Dyscalculia: Why do numbers make no sense to some people?€¦ · dyscalculia & dyslexia (with Karen Waldie) • PhD, University of Oregon ... • Causes of dyscalculia • Auckland

Dyscalculia: Why do numbers

make no sense to some people?

Dyscalculia: Why do numbers

make no sense to some people?

Dr. Anna J. WilsonResearch Fellow

Department of Psychology

University of Auckland

Dr. Anna J. WilsonResearch Fellow

Department of Psychology

University of Auckland

My backgroundMy background

• BSc, The University of Auckland (Psychology)

– Exchange to University of California, Berkeley

• PhD, University of Oregon (Psychology)

– Dissertation: Numerical & spatial cognition

– Supporting area: Math learning disabilities

• BSc, The University of Auckland (Psychology)

– Exchange to University of California, Berkeley

• PhD, University of Oregon (Psychology)


– Supporting area: Math learning disabilities– Supporting area: Math learning disabilities

• Postdoctoral fellowship, INSERM U562, Paris

– Development & testing of remediation software for dyscalculia (with Stanislas Dehaene)

• Research fellow, University of Auckland

– Neural correlates of dyscalculia & relationship between dyscalculia & dyslexia (with Karen Waldie)






www.aboutdyscalculia.orgwww.aboutdyscalculia.org

• PhD, University of Oregon




– Development & testing of remediation software for

• PhD, University of Oregon




– Development & testing of remediation software for – Development & testing of remediation software for dyscalculia (with Stanislas Dehaene)



www.aboutdyscalculia.org




www.aboutdyscalculia.org

Talk outlineTalk outline

• What is dyscalculia?

• Numerical cognition

• Causes of dyscalculia

• Auckland comorbidity project




• Auckland comorbidity project• Auckland comorbidity project

• Identification

• Remediation

• The future


• Identification

• Remediation

• The future

• Severe difficulty in mathematics presumed to be due to a specific impairment in brain function

• Also called “Mathematics Disorder” (DSM-IV), or “mathematical learning disabilities”

• Severe difficulty in mathematics presumed to be due to a specific impairment in brain function

• Also called “Mathematics Disorder” (DSM-IV), or “mathematical learning disabilities”

Developmental dyscalculiaDevelopmental dyscalculia

or “mathematical learning disabilities”

• Prevalence: around 6% (same as dyslexia!)

• Has genetic component (runs in families)

• Understudied compared to dyslexia

or “mathematical learning disabilities”

• Prevalence: around 6% (same as dyslexia!)

• Has genetic component (runs in families)

• Understudied compared to dyslexia

Kosc, 1974; Shalev & Gross-Tsur, 2001; Geary, 1993, 2004; Badian, 1983; Lewis, Hitch, & Walker, 1994

Delay in acquisition of:

– Counting

– Addition strategies (counting on vs. counting all)

– Memorization of number facts (e.g. times tables)

Delay in acquisition of:

– Counting

– Addition strategies (counting on vs. counting all)

– Memorization of number facts (e.g. times tables)

Surface symptomsSurface symptoms3 x 2 =

3 x 3 =

3 x 4 =

Geary (1993, 2004) - review

Difficulties with story problems?

(e.g. Nancy Jordan’s research)

- esp. when dyslexia present!

Geary (1993, 2004) - review

Difficulties with story problems?

(e.g. Nancy Jordan’s research)

- esp. when dyslexia present!

2 + 5 = ?

Counting all

“1..2... 1...2...3...4..5..

1...2...3...4...5...6...7”

Counting on

“2...3...4...5...6...7”

Counting on (max)

“5...6...7”

• Difficulty representing quantity (“number sense”).

– Slow to compare numbers (Llanderl et al., 2004)

– Slow to enumerate 1-3 objects (“subitizing”)(Reeve et al., in press)

• Difficulty representing quantity (“number sense”).

– Slow to compare numbers (Llanderl et al., 2004)

– Slow to enumerate 1-3 objects (“subitizing”)(Reeve et al., in press)

Core cognitive symptomsCore cognitive symptoms

• Number symbols processed less automatically

– Number stroop task(Rouselle & Nöel, 2007;Rubinsten & Henik 2005)

• Mental number line slow to develop

• Number symbols processed less automatically

– Number stroop task(Rouselle & Nöel, 2007;Rubinsten & Henik 2005)

• Mental number line slow to develop

7 9 7 9

Some examples…Some examples…

Llanderl, Bevan & Butterworth, 2004. Note that the impairment is in response time as well as accuracy

7 9

Llanderl, Bevan & Butterworth, 2004.

