Brian Butterworth Institute of Cognitive Neuroscience, UCL Centre - - PowerPoint PPT Presentation

Brian Butterworth

Institute of Cognitive Neuroscience, UCL Centre for Educational Neuroscience

Hjørring 20 March 2014

Number skills are very important

• 1. Poor number skills are a handicap

– 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? )

• 2. Poor number skills are costly to society
• 3. Costs UK about DKK24 billion per year in lost taxes,

unemployment benefit, legal and health costs, and additional education

• 4. If maths education standard were raised to level of

Finland, then UK would increase long-run GDP growth by 0.49% and Denmark by 0.82%(OECD 2010)

Not just arithmetical competence

But understanding the meaning of numbers in everyday life in a numerate society is vital

A typical Saturday in London

About 30 numbers

Over 700 numbers

Numbers are important for time

Numbers are important even in death

We probably see at least 1000 different numbers every hour of our waking lives We may even dream numbers Even if we don’t notice them, they are registered by the brain and can affect cognition and behaviour

Four types of number

• Cardinals: a cardinal number or ‘numerosity’ is an abstract

property of a set

• Ordinals: an ordinal number defines a well-ordered sequence,

such as pages in a book

• Measures: a measure number differs from cardinals and
• rdinals because a measure number does not have a unique

successor

• Labels: labels aren’t really numbers at all, but because there

is an infinite number of numbers they are useful for labelling large sets, such as telephone numbers, barcodes, etc

• Most languages and cultures use the same words for all four,

which makes it hard for learners to distinguish their meanings

Arithmetic is about sets and their numerosities

Arithmetic is about sets

• Sets

– A set has definite number of members – Adding or taking away a member changes the number – Other transformations conserve number – 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

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Testing numerosity processing abilities

Tests of numerosity estimation

• How many dots are there? Shout out the

answer as quickly as possible

Number and time

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How many dots?

The four parameter model

Testing numerosity comparison abilities

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 7

Symbolic Non-Symbolic

Simple tests of numerosity processing

How many dots?

3 7

Larger number?

3 7

Taller number?

With these simple tests we can measure individual differences in the ability to process numerosities

And we can use this to predict at a very early age which children will struggle to learn arithmetic

Measuring numerosity processing and arithmetic longitudinally

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 et al, 2012, J Experimental Psychology: General

Latent class clusters

• Children improve with age. How to assess whether they

improve relative to peers?

• Criterion or cluster analysis?
• Is a learner always in the same cluster?

– Cluster based on parameters of the dot enumeration measure, adjusted for basic RT – At each age, there were exactly three clusters, which we labelled Slow, Medium and Fast – Ordinal correlations show that cluster membership stable

Latent class clusters

SLOW MEDIUM FAST SLOW MEDIUM FAST K 18%

50% 32% Yr5 9% 50% 41%

Cluster at K predicts arithmetic to age 10 yrs

20 40 60 80 100 Slow Medium Fast

Single-Digit Addition at 6 yrs

Slow Medium Fast

Are dyslexics worse in basic capacities?

Landerl, Bevan & Butterworth, 2004, Cognition

3 7

3 7

Landerl et al, 2009, J Exp Child Psychology

Dyslexics same on numerosity processing

Landerl, Bevan & Butterworth, 2004, Cognition

3 7

3 7

Landerl et al, 2009, J Exp Child Psychology

The important thing to note is that the children in the slow group are bad at both arithmetic and numerosity processing

Dyscalculia is a core deficit in the capacity to process numerosities which leads to a disability in learning arithmetic in the normal way

What is the prevalence of dyscalculia given this definition?

The Havana study Initial assessment of 11652 children in Central Havana using curriculum-based mathematics test Special battery using timed dot enumeration (adjusted for basic RT)

Reigosa Crespo et al, 2012, Developmental Psychology

Prevalence of dyscalculia using a numerosity processing criterion

The Havana study Initial assessment of 11652 children in Central Havana using curriculum-based mathematics test Special battery using timed dot enumeration and timed arithmetic (adjusted for basic RT)

Prevalence

• “Calculation dysfluent” – 9.4% (M:F 1:1)
• Dyscalculic (calculation dysfluency PLUS poor

numerosity processing) – 3.4% (4:1)

• Numerosity processing alone 4.5% (2.4:1)

What are dyscalculics like?

