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? )

Outline of talk

•  Reading difficulties and arithmetic difficulties –  Co-occurrence

•  Causes of arithmetic difficulties and dyscalculia –  Numerosity processing and arithmetic –  Dyscalculia is a core deficit in numerosity processing –  Neural basis of arithmetic –  Genetics of arithmetic

•  Reading and arithmetic compared –  Core processing –  Neural basis –  Genetics of reading and dyslexia

•  Co-occurrence of neurodevelopmental disorders •  Conclusions

Reading difficulties and arithmetic difficulties

Co-occurrence of reading and arithmetic disorders

•  40% (Lewis et al, 1994, J. Child Psychology & Psychiatry) •  Reading disorders (RD) with arithmetic disorders (AD) 11-56%

–  Depends on test –  RD – comprehension 42% vs RD – word recognition 28% (Dirks et al,

2008, J. Learning Disabilities

•  Higher than prevalence for each –  RD 4-9% –  AD 3-7%

•  Now, the co-occurrence rate will depend on the criteria for reading and maths difficulties –  So, dyslexia teachers will see many children referred for reading

difficulties, but who also have maths difficulties

Systematic Austrian study

•  Population-based sample of 2586 children Grade 2 to 4 •  Sentence comprehension and arithmetic tests

N % +AD% +RD% AD – 1 SD 399 15.4 39.6 AD – 1.5 SD 158 6.1 37.3 RD – 1 SD 384 14.8 38.8 RD - 1.5 SD 181 7.0 22.7

Landerl & Moll, 2010, J Child Psychology & Psychiatry

Expected probability of AD+RD = 0.61*0.7=0.42 = less than 1 per 100

Why the high co-occurrence rate?

•  Does dyslexia cause dyscalculia? •  Do they have a common cause?

–  IQ –  Working Memory deficits –  Long-term memory deficits –  Language deficits –  Pleiotropy – one gene, many consequences

•  Does dyslexia PLUS dyscalculia make maths worse than dyscalculia alone? For example, when dealing with symbols.

Cognitive basis of arithmetic

But first

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

11

Numerosity processing capacity

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

Comparing numerosities: the ‘distance effect’

Data from Butterworth et al, 1999

Distance

3 7 Symbolic

Non-Symbolic

How we can use these tests to assess individual differences

Should we, can we, use normative criteria?

PISA 2009 Reading

PISA 2009 maths

Another approach

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,

RCPM

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

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? –  Cluster based on parameters of the dot enumeration measure, adjusted

for basic Reaction Time –  At each age, there were exactly three clusters, which we labelled Slow,

Medium and Fast –  Ordinal correlations show that cluster membership stable

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

Dyscalculia is different from just being bad at maths

Official definitions are not helpful

22

Official definitions

✤ DSM IV ✤ Mathematics disability. The child must substantially

underachieve on a standardized test relative to the level expected given age, education, and intelligence and must experience disruption to academic achievement or daily living

✤  International Classification of diseases (ICD) 10 ✤ Specific disorder of arithmetical skills. Involves a specific

impairment in arithmetical skills that is not solely explicable on the basis of general mental retardation or of inadequate schooling. The deficit concerns mastery of basic computational skills of addition, subtraction, multiplication, and division rather than of the more abstract mathematical skills involved in algebra, trigonometry, geometry, or calculus.

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 -

Emotional consequences of dyscalculia

“ I feel like screaming and saying 'why are you doing this, why are you doing this?' and I feel like punching the teachers…” “... I'm not good, and I don't like it when my mum says that - that's why I don't like times tables at all.” Stigmatization He just comes up to us and says “ha ha - you don’t know anything - you are so dumb” and then he asks me, like, questions like “thousand times thousand” which he knows and I don’t know …which is very hard for us [High ability child about a low ability child] Yeah, and then she goes hide in the corner - nobody knows where she is and she’s crying there

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

Using the numerosity processing tests

29  

•  Two capacity tasks –  Number Comparison –  Dot estimation –  (Simple reaction time)

•  One attainment task –  Item-timed arithmetic

•  Software for your PC •  Results given as standard scores and

automatically calculated by computer in a printable form

•  Critical Diagnoses: –  lowest 5% on capacity measures Number

comparison and Dot estimation –  Low performance on attainment but not

on the other tests: poor learning/teaching

DfES evaluation www.schoolzone.co.uk/pip/evaluations/evaluation.asp?p=GRAN-7446104"

Numerosity tests in the classroom

Butterworth, 2003, Dyscalculia Screener

Dyscalculic learner

31

xxxxxxxxxxx

14 yr old female

Bad at arithmetic but not dyscalculic

32

xxxxxxxxxxx

9 yr old female 15 yr old male

Prevalence of arithmetical disorders and dyscalculia

Havana study: 11562 children in Havana Centro.

Reigosa Crespo, Valdés Sosa, Butterworth, et al, 2012, Developmental Psychology

•  Calculation disorder based on timed arithmetic – 9.4% –  No gender difference

•  Dyscalculic (calculation disorder PLUS poor numerosity processing as measured by timed dot enumeration) – 3.4% –  Male:Female 4:1

Neural basis of arithmetic

Left hemisphere: INTRAPARIETAL SULCUS (ANTERIOR) INTRAPARIETAL SULCUS (POSTERIOR) ANGULAR GYRUS

Right hemisphere INTRAPARIETAL SULCUS (ANTERIOR) INTRAPARIETAL SULCUS (POSTERIOR)

From Dehaene et al, 2003

Number processing network For comparing and estimating numerical magnitude

and retrieving arithmetical facts from memory

The calculating brain

The calculation network Zago et al, Neuroimage, 2001

Left hemisphere: INTRAPARIETAL SULCUS (ANTERIOR) INTRAPARIETAL SULCUS (POSTERIOR) ANGULAR GYRUS

Right hemisphere INTRAPARIETAL SULCUS (ANTERIOR) INTRAPARIETAL SULCUS (POSTERIOR)