7 9

Mental number line developmentMental number line development

0 100"Put a mark where 64 goes"

Siegler & Booth, 2004 Individual differences on this task correlate with maths achievement scores.

Mental number line in dyscalculiaMental number line in dyscalculia

0 100"Put a mark where 64 goes"

a) Number placement at T1: 0-100 number line

80

100

Mean

esti

mate

d m

ag

nit

ud

e

b) Number placement at T1: 0-1000 number line

700

800

900

1000

Mean

esti

mate

d m

ag

nit

ud

e

Wilson, Krinzinger, Nuerk, Dehaene & Willmes, in prep

0

20

40

60

0 20 40 60 80 100

Actual magnitude

Mean

esti

mate

d m

ag

nit

ud

e

Dyscalculic

Control

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800 900 1000

Actual magnitudeM

ean

esti

mate

d m

ag

nit

ud

e

Dyscalculic

Control

Difficulty with:

• Subtraction

• Using finger counting (slow, inaccurate, trouble recognising finger configurations)

• Decomposing numbers (e.g. recognizing that 10 is

Difficulty with:

• Subtraction

• Using finger counting (slow, inaccurate, trouble recognising finger configurations)

• Decomposing numbers (e.g. recognizing that 10 is

Likely other symptomsLikely other symptoms

• Decomposing numbers (e.g. recognizing that 10 is made up of 4 and 6)

• Understanding place value

• Learning/understanding multi-step calculation procedures and problem solving

Anxiety about or negative attitude towards maths

• Decomposing numbers (e.g. recognizing that 10 is made up of 4 and 6)

• Understanding place value

• Learning/understanding multi-step calculation procedures and problem solving

Anxiety about or negative attitude towards maths

• Blocked from certain professions (lower salary)

• Difficulty managing money

• Difficulty understanding statistics/numbers (influence on decision making)

• Low self-esteem, anxiety, avoidance

• Blocked from certain professions (lower salary)

• Difficulty managing money

• Difficulty understanding statistics/numbers (influence on decision making)

• Low self-esteem, anxiety, avoidance

Consequences in adultsConsequences in adults

• Low self-esteem, anxiety, avoidance• Low self-esteem, anxiety, avoidance

“I have always had difficulty with simple addition and subtraction since young, always still have to ‘count on my fingers quickly’ e.g. 5+7 without anyone knowing. Sometimes I feel very embarrassed! Especially under pressure I just panic.”

“I struggled through school with maths to the point the teachers gave up on me. I can only count on my fingers or with a calculator. I can't count out change, no matter how small and often get flustered with any tasks involving numbers. Despite trying hard I could never remember my 'times tables'. Division etc just bewildered me totally.

“I struggled through school with maths to the point the teachers gave up on me. I can only count on my fingers or with a calculator. I can't count out change, no matter how small and often get flustered with any tasks involving numbers. Despite trying hard I could never remember my 'times tables'. Division etc just bewildered me totally.

Consequences in adultsConsequences in adults

'times tables'. Division etc just bewildered me totally. English was one of my best subjects at school.”

“I have no trouble whatsoever reading or writing, understanding literary concepts and theories etc., but spend an hour sitting in the bank trying to work out how much money is in my cheque account! Last year I returned to University, attempting to avoid any papers containing mathematics, but hidden in nearly everything are formulas and calculations.”

'times tables'. Division etc just bewildered me totally. English was one of my best subjects at school.”

“I have no trouble whatsoever reading or writing, understanding literary concepts and theories etc., but spend an hour sitting in the bank trying to work out how much money is in my cheque account! Last year I returned to University, attempting to avoid any papers containing mathematics, but hidden in nearly everything are formulas and calculations.”

Both verbal and non-verbal:

• Dyslexia (50%)

• ADHD (30%)

• Dyspraxia

Both verbal and non-verbal:

• Dyslexia (50%)

• ADHD (30%)

• Dyspraxia

Co-morbid difficultiesCo-morbid difficulties

• Dyspraxia

• Spatial difficulties

Why is there such a high association between these disorders?? What is the implication for remediation?

