy Matter More? )

What is dyscalculia?

•  Is it just being bad/very bad at maths? •  No. In the same way that dyslexia is not just being very

bad at reading. •  There is an underlying specific deficit that causes

learners to be very bad at maths •  Though of course, there are many reasons to be bad at

maths –  Lack of opportunity to learn –  Inappropriate teaching –  Missing lessons –  Lack of numerical activities in the home –  Cognitive disabilities

I’ll return to what dyscalculia really is

•  But first we need to understand the cognitive basis of arithmetic

•  And then the neural basis of arithmetic

Cognitive basis of arithmetic

Back to basics

Arithmetic is about sets

Arithmetic is about sets and their numerosities •  Sets

–  A set has definite number of members (“numerosity”) –  Adding or taking away a member changes the numerosity –  Other transformations conserve numerosity –  Numerical order can be defined in terms of sets and subsets –  Arithmetical operations can be defined in terms of operations on sets

•  We learn about counting and arithmetic using sets –  And about the meaning of number terms

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Arithmetical development depends on numerosity processing capacity

For which there are very simple tests

Enumerating sets: the ‘size effect’

0

500

1000

1500

2000

2500

1 2 3 4 5 6 7 8 9Number of dots

Rea

ctio

n tim

e

subitizing

counting

Data from Butterworth et al, 1999

Shout out the which side has more squares: Left or Right

We can do the same with numerical symbols

Shout out the larger number as quickly as possible

2 9

6 5

3 8

Comparing numerosities: the ‘distance effect’

Data from Butterworth et al, 1999

Distance

3 8Symbolic

Non-Symbolic

3 8

Taller number?

We can use these tests child to assess individual difference in the ability to

process numerosities

These are not tests of arithmetic, but they could be tests of the cognitive prerequisite for

learning arithmetic

Not norms but cluster analysis

•  Children improve with age. How to assess whether they improve relative to peers?

•  Is a learner always in the same cluster? –  A cluster is not defined by an arbitrary criterion (e.g. ≤5%, 10% ≤1 SD,

2SD, etc) but what the data actually looks like

•  We used clusters based on parameters of the dot enumeration measure, adjusted for basic Reaction Time

•  Can this simple measure predict which children will have trouble learning arithmetic?

•  If so, it will mean that the capacity to enumerate sets is essential to learning arithmetic

Melbourne longitudinal study

159 children from 5½ to 11, tested 7 times, over 20 cognitive tests per time;

item-timed calculation, dot enumeration & number comparison (adjusted for simple RT) at each time,

Raven’s Coloured Progressive Matrices (IQ)

Reeve, Humberstone, Reynolds & Butterworth, 2012, J Experimental Psychology: General

Enumeration times by age & cluster

0

2000

4000

6000

8000

1 2 3 4 5 6 7 8

RT  in  msecs

Number  of  Dots

6  years 7  years8.5  years 9  years11  years

0

2000

4000

6000

8000

1 2 3 4 5 6 7 8

RT  in  msecs

Number  of  Dots

6  years 7  years8.5  years 9  years11  years

0

2000

4000

6000

8000

1 2 3 4 5 6 7 8

RT  in  msecs

Number  of  Dots

6  years 7  years8.5  years 9  years11  years

SLOW MEDIUM FAST

Cluster at K predicts age-appropriate arithmetic to age 10 yrs

0

20

40

60

80

100

Slow Medium Fast

Single-Digit Addition at 6 yrs

Slow Medium Fast

Conclusion

•  There’s a small cluster (about 7% in this sample) with poor ability to enumerate sets: a core deficit in numerosity processing

•  This core deficit persists from kindergarten to 11 years •  It predicts who will and who will not have trouble learning

arithmetic at least to the age of 11 years •  Implication: use this test in kindergarten or year 1 so that

you know which children are likely to have difficulty

Core deficit in numerosity processing also predicts how learners do arithmetic

Strategy change in the first two years of school

The neural basis of arithmetic and numerosity processing

Areas active in calculation

Arithmetical brain

Read Retrieve Compute

RETRIEVE+RECRUIT VS READ Zago et al, 2001, Neuroimage

SUBTRACTION+MULTIPLICATION VS READ Andres et al, 2011, Neuroimage

The arithmetical brain

The calculation network Zago et al, Neuroimage, 2001

Left hemisphere: INTRAPARIETAL SULCUS ANGULAR GYRUS

Right hemisphere INTRAPARIETAL SULCUS)

Left hemisphere: FRONTAL LOBE

IPS processes NUMEROSITIES

Task: more green or more blue?