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)

Numerosity processing part of calculation network

Neurotypical brain processes numerosities in Intraparietal Sulcus Castelli et al, PNAS, 2006

The calculation network Zago et al, Neuroimage, 2001

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, 2013, Trends in Neuroscience and Education

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

Cognitive factors in dyslexia and arithmetical disability

Testing capacity for numbers and sets: First London study

•  9 year old with severe arithmetical disabilities (dyscalculics) –  3 SD worse than age-group on timed arithmetic –  Identified by teachers as having particular problems with learning

arithmetic –  Normal or superior IQ –  Normal reading, language, short-term memory

•  Matched controls •  Dyslexic group

–  Are they worse than controls on any of the number tasks?

•  Double deficit group –  Does the additional deficit make you worse than the single deficit

dyscalculic group?

Landerl, Bevan, & Butterworth, Cognition, 2004

Dyscalculics slower and less accurate

•  To enumerate small numerosities (<9) •  To select the larger of two digits

–  But not the taller of two digits

•  No effect of dyslexia on these tasks

46

Dyslexia and dyscalculia are different

•  Dyslexia is typically the result of a phonological problem. Dyscalculia is a problem with numerosity.

•  Different brain networks for reading and maths, and may be different genes too.

•  Number comparison: if dyslexia causes problems with numerosity processing or makes it worse, then it should show up on a simple task

Does dyslexia make you worse at arithmetic?

Landerl, Bevan & Butterworth, 2004, Cognition

Controls Dyslexics Dyscalculics Dyslexics/dyscalculics

49.4 49.2 38.9 38.7

Landerl et al, 2009, J Exp Child Psych

Are dyslexics worse in basic capacities?

Landerl, Bevan & Butterworth, 2004, Cognition

3  7 3 7

Landerl et al, 2009, J Exp Child Psychology

Neural basis of dyslexia and dyscalculia

Reading-specific brain areas

Carreiras et al 2009 Nature

Grey matter differences between dyslexic and dyscalculic brains

Silani et al, 2005, Brain

DYSCALCULIC BRAIN

Isaacs et al, 2001, Brain

DYSLEXIC BRAIN

Genetic basis of dyslexia and dyscalculia

Twin studies

•  Measuring MZ and DZ concordance –  Heritability estimates for dyslexia ~40-50% –  Heritability estimates for maths ~ 30%

•  Measuring MZ and DZ concordance in 7 year old twins (Kovas et al, 2005, Intelligence) –  Genetic influences on reading and arithmetic –  About 20% common to reading and maths –  About 30% specific to maths

•  Cross-trait correlations between twins (Ranpura et al, in preparation)

–  correlations between MZ twins on numerosity processing and arithmetic efficiency > correlations between DZ twins

Co-occurrence of neurodevelopmental disorders

Complex causal relationships

Butterworth & Kovas, 2013, Science

Co-occurrences

Butterworth & Kovas, 2013, Science

Conclusions

•  Dyslexia and arithmetical disorders co-occur much more often than would be expected by chance

•  Dyscalculia is a core deficit in numerosity processing •  Dyscalculia and dyslexia are different

–  No common cognitive basis –  No common neural basis –  No common genetic basis

•  BUT this still leaves a mystery: why do they co-occur so often?

•  AND why do neurodevelopmental disorders co-occur so often?

Grand challenges for the future

•  Develop an understanding of how individual differences in brain development interact with formal education. Investigate how cognitive processes, their neural basis, and their genetic etiology influence the individual’s experience of his or her learning environment.

•  Adapt learning pathways to individual needs. Each child has a unique cognitive and genetic profile. The educational system should be able to monitor and adapt to the learner’s current repertoire of skills and knowledge.

•  A promising approach involves the development of technology enhanced learning applications that are capable of adapting to individual needs for each of the basic disciplines.

The End

www.mathematicalbrain.com For my papers on dyscalculia and useful links http://number-sense.co.uk For games to help dyscalculic Learners and an online forum

Useful  references  •  Bu.erworth,  B.,  &  Kovas,  Y.  (2013).  Understanding  NeurocogniCve  

Developmental  Disorders  Can  Improve  EducaCon  for  All.  Science,  340(6130),  300-­‐305.  

•  Bu.erworth,  B.,  Varma,  S.,  &  Laurillard,  D.  (2011).  Dyscalculia:  From  brain  to  educaCon.  Science,  332,  1049-­‐1053.    

•  Bu.erworth,  B.,  &  Walsh,  V.  (2011).  Neural  basis  of  mathemaCcal  cogniCon.  .  Current  Biology,  21(16),  R618-­‐R621    

•  Landerl,  K.,  Bevan,  A.,  &  Bu.erworth,  B.  (2004).  Developmental  Dyscalculia  and  Basic  Numerical  CapaciCes:  A  Study  of  8-­‐9  Year  Old  Students.  Cogni6on,  93,  99-­‐125.    

•  Landerl,  K.,  Fussenegger,  B.,  Moll,  K.,  &  Willburger,  E.  (2009).  Dyslexia  and  dyscalculia:  Two  learning  disorders  with  different  cogniCve  profiles.  Journal  of  Experimental  Child  Psychology,  103(3),  309-­‐324.    

•  Reeve,  R.,  Reynolds,  F.,  Humberstone,  J.,  &  Bu.erworth,  B.  (2012).  Stability  and  Change  in  Markers  of  Core  Numerical  Competencies.  Journal  of  Experimental  Psychology:  General,  141(4),  649-­‐666.