• Dyspraxia

• Spatial difficulties

Why is there such a high association between these disorders?? What is the implication for remediation?

What causes dyscalculia?

How can it be indentified early?

Can it be “prevented”?

What is the best type of remediation?





The big questionsThe big questions


Why does it co-occur so often with other learning disabilities?

Are there subtypes; if so do they need different remediation approaches?

In order to answer these we need to know about how maths works in the brain.




In order to answer these we need to know about how maths works in the brain.










• Identification

• Remediation

• The future


• Identification

• Remediation

• The future

Numerical cognitionNumerical cognition

• Study of representation ofnumber in the brain

• Methods: Animals, infants, cross-cultural linguistics, brain imaging, cognitive psychology

• Study of representation ofnumber in the brain

• Methods: Animals, infants, cross-cultural linguistics, brain imaging, cognitive psychologylinguistics, brain imaging, cognitive psychology

• Good introductory books:

linguistics, brain imaging, cognitive psychology

• Good introductory books:

Stanislas

Dehaene

Mathematics is componentialMathematics is componential

• Non-verbal

– number, approximation, comparison

• Verbal

– number facts (multiplication, addition)

• Non-verbal


• Verbal

– number facts (multiplication, addition)– number facts (multiplication, addition)

• Logical

– problem solving, higher maths

• Spatial

– geometry? Number line?


• Logical


• Spatial


Non-verbal bases of numberNon-verbal bases of number

• Number is not “constructed” or dependent on logic/language as Piaget thought

• Animals can add, subtract, compare quantities!

• Number is not “constructed” or dependent on logic/language as Piaget thought

• Animals can add, subtract, compare quantities!quantities!

• As can pre-verbal human infants...

quantities!

• As can pre-verbal human infants...

Platt & Johnson (1971). Rats taught to press button a certain number of times for reward.

Mode at the right value, but responses approximate.

Platt & Johnson (1971). Rats taught to press button a certain number of times for reward.

Mode at the right value, but responses approximate.

Approximate number: Demonstration

Which side has more dots?

++

++

++

Ratio = 0.5

Faster, more accurate

Ratio = 0.79

Slower, less accurate

Approximate numberApproximate number

Ability to discriminate depends on ratio of the two

numbers. This "distance effect" is found in

animals, and human adults and children.




e.g. see Brannon (2003) for review

++

12 2412 24

++

19 2419 24

++

12 24 24 1912 24

Ratio = 0.5

Dots: faster, more accurate

Digits: the same!!

24 19

Ratio = 0.79

Dots: slower, less accurate

Digits: the same!!








e.g. see Brannon (2003) for review

Approximate arithmeticApproximate arithmetic

Barth (2005) –

Five year old children

Barth (2005) –

Five year old children


What have we learned about it so far?

• Non-verbal

• Non-symbolic

• Present in animals / human infants

What have we learned about it so far?

• Non-verbal

• Non-symbolic

• Present in animals / human infants• Present in animals / human infants

• Still accessed in skilled adults

• Used for representation and operations

Next: Has a specific brain basis

• Present in animals / human infants

• Still accessed in skilled adults

• Used for representation and operations

Next: Has a specific brain basis

Number senseNumber sense

“ Number sense ” is a short-hand term for our ability to

quickly understand, approximate, and manipulate

numerical quantities. (Dehaene, 2001)

Caution: term used in different

“ Number sense ” is a short-hand term for our ability to

quickly understand, approximate, and manipulate

numerical quantities. (Dehaene, 2001)

Caution: term used in differentCaution: term used in differentways in education (vs.in numerical cognition)see Berch, 2005 review

Caution: term used in differentways in education (vs.in numerical cognition)see Berch, 2005 review

Number sense in adultsNumber sense in adults

z = 44 x = 39x = - 48

Left hemisphere Right hemisphere

50 %z = 49

HIPS

Axial slice

Using number sense activates the intraparietal sulcus (IPS):

(This same area is involved in thinking about space.)