Castelli, Glaser, & Butterworth, 2006, PNAS

Discrete Analogue

Discrete (how many) activations minus analogue (how much) activations à Numerosity sensitive activations

Activation in the INTRAPARIETAL SULCI depends on the ratio of green and blue rectangles: closer > farther (e.g. 11vs 9 >14 vs 6)

What is dyscalculia?

First, politics

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Dyscalculia at 8

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From …Sorry, wrong number, a film by Brian Butterworth & Alex Gabbay

Dyscalculia at 10

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From …Sorry, wrong number, a film by Brian Butterworth & Alex Gabbay

Dyscalculia at 14

Arvinder.mov

Case JB

•  9years 7 months old, Right Handed male. Normal in all school subjects except maths, which he finds impossible. Not dyslexic. Counts up to 20 slowly. Can read and write numbers up to 3 digits.

•  Failed Britsh Abilities Scale arithmetic questions •  Knows that 4 is the next number after 3 (has a sense of

ordinality) •  Believes that 3+1 is 5 •  Dot enumeration: 1-3 accurate. Guesses larger numbers •  Cannot say which of two numbers is bigger

What it’s like for the dyscalculic learner(9yr olds)

Moderator: How does it make people feel in a maths lesson when they lose track?

Child 1: Horrible. Moderator: Horrible? Why’s that? Child 1: I don‘t know. Child 3 (whispers): He does know. Moderator: Just a guess. Child 1: You feel stupid.

Focus group study (lowest ability group) Bevan & Butterworth, 2007

What it’s like for the dyscalculic learner

Child 5: It makes me feel left out, sometimes. Child 2: Yeah. Child 5: When I like - when I don’t know something, I

wish that I was like a clever person and I blame it on myself –

Child 4: I would cry and I wish I was at home with my mum and it would be - I won’t have to do any maths -

What it’s like for their teacher

•  KP: … they kind of have a block up, as soon as we get to starting to do it. Then they seem to just kind of phase out.

•  ML1: In a class of thirty I’ve got six. You’ve got a lot of problems. And when I’m on my own, I don’t – I really feel very guilty that I’m not giving them the attention they need.

•  JL: …lots of times they’re trying to cover it up ... they’d rather be told off for being naughty than being told off that they’re thick.

Identifying the core deficit in the classroom

Dot enumeration

Formal test of addition

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Butterworth, 2003, Dyscalculia Screener

Dyscalculic learner

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xxxxxxxxxxx

14 yr old female

Bad at arithmetic but not dyscalculic

40

xxxxxxxxxxx

9 yr old female 15 yr old male

Neural basis of dyscalculia

So, if there a deficit in numerosity processing is at the core of dyscalculia

Then there should be abnormalities in the INTRAPARIETAL SULCI

Isaacs et al, 2001

Rotzer et al 2008 NeuroImage

Abnormal structure in numerosity network in dyscalculics

Isaacs et al, 2001, Brain Ranpura et al in prep

Castelli et al, 2006, PNAS

Abnormal activations in the IPS

NSC – close NSF - far

12 year olds: dyscalculics and matched controls

Price et al, 2007, Current Biology

Numerosity  representa/on,  manipula/on  

Arithme(c  fact  retrieval  

ARITHMETIC    

Number  Symbols  

Fusiform  Gyrus  

Angular  Gyrus  

Intraparietal  Sulcus  

Parietal  lobe  

Occipito-­‐  Temporal  

Biological  

Cogni(ve  

Behavioural   Simple  number  tasks  

Gene(cs  

Frontal  lobe  

Concepts,  principles,  procedures  

Analogue  magnitudes  

Educa(onal  context  

Prac(ce  with  numerosi(es  

Exercises  on  manipula(on  of  

numbers  

Experience  of  reasoning  about  

numbers  

Exposure  to  digits  and  facts  

Prefrontal  Cortex  

Summary  of  the  neuroscience  

Numerosity processing as a target for intervention

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From neuroscience to education

From diagnosis to educational remedy?

