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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
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.
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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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?
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
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."
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• 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
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
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
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
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
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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
Grey matter differences between dyslexic and dyscalculic brains
Silani et al, 2005, Brain
DYSCALCULIC BRAIN
Isaacs et al, 2001, Brain
DYSLEXIC BRAIN
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
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.