Tasks that activate this region:• Comparison of numbers• Subtraction• Approximation• Estimation• Non-symbolic tasks

Automatically activated by viewing numbers

Dehaene, Piazza, Pinel, & Cohen (2003)

22 %

e.g. comparison

Neurons & approximate numberNeurons & approximate number

Areas that respond to a change of numerosity

The “distance effect shows up in responses of neuronsThe “distance effect shows up in responses of neurons

0.5 1 2-0.4

-0.2

0

0.2

0.4

0.5 1 2-0.4

-0.2

0

0.2

0.4

% of activation to a number of dots after

a adaptation period

% d

’activation

Ratio / targetRatio / target

Weber

fraction

Weber

fraction

Piazza, 2004

Nieder &

Miller,

2004

Number sense in childrenNumber sense in children

Neural correlates the same

as in adults.

Non symbolic

tasks

Cantlon, Brannon, Carter & Pelphrey 2006

fMRI in 4 year olds

Mathematics is componentialMathematics is componential

• Non-verbal Intraparietal sulcus (IPS)


• Verbal Perisylvian language network


• Non-verbal Intraparietal sulcus (IPS)


• Verbal Perisylvian language network

– number facts (multiplication, addition)– number facts (multiplication, addition)

• Logical Frontal lobes?


• Spatial Parietal lobes?



• Logical Frontal lobes?


• Spatial Parietal lobes?


Supramarginal

gyrus

Angular gyrus

Superior Frontal Gyrus

Middle Frontal

Gyrus

Intraparietal

sulcus

Inferior

Frontal Gyrus

Middle Temporal Gyrus

Inferior temporal Gyrus










• Identification

• Remediation

• The future


• Identification

• Remediation

• The future

Causes of dyscalculiaCauses of dyscalculia

left hemisphere right hemisphere

"Core deficit" hypothesis"Core deficit" hypothesis: :

Deficit in number senseDeficit in number sense(Butterworth, 1999; Gersten & Chard, 1999; Wilson & Dehaene, 2007)

Dehaene, S. (1992). Cognition, 44, 1-42.

Dehaene, S., & Cohen, L. (1995). Mathematical Cognition, 1, 83-120.

verbal"six"

quantity

visual6

visual6

quantity

Brain bases of dyscalculiaBrain bases of dyscalculia

Dyscalculic adults born pre-term –Dyscalculic children - less grey matter in Dyscalculic adults born pre-term –less gray matter in IPS

(Isaacs, Edmonds & Lucas, 2001)

Superimposed images of sulci

Turner

subjects

Controls

Molko, Cachia and Riviere (2004) Turners subjects -

structural and functional alternations in IPS.

Dyscalculic children - less grey matter in IPS (Rotzer et al., 2008)

Dyscalculic children – less activation in IPS during magnitude tasks (Kucian et al., 2006)

Causes of dyscalculiaCauses of dyscalculia

left hemisphere right hemisphere

"Core deficit" hypothesis"Core deficit" hypothesis: :

Deficit in number senseDeficit in number sense(Butterworth, 1999; Gersten & Chard, 1999; Wilson & Dehaene, 2007)

"Access" hypothesis :

Deficit in link between

number sense and symbols(Rouselle & Nöel, 2007)

Dehaene, S. (1992). Cognition, 44, 1-42.

Dehaene, S., & Cohen, L. (1995). Mathematical Cognition, 1, 83-120.

verbal"six"

quantity

visual6

visual6

quantity

��

��

• Number sense / number sense access

– Everything affected except counting, fact retrieval

– May have difficulty with non-symbolic tasks

• Verbal

– Difficulty with counting, fact retrieval, word problems

– Associated with dyslexia?

• Number sense / number sense access

– Everything affected except counting, fact retrieval

– May have difficulty with non-symbolic tasks

• Verbal

– Difficulty with counting, fact retrieval, word problems


One subtype proposalOne subtype proposal


• Executive

– Difficulty with fact retrieval, use of strategy/procedure

– Associated with ADHD??

• Spatial

– Difficulty with subitizing, apprehension of non-symbolic quantity… mental number line?

Wilson & Dehaene (2007)


• Executive

– Difficulty with fact retrieval, use of strategy/procedure

– Associated with ADHD??

• Spatial

– Difficulty with subitizing, apprehension of non-symbolic quantity… mental number line?

