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
ordinals 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
16
Testing numerosity processing abilities
Tests of numerosity estimation
• How many dots are there? Shout out the
answer as quickly as possible
Number and time
24
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
0
2000
4000
6000
8000
1 2 3 4 5 6 7 8
RT
in m
secs
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 m
secs
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 m
secs
Number of Dots
6 years 7 years8.5 years 9 years11 years
SLOW MEDIUM FAST SLOW MEDIUM FAST
K 18% 50% 32%
Yr5 9% 50% 41%
Cluster at K predicts arithmetic to age 10 yrs
0
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
53
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.
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
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 & 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
65
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
of 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
77
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
80
Assessment:
Identifying the core deficit in the
classroom
The Dyscalculia Screener
Butterworth, 2003, Dyscalculia Screener
Dyscalculic learner
83
xxxxxxxxxxx
14 yr old female
Bad at arithmetic but not dyscalculic
84
xxxxxxxxxxx
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
onto 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
0
0
0
0
0
0
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
0123456789
0 10 20 30 40 50 60 70
SEN1 Yr4
SEN1 Yr40
2
4
6
8
10
12
14
0 10 20 30 40 50 60 70
SEN2 Yr 4
SEN2 Yr 402468
101214161820
0 10 20 30 40 50 60 70
SEN3 Yr4
SEN3 Yr40
2
4
6
8
10
12
14
16
18
20
0 10 20 30 40 50 60 70 80
SEN4 Yr 4
SEN4 Yr 40
2
4
6
8
10
12
14
16
18
20
0 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 0 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
132
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
134
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 of 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.