47

Dyscalculia at 7 years

Dyscalculia at 8

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

Dyscalculia at 10

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

Dyscalculia at 14

Arvinder.mov

Dot enumeration

Formal test of addition

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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
• rdinality)
• 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.

How does the brain deal with sets and arithmetic?

Left hemisphere: INTRAPARIETAL SULCUS ANGULAR GYRUS Right hemisphere INTRAPARIETAL SULCUS

Dehaene et al, 2003, Cognitive Neuropsychology

Arithmetic calculation uses the basic number processing regions in the parietal plus frontal lobes

Zago et al, 2001, Neuroimage

TOP VIEW

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  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 is part of the arithmetical calculation network

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

Then there should be abnormalities in the INTRAPARIETAL SULCI

Rotzer et al 2008 NeuroImage

Abnormal structure in numerosity network in dyscalculics

Isaacs et al, 2001, Brain Ranpura et al, 2013, Trends In Neuroscience & 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

Why is there a specialized brain region for processing numerosities?

Studies of genetic abnormalities and studies of twins suggest two things: 1. Numerical abilities and disabilities are inherited 2. Individual differences in the structure of the brain region of interest (ROI) is also inherited

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Genetics of maths abilities

Twin studies

• If one twin has very low numeracy, then 58% of monozygotic co-twins and 39% of

dizygotic co-twins also very low numeracy (Alarcon et al, 1997, J Learning Disabilities) – So, significantly heritable

• Third of genetic variance in 7 year olds specific to mathematics (Kovas et al, 2007,

Monograph of the Society for Research in Child Development) Family study

• Nearly half of siblings of children with very low numeracy also have very low

numeracy (5 to 10 times greater risk than controls) (Shalev et al, 2001, J Learning Disabilities) X chromosome disorders

• Damage to the X chromosome can lead to parietal lobe abnormalities with numeracy

particularly affected. – Turner’s Syndrome. (e.g. Bruandet et al., 2004; Butterworth et al, 1999; Molko et al, 2004 ) – Fragile X (Semenza, 2005); – Klinefelter (and other extra X conditions). (Brioschi et al, 2005)

Twin study in progress

104 MZ 56 DZ Mean Age 11.8 yrs

40 behavioural tests Structural scans for all Exclusions: gestational age < 32 weeks; Cognitive test < 3SD; Motion blurring on MRI Research at UCL by Ashish Ranpura Elizabeth Isaacs Caroline Edmonds Jon Clayden Chris Clark Brian Butterworth

Factors for the whole sample

Factor 1 (24% of total variance) Number processing: WOND-NO, Addition (IE), Subtraction(IE), Multiplication (IE), Dot enumeration Factor 2 (19%) Intelligence: IQ measures, Vocabulary, and working memory (span) Factor 3 (12%) Speed: Processing speed, Performance IQ Factor 4 (9%) Fingers: finger sequencing, tapping, hand-position imitation preferred hand, non-preferred hand Mahalanobis distance to identify outliers from sample mean on basis

• f numerical dimension of Factor 1.

Highly significant predictor of dyscalculia as defined by significant discrepancy between FSIQ and WOND-NO (Isaacs at al, 2001) .

Heritability of cognitive measures

Based on a comparison of MZ and DZ twin pairs in the usual way

h2 Genetic factor c2 Shared environment e2 Unique environment Timed addition 0.54 0.28 0.17 Timed subtraction 0.44 0.38 0.18 Timed multiplication 0.55 0.31 0.15 Dot enumeration 0.47 0.15 0.38

Heritability of numerosity processing ability AND calculation

h1h2rG Addition Efficiency 0.54 Subtraction Efficiency 0.28 Multiplication Efficiency 0.36 Finger Sequencing 0.25

Cross Twin Cross Trait genetic correlations for Dot Enumeration: Is the relationship between dot enumerations and calculation closer for MZ (identical twins) than DZ (fraternal twins)

Grey matter and age

Top quartile Mahal - poor Bottom quartile Mahal - good

Significant difference in grey matter density here

Heritability of the ROI abnormality

h2 c2 e2 ROI 0.28 0.34 0.38 h1h2rG ROI & Mahalanobis 0.34

Can fish count?

An important question for education.