Wilson & Dehaene (2007)










• Identification

• Remediation

• The future


• Identification

• Remediation

• The future









The big questionsThe big questions







Auckland comorbidity projectAuckland comorbidity project

Postdoctoral fellowship with KarenWaldie, funded by Univ. of Auckland.

Phase I:

80 adults with dyscalculia, dyslexia,

Postdoctoral fellowship with KarenWaldie, funded by Univ. of Auckland.

Phase I:

80 adults with dyscalculia, dyslexia,80 adults with dyscalculia, dyslexia,both or neither (20 per group)

• Cognitive testing (symptoms, subtypes)

• Brain imaging (fMRI; neural markers)

Phase II (if funded!): similar study in children

80 adults with dyscalculia, dyslexia,both or neither (20 per group)

• Cognitive testing (symptoms, subtypes)

• Brain imaging (fMRI; neural markers)

Phase II (if funded!): similar study in children

An aside...An aside...

Many people mistakenly think that “if it’s in the brain it can’t be changed”

Nothing could be more wrong!

Many people mistakenly think that “if it’s in the brain it can’t be changed”

Nothing could be more wrong!Nothing could be more wrong!

• The brain is the basis of all learning

• Brain function and even structure is highly “plastic”, especially at a young age

• The mild impairments associated with learning disabilities are nothing like the brain damage caused by stroke/lesion

Nothing could be more wrong!

• The brain is the basis of all learning

• Brain function and even structure is highly “plastic”, especially at a young age

• The mild impairments associated with learning disabilities are nothing like the brain damage caused by stroke/lesion

An example from reading...An example from reading...

Fast ForWord

(Merzenich et al., 2006; Tallal et al., 2006;

Scientific Learning Corporation)

Fast ForWord

(Merzenich et al., 2006; Tallal et al., 2006;

Scientific Learning Corporation)

• Adaptive game software for reading

• Specific Language Impairment, Dyslexia• Specific Language Impairment, Dyslexia

• Intensive individual intervention(1h/day for 12 wks)

Temple et al. 2003










• Identification

• Remediation

• The future


• Identification

• Remediation

• The future

IdentificationIdentification

Test for:

• Mathematics level (standardised test)

– e.g. PAT, Woodcock Johnson, WRAT, KeyMath

• Profile of performance in different components

• IQ (rule out general difficulties)

Test for:

• Mathematics level (standardised test)

– e.g. PAT, Woodcock Johnson, WRAT, KeyMath

• Profile of performance in different components

• IQ (rule out general difficulties)• IQ (rule out general difficulties)

• Dyslexia, ADHD, spatial difficulties, dyspraxia if suspected

Important to rule out:educational experiences, motivation

• IQ (rule out general difficulties)

• Dyslexia, ADHD, spatial difficulties, dyspraxia if suspected

Important to rule out:educational experiences, motivation

Profiling testsProfiling tests

Ideally: Measurements of response time as well as accuracy. Separate breakdowns for different operations and components

• KeyMath (5-22 yrs)

Ideally: Measurements of response time as well as accuracy. Separate breakdowns for different operations and components

• KeyMath (5-22 yrs)• KeyMath (5-22 yrs)

• TEMA-3 (3-8 yrs)

• CMAT (7-19 yrs)

• Diagnostic mathematics profiles (AUS)

• Booker Profiles? (AUS)

• KeyMath (5-22 yrs)

• TEMA-3 (3-8 yrs)

• CMAT (7-19 yrs)

• Diagnostic mathematics profiles (AUS)

• Booker Profiles? (AUS)

Dyscalculia Screener (nferNelson)Dyscalculia Screener (nferNelson)

Brian Butterworth, University College London

www.mathematicalbrain.com

Computerised, for use in schools

– Number stroop

– Subitizing / Counting

Brian Butterworth, University College London

www.mathematicalbrain.com

Computerised, for use in schools

– Number stroop

– Subitizing / Counting– Subitizing / Counting

– Mental arithmetic

Administration time: 30 minutes

Advantages: Precise measures including reaction time, standardised, fast

Disadvantages: Assumes dyscalculia caused by core deficit in number sense

– Subitizing / Counting

– Mental arithmetic

Administration time: 30 minutes

Advantages: Precise measures including reaction time, standardised, fast

Disadvantages: Assumes dyscalculia caused by core deficit in number sense










• Identification

• Remediation

• The future


• Identification

• Remediation

• The future

Individual remediationIndividual remediation

• Focus on understanding (esp. quantity)

• Drilling of facts only useful up to a point

• Use concrete materials

• Start at an easy level (success important!)