No clear logical pathway

à use established pedagogical principles

à use ideas from best practitioners

à use technology to capture and test ideas

The End

www.mathematicalbrain.comFor my papers on dyscalculia and useful links

DfE  2014  •  Search  for  ‘Dyscalculia’  on  the  DfE  website  and  what  do  you  get?    •  Guidance:  Employing  disabled  people  and  people  with  health  condi(ons  •  6.1  Suppor/ng  people  with  hidden  impairments  

–  The  Hidden  Impairment  Toolkit  offers  hints  and  (ps  on  how  employers  can  beRer  support  people  with  hidden  impairments  such  as:  

–  Au(s(c  Spectrum  condi(ons  including  Asperger  Syndrome  –  ARen(on  Deficit  Hyperac(vity  Disorder  –  Dyslexia  –  Dyspraxia  –  Dyscalculia  –  speech  and  language  impairments  –  The  

Do  It  Profiler  gives  resources  for  employers  to  help  them  to  beRer  understand  the  issues  around  specific  learning  disabili(es  and  their  relevance  to  the  workplace.  

•  Hidden  Impairment  Toolkit:  Following  a  recent  internal  review  of  our  group  we  are  currently  upda(ng  our  resources  for  employers  which  includes  our  website.  

•  Do  It  Profiler:  Also  available  is  a  free  guide,  developed  by  interna(onal  experts  in  the  field,  to  informa(on  for  employers  and  employees  on  hidden  impairments,  including:  

–      Dyslexia  –      Dyspraxia  –      ADHD  –      Au(sm  Spectrum  Condi(ons  –      Speech,  language  and  communica(on  impairments  –      Mental  health  condi(ons  including  anxiety,  depression,  schizophrenia,  bipolar  disorder,  personality  disorder  –  This  includes  an  easy  to  use  guide  to  assist  with  making  reasonable  adjustments  in  the  workplace.  

Official definitions ✤  DSM  IV  Mathema/cs  disability.    

✤  The  child  must  substan(ally  underachieve  on  a  standardized  test  rela(ve  to  the  level  expected  given  age,  educa(on,  and  intelligence  and  must  experience  disrup(on  to  academic  achievement  or  daily  living  

✤  DSM  5  315.1  Learning  disabili/es  ✤  A  persistent  difficulty  learning  academic  skills  for  at  least  6  months  despite  

interven(on  targe(ng  the  area(s)  of  difficulty.  –  Specifier  

•  In  number  sense,  fact  and  calcula(on,  and  in  mathema(cal  reasoning  –  Severity:  Mild,  Moderate  or  Severe  –  The  academic  and  learning  difficul(es  occur  in  the  absence  of:  

•   Intellectual  Disabili(es,    Visual  or  hearing  impairments,  Mental  disorders  (e.g.  depression,  anxiety,  etc.),  Neurological  disorders,  Psycho-­‐social  difficulty,  Language  differences,  Lack  of  access  to  adequate  instruc(on  

–  DSM  IV  used  an  IQ  discrepancy  criterion.  DSM  5  does  not,  except  that  there  is  an  exclusionary  rule  –  no  very  low  IQs  (e.g.  <70)  

✤  Interna/onal  Classifica/on  of  diseases  (ICD)  10  ✤  Specific  disorder  of  arithme/cal  skills.  Involves  a  specific  impairment  in  arithme(cal  

skills  that  is  not  solely  explicable  on  the  basis  of  general  mental  retarda(on  or  of  inadequate  schooling.  The  deficit  concerns  mastery  of  basic  computa(onal  skills  of  addi(on,  subtrac(on,  mul(plica(on,  and  division  rather  than  of  the  more  abstract  mathema(cal  skills  involved  in  algebra,  trigonometry,  geometry,  or  calculus.    

Italy  2010.  Law  170  •  New  regula(ons  concerning  specific  disorders  of  learning.  •  Ar(cle  1.1.  The  present  law  recognizes  dyslexia,  dysgraphia,  

dysorthographia  and  dyscalculia  as  Specific  Learning  Disabili(es…  They  manifest  themselves  in  cases  of  adequate  cogni(ve  capaci(es,  and  in  absence  of  neurological  or  sensory  deficits.  Yet,  they  cons(tute  an  important  limita(on  for  daily  ac(vi(es.  

•  Ar(cle  1.5.  The  present  law  refers  to  dyscalculia  as  a  specific  deficit  which  manifests  itself  as  a  difficulty  in  grasping  the  automa(sms  of  calcula(on  and  number  processing.    

•  Ar(cle  2  states  among  other  things,  that  there  will  be  appropriate  teaching  to  realize  poten(al,  a  reduc(on  in  social  and  emo(onal  consequence,  train  teachers  appropriately,  make  people  aware  of  the  problem,  promote  early  diagnosis  and  rehabilita(on,    and  ensure  equal  opportuni(es  to  develop  social  and  professional  capaci(es.