Primate A: macaques

Tudusciuc & Nieder, 2007, PNAS

Primate B: human infants

Participants: 72 infants 22 wks av Stimuli: see picture Method: Habituation with H1 or H2 until 50% decrement in looking time averaged over three successive trials. PH ( post habituation) using same criterion. Result: infants look longer in PH for 3 vs 2, but not 6 vs 4 Implication: “subitizing underlies infants’ performance in the small number conditions” Starkey & Cooper, 1980, Science

Approximations of larger numerosities

Participants:16 6mth olds Stimuli: non-numerosity dimensions - dot size & arrangement, luminance, density - randomly varied during habituation Method: Measure looking time during habituation, and then during test. Results: Infants look longer at 8 vs 16, but not 8 vs 12. Implication: Infants cannot be using non numerical dimensions, but can make discriminations if the ratio is large enough (2:1, but not 3:2) True representations of number used, but not object- tracking system; “infants depend on a mechanism for representing approximate but not exact numerosity” Xu & Spelke, 2000

Newborns represent abstract number

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Izard et al, 2009, PNAS

Animal numerosity processing

• Primates

– Monkeys, chimps, human infants

• Mammals

– Lions, elephants, lemurs

• Birds

– Corvids, parrots, chicks

• Reptiles

– Salamanders, toads

• Fish

– Guppies, mosquito fish

• Insects

– Bees

Numerosity representation, manipulation

Arithmetic fact retrieval ARITHMETIC Number Symbols Fusiform Gyrus Angular Gyrus

Intraparietal Sulcus

Parietal lobe Occipito- Temporal

Biological Cognitive Behavioural

Simple number tasks

Genetics

Frontal lobe

Concepts, principles, procedures Analogue magnitudes

Educational context

Practice with numerosities Exercises on manipulation of numbers Experience of reasoning about numbers Exposure to digits and facts

Prefrontal Cortex

Summary of the neuroscience

Numerosity processing as a target for assessment and intervention

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Assessment: Identifying the core deficit in the classroom

The Dyscalculia Screener

Butterworth, 2003, Dyscalculia Screener

Dyscalculic learner

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14 yr old female

Bad at arithmetic but not dyscalculic

84

9 yr old female 15 yr old male

Intervention

The usual methods for helping children who are falling may not work!

Here’s what a teacher says

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

Example of cardinal-ordinal confusion

Experimenter: So how many are there? Adam (3yrs, counting three objects): One, two, five! Experimenter (Pointing to the three objects): So there’s five here? Adam : No. That’s five (pointing to the item he’d tagged ‘five’) (Gelman & Gallistel, The Child’s Understanding of Number) So, working with collections of objects – sets – helps the learner understand the difference between cardinals (numerosities) and ordinals

Can neuroscience help improve education for dyscalculics?

From neuroscience to education

• We have the diagnosis: deficits in processing numerosities
• This suggests that we should target this deficit in interventions
• But how?

– Brain research suggests ‘prediction-error’ learning: that is, the learner makes a prediction about which action will achieve a goal, acts on it, sees the difference between action and goal, and adjusts the prediction. – This implies that the learner must act, and the feedback from the action must be informative That is, the learner must be able to see the difference between the action and the goal – This is equivalent to the pedagogical principle of ‘constructionism’ (Papert) – In my experience, this is what good special needs teachers do – Multiple choice questions with right-wrong feedback is not optimal – not much action and the feedback is not very informative

Using learning technologies

• The technology can require the learner to act to

achieve a goal

• It can show the difference between the action and

the goal

• It can adapt to the learner’s current cognitive state

and the ‘zone of proximal development’ (Vygotsky)

• For dyscalculics the zone may be much smaller than

is typical

• Learning technologies can keep a record of learner

progress – both in terms of accuracy and speed

Adaptive technologies based on cognitive neuroscience

Number Race (Räsänen, Wilson, Dehaene, etc)

http://sourceforge.org

Number Bonds, Dots2Track, etc (Laurillard et al)

http://low-numeracy.ning.com

Rescue calcularis (Kucian et al)

Example intervention 1

‘Dots-to-track’

• Uses regular dot patterns for 1 to 10
• Links patterns to representation on number line and to

written digit and to sound of digit Aims to help the learner

• recognise rather than count dot patterns
• see regular patterns within random collections
• using learning through practice, not instruction

Learner constructs the answer, rather than selects it

Pedagogic principle: constructionism

Feedback shows the effect of their answer as the corresponding pattern Watch the grey dots