• Focus on understanding (esp. quantity)

• Drilling of facts only useful up to a point

• Use concrete materials

• Start at an easy level (success important!)• Start at an easy level (success important!)

• Provide lots of practice

• Reduce need for memorisation

• Ask a lot of questions to get the child engaged and thinking

• Make learning active and fun

• Start at an easy level (success important!)

• Provide lots of practice

• Reduce need for memorisation

• Ask a lot of questions to get the child engaged and thinking

• Make learning active and fun

How to help in the classroomHow to help in the classroom

• Give children their own set of work, at their level

• Allow extra time

• Use written and verbal instructions and

• Give children their own set of work, at their level

• Allow extra time

• Use written and verbal instructions and • Use written and verbal instructions and questions

• Extra scaffolding, especially for multi-step procedures

• Reduce opportunity for comparison with peers

• Use written and verbal instructions and questions

• Extra scaffolding, especially for multi-step procedures

• Reduce opportunity for comparison with peers

What about subtypes?What about subtypes?

In the absence of a verdict from research a good way to approach subtypes is by using a componential analysis to plan remediation.

e.g. If child is good at multiplication but has trouble

In the absence of a verdict from research a good way to approach subtypes is by using a componential analysis to plan remediation.

e.g. If child is good at multiplication but has trouble e.g. If child is good at multiplication but has trouble with number sense, focus on number sense!

If child has dyslexia and trouble with word problems, focus on reading/interpreting.

Note that this necessitates a componential assessment

e.g. If child is good at multiplication but has trouble with number sense, focus on number sense!

If child has dyslexia and trouble with word problems, focus on reading/interpreting.

Note that this necessitates a componential assessment

Remediation workbooksRemediation workbooks

Dyscalculia Guidance by Brian Butterworth & Dorian Yeo. (2004).

The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths by Ronit Bird (2007).

Dyscalculia: Action Plans for Successful Learning in Mathematics by GlynisHannell. (2005).

Dyslexia, Dyspraxia and Mathematics by Dorian Yeo. (2003).

Mathematics for dyslexics including dyscalculia by Steve Chinn and Richard Ashcroft. (2007, 3rd Edn).

The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties by Steve Chinn. (2004).

Dyscalculia Guidance by Brian Butterworth & Dorian Yeo. (2004).

The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths by Ronit Bird (2007).

Dyscalculia: Action Plans for Successful Learning in Mathematics by GlynisHannell. (2005).

Dyslexia, Dyspraxia and Mathematics by Dorian Yeo. (2003).

Mathematics for dyslexics including dyscalculia by Steve Chinn and Richard Ashcroft. (2007, 3rd Edn).

The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties by Steve Chinn. (2004).

SoftwareSoftware

Bubble Reef

by ICDC

Bubble Reef

by ICDC

Number Sharkby White SpaceNumber Sharkby White Space

To Market, To Marketby Learning in MotionTo Market, To Marketby Learning in Motion

The Number Race

by myself and Stan Dehaene

The Number Race

by myself and Stan Dehaene

by ICDCby ICDC

Knowsley Woods

by ICDC

Knowsley Woods

by ICDC

The Number RaceThe Number Race

http://www.unicog.org/main/pages.php?page=NumberRace

Adaptive game to remediate/teach early number sense

• Non-profit model ("open source" = free to obtain,

http://www.unicog.org/main/pages.php?page=NumberRace

Adaptive game to remediate/teach early number sense

• Non-profit model ("open source" = free to obtain, • Non-profit model ("open source" = free to obtain, copy, distribute, modify)

• Programmed by myself

Wilson et al. 2007a,b

Languages:

• Non-profit model ("open source" = free to obtain, copy, distribute, modify)

• Programmed by myself

Wilson et al. 2007a,b

Languages:

Research based instructional principlesResearch based instructional principles

• Enhance number sense– intensive number comparison (e.g. largest of 3, 9?)– speed deadline– link between number and space