Pedagogic principle: informational feedback

And counts (with audio) their pattern

• nto the number line

Watch the grey dots

Pedagogic principle: concept learning through contrasting instances

Then counts (with audio) the target pattern onto the number line

Pedagogic principle: concept learning through contrasting instances

The learner is then asked to construct the correct answer on their line

Pedagogic principle: constructionism

Again the feedback shows the effect of a wrong answer

Pedagogic principle: constructionism

The correct answer matches the pattern to digit and number line

Pedagogic principle: reinforce associated representations

The next task selected should use what has already been learned

Pedagogic principle: reinforce and build on what has been learned

The next stage encourages recognition of the pattern, rather than counting, by timing the display Pedagogy: focus attention on salience of numerosity rather than sequence

If the learner fails the task it adapts by displaying for 1 sec longer until they can do it, then begins to speed up Pedagogy: adapt the level of the task to being just challenging enough

The next stage is to generalise to random collections

Pedagogy: generalise concept of numerosity from patterns to collections

Successive tasks encourage the learner to see known patterns embedded

Pedagogy: build the concept of the numerosity of a set and its subsets

4

Number Bonds to 10

Level 1 Stage 1 Even numbers, Length, Colour

Level 1 Stage 2

Odd, Length, Colour

Level 1 Stage 3

All, Length, Colour

Level 2 Stage 3

All, Length

Level 3, Stage 3

All, Length, Colour, Digits (Stages 1 and 2 at each Level use just Even and Odd numbers, respectively)

1 2 3 4 5 6 7 8 9 10 3 7

1 2 3 4 5 6 7 8 9 10 3 7 3 7

1 2 3 4 5 6 7 8 9 10 3 7 6 5 3 7

1 2 3 4 5 6 7 8 9 10 3 7 6 4

Level 4, Stage 3

Length, Digits

1 2 3 4 5 6 7 8 9 10 3 7

1 2 3 4 5 6 7 8 9 10 5 4 3 7

Level 5, Stage 3

Digits

1 2 3 4 5 6 7 8 9 3 5

1 2 3 4 5 6 7 8 9 3 6

1 2 3 4 5 6 7 8 9 3 7

Automatic data collection

9

Digital game elicits mean 173 trials in 13 minutes for ALDs (minimum possible is 100 if all correct) In ALD classes, these take ~2 minutes per trial

1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70

SEN1 Yr4

2 4 6 8 10 12 14 10 20 30 40 50 60 70

SEN2 Yr 4

2 4 6 8 10 12 14 16 18 20 10 20 30 40 50 60 70

SEN3 Yr4

2 4 6 8 10 12 14 16 18 20 10 20 30 40 50 60 70 80

SEN4 Yr 4

SEN4 Yr 4

2 4 6 8 10 12 14 16 18 20 10 20 30 40 50 60 70 80

SEN4 + Mainstream learner Yr 4

Mainstream, Yr 4

Adaptation (to 4 learners)

SEN group, Yr 4

• As recognition RTs improve higher numbers are introduced, so RTs

slow down then improve, creating saw-tooth pattern of RTs Mainstream learner, Yr 4

• All patterns are recognised within 2 secs

Trials for one type of task RT in secs

• Learners improve their recognition, but need more time to be as fast as

mainstream learners

One SEN pupil, Year 4 Time on task: 17.6 minutes over 5 Dots-to-Track enumeration tasks

Progress to recognition of pattern

Task 1 Task 2 Task 3 Task 1s Task 3s Errors 1 2 5 2 Mean RT 4.9 4.3 3.8 4.4 3.8

Few errors on untimed tasks, improving RTs Task timed at 1s to promote recognition of pattern  increases errors and RTs Next task changes display time to 3s  errors reduce and RTs improve  Further trials are needed, reducing time of display until recognition  Program must introduce timed display more gradually

Tasks 1-3 untimed

Task 4 displayed 1s Task 5 displayed 3s

How can technology help?

• a practice environment that assists interactions

with numbers and their meaning

• a teacher model that adapts the difficulty of the

task to the performance of the learner

• a personal device to support the learner away

from the classroom in learning the concept

• automatic data-tracking from each child to

monitor and encourage progress

Why dyscalculia important is important for all of us

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Dyslexia and dyscalculia

• Developmental dyslexia. This affects the literacy skills of

between 4-8% of children:

– it can reduce lifetime earnings by £81,000, and reduce the probability of achieving five or more GCSEs (A*-C) by 3-12 percentage points.

• Developmental dyscalculia – because of its low profile but

high impacts, its priority should be raised. Dyscalculia relates to numeracy and affects between 4-7% of children. It has a much lower profile than dyslexia but can also have substantial impacts:

– it can reduce lifetime earnings by £114,000 and reduce the probability of achieving five or more GCSEs (A*-C) by 7–20 percentage points. – Home and school interventions have again been identified by the Project. Also, technological interventions are extremely promising, offering individualised instruction and help, although these need more development.

Conclusions

• Neuroscience can identify brain networks involved in numbers

and arithmetic

• Dyscalculia

– a deficit in the core capacity to process numerosity of sets, the basis of arithmetical learning

• Identifying the core deficit in contrast to other types of

arithmetical learning difficulties

– Using simple timed tests of numerosity processing

• The neural basis of dyscalculia

– Abnormalities in numerosity-processing parts of the brain

• Educational implications

– Focus on strengthening basic numerosity processing

• Why dyscalculia is important for all of us

– Improving calculation skills will improve the life chances of sufferers and reduce the burden on the rest of us

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The End

www.mathematicalbrain.com For my papers on dyscalculia and useful links http://low-numeracy.ning.com For games to help dyscalculia Learners and an online forum www.education.gov.uk/lamb/module4/M04U16.htm l For government information (you can’t find it by a search on the DfE website).

Useful references

• Butterworth, B. (2005). Developmental dyscalculia. In J. I. D. Campbell (Ed.), Handbook of

Mathematical Cognition (pp. 455-467). Hove: Psychology Press.

• Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology &

Psychiatry, 46(1), 3-18.

• Butterworth, B., & Laurillard, D. (2010). Low numeracy and dyscalculia: identification and
• intervention. ZDM Mathematics Education, 42, 527-539
• Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: From brain to education. Science,

332, 1049-1053. doi: 10.1126/science.1201536

• Butterworth, B., & Yeo, D. (2004). Dyscalculia Guidance. GL Assessment
• Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental Dyscalculia and Basic Numerical

Capacities: A Study of 8-9 Year Old Students. Cognition, 93, 99-125.

• Landerl, K., Fussenegger, B., Moll, K., & Willburger, E. (2009). Dyslexia and dyscalculia: Two learning

disorders with different cognitive profiles. Journal of Experimental Child Psychology, 103(3), 309- 324.

• Reeve, R., Reynolds, F., Humberstone, J., & Butterworth, B. (2012). Stability and Change in Markers
• f Core Numerical Competencies. Journal of Experimental Psychology: General, 141(4), 649-666
• Nieder, A., & Dehaene, S. (2009). Representation of Number in the Brain. Annual Review of

Neuroscience, 32(1), 185-208.

But first

A political point

DfE 2012

• Dyscalculia

– 1 entry – “Pupils with dyscalculia have difficulty in acquiring mathematical skills. Pupils may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers and have problems learning number facts and procedures.” – “This page may not reflect Government policy”

DfES 2001

Dyscalculia is a condition that affects the ability to acquire arithmetical skills. Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers, and have problems learning number factsand procedures. Even if they produce a correct answer or use a correct method, they may do so mechanically and without confidence. …. Purely dyscalculic learners who have difficulties only with number will have cognitive and language abilities in the normal range, and may excel in nonmathematical subjects.

National Numeracy Strategy. Guidance to support pupils with dyslexia and dyscalculia.

Italy 2010. Law 170

• New regulations concerning specific disorders of learning.
• Article 1.1. The present law recognizes dyslexia, dysgraphia,

dysorthographia and dyscalculia as Specific Learning Disabilities… They manifest themselves in cases of adequate cognitive capacities, and in absence of neurological or sensory deficits. Yet, they constitute an important limitation for daily activities.

• Article 1.5. The present law refers to dyscalculia as a specific deficit

which manifests itself as a difficulty in grasping the automatisms of calculation and number processing.

• Article 2 states among other things, that there will be appropriate

teaching to realize potential, a reduction in social and emotional consequence, train teachers appropriately, make people aware of the problem, promote early diagnosis and rehabilitation, and ensure equal opportunities to develop social and professional capacities.