• Cement non-symbolic symbolic links– repeated association of non-symbolic & symbolic

numbers

• Enhance number sense– intensive number comparison (e.g. largest of 3, 9?)– speed deadline– link between number and space

• Cement non-symbolic symbolic links– repeated association of non-symbolic & symbolic

numbersnumbers– encourage increasing reliance on symbols

• Conceptualise and automatise arithmetic– concrete representations of operations– speed deadline

• Maximize motivation– positive reinforcement– difficulty adaptation– entertaining format (game!)

numbers– encourage increasing reliance on symbols

• Conceptualise and automatise arithmetic– concrete representations of operations– speed deadline

• Maximize motivation– positive reinforcement– difficulty adaptation– entertaining format (game!)

Adaptive algorithmAdaptive algorithm

• AI (artificial intelligence) module builds a model of children's "knowledge space"

• Presents problems on borders of knowledge (not too easy, not too hard)

• Tries to push these borders

• AI (artificial intelligence) module builds a model of children's "knowledge space"

• Presents problems on borders of knowledge (not too easy, not too hard)

• Tries to push these borders 0.8

1


• General: can beused for any task if learningdimensions known


• General: can beused for any task if learningdimensions known

00.2

0.40.6

0.81

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

nota

tion

speed

distance










• Identification

• Remediation

• The future


• Identification

• Remediation

• The future

Future goalsFuture goals

Identify children as young as possible and provide preventative intervention

Why?

• Brain more "plastic" at young age

Identify children as young as possible and provide preventative intervention

Why?

• Brain more "plastic" at young age• Brain more "plastic" at young age

• Maths is highly cumulative

• Avoid negative experiences associated with failure

• Quicker and cheaper

• Brain more "plastic" at young age

• Maths is highly cumulative

• Avoid negative experiences associated with failure

• Quicker and cheaper

Early identificationEarly identification

• Currently can do behavioural screening, either

– Non-symbolic in infancy

– Symbolic in kindergarten

• Can predict future performance from behavioural measures in kindergarten

• Currently can do behavioural screening, either

– Non-symbolic in infancy

– Symbolic in kindergarten

• Can predict future performance from behavioural measures in kindergartenbehavioural measures in kindergarten(e.g. Mazzocco & Thompson, 2005)

• But still have many false positives

• More work needed to develop measures

behavioural measures in kindergarten(e.g. Mazzocco & Thompson, 2005)

• But still have many false positives

• More work needed to develop measures

Future goalsFuture goals

Identify genetic markers so we know which kids are at risk.

Need to: find genes

Need dyscalculic families!

Identify genetic markers so we know which kids are at risk.

Need to: find genes

Need dyscalculic families!Need dyscalculic families!

Identify neural markers.

Need to: develop inexpensive and quick brain imaging techniques.

Need dyscalculic families!

Identify neural markers.

Need to: develop inexpensive and quick brain imaging techniques.

A copy of this presentationA copy of this presentation

...Can be found on:

My website:www.aboutdyscalculia.org

...Can be found on:

My website:www.aboutdyscalculia.orgwww.aboutdyscalculia.org(look under “news”)

Contact information:[email protected]

www.aboutdyscalculia.org(look under “news”)

Contact information:[email protected]

ReferencesReferencesBadian, N. A. (1983). Dyscalculia and nonverbal disorders of learning. In H. R. Myklebust (Ed.), Progress in Learning

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Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. PNAS, 102(39), 14116-14121.

Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333-339.

Brannon, E. M. (2003). Number knows no bounds. Trends in Cognitive Sciences, 7(7), 279-281.

Butterworth, B. (1999). The mathematical brain. London: Macmillan.

Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4(5), e125.

Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1-2), 1-42.

Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. Oxford: Oxford University Press.

Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16-36.

Badian, N. A. (1983). Dyscalculia and nonverbal disorders of learning. In H. R. Myklebust (Ed.), Progress in Learning Disabilities (Vol. 5, pp. 235-264). New York: Stratton.

Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. PNAS, 102(39), 14116-14121.

Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333-339.

Brannon, E. M. (2003). Number knows no bounds. Trends in Cognitive Sciences, 7(7), 279-281.

Butterworth, B. (1999). The mathematical brain. London: Macmillan.

Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4(5), e125.

Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1-2), 1-42.

Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. Oxford: Oxford University Press.

Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16-36.Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16-36.

Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1(1), 83-120.

Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506.

Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological and genetic components. Psychological

Bulletin, 114(2), 345-362.

Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15.Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical

disabilities. The Journal of special education, 33(1), 18.

Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124(9), 1701-1707.

Kucian, K., Loenneker, T., Dietrich, T., Dosch, M., Martin, E., & von Aster, M. (2006). Impaired neural networks for approximate calculation in dyscalculic children: A functional mri study. Behavioral and Brain Functions, 2, 31.

Kosc, L. (1974). Developmental Dyscalculia. Journal of Learning Disabilities, 7(3), 164-177.

Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students. Cognition, 93(2), 99-125.

Lewis, C., Hitch, G. J., & Walker, P. (1994). The prevalence of specific arithmetic difficulties and specific reading difficulties in 9- to 10-year old boys and girls. Journal of Child Psychology and Psychiatry, 35(2), 283-292.

Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16-36.

Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1(1), 83-120.

Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506.

Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological and genetic components. Psychological

Bulletin, 114(2), 345-362.

Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15.Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical

disabilities. The Journal of special education, 33(1), 18.

Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124(9), 1701-1707.

Kucian, K., Loenneker, T., Dietrich, T., Dosch, M., Martin, E., & von Aster, M. (2006). Impaired neural networks for approximate calculation in dyscalculic children: A functional mri study. Behavioral and Brain Functions, 2, 31.

Kosc, L. (1974). Developmental Dyscalculia. Journal of Learning Disabilities, 7(3), 164-177.

Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students. Cognition, 93(2), 99-125.

Lewis, C., Hitch, G. J., & Walker, P. (1994). The prevalence of specific arithmetic difficulties and specific reading difficulties in 9- to 10-year old boys and girls. Journal of Child Psychology and Psychiatry, 35(2), 283-292.

References cntd.References cntd.Mazzocco, M. M. M., & Thompson, R. E. (2005). Kindergarten predictors of math learning disability. Learning

Disabilities Research and Practice, 20(3), 142-155.

Merzenich, M. M., Jenkins, W. M., Johnston, P., Schreiner, C., Miller, S. L., & Tallal, P. (1996). Temporal processing deficits of language-learning impaired children ameliorated by training. Science, 271(5245), 77-81.

Molko, N., Cachia, A., Riviere, D., Mangin, J. F., Bruandet, M., Le Bihan, D., et al. (2003). Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin. Neuron, 40(4), 847-858.

Nieder, A., & Miller, E. K. (2004). A parieto-frontal network for visual numerical information in the monkey. PNAS, 101(19), 7457-7462.

Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547-555.

Rotzer, S., Kucian, K., Martin, E., Aster, M. v., Klaver, P., & Loenneker, T. (2008). Optimized voxel-based morphometryin children with developmental dyscalculia. NeuroImage, 39(1), 417-422.

Rousselle, L., & Noel, M.-P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361-395.

Mazzocco, M. M. M., & Thompson, R. E. (2005). Kindergarten predictors of math learning disability. Learning Disabilities Research and Practice, 20(3), 142-155.

Merzenich, M. M., Jenkins, W. M., Johnston, P., Schreiner, C., Miller, S. L., & Tallal, P. (1996). Temporal processing deficits of language-learning impaired children ameliorated by training. Science, 271(5245), 77-81.

Molko, N., Cachia, A., Riviere, D., Mangin, J. F., Bruandet, M., Le Bihan, D., et al. (2003). Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin. Neuron, 40(4), 847-858.

Nieder, A., & Miller, E. K. (2004). A parieto-frontal network for visual numerical information in the monkey. PNAS, 101(19), 7457-7462.

Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547-555.

Rotzer, S., Kucian, K., Martin, E., Aster, M. v., Klaver, P., & Loenneker, T. (2008). Optimized voxel-based morphometryin children with developmental dyscalculia. NeuroImage, 39(1), 417-422.

Rousselle, L., & Noel, M.-P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361-395.comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361-395.

Rubinsten, O., & Henik, A. (2005). Automatic Activation of Internal Magnitudes: A Study of Developmental Dyscalculia. Neuropsychology, 19(5), 641.

Shalev, R. S., & Gross-Tsur, V. (2001). Developmental dyscalculia. Pediatric Neurology, 24(5), 337-342.

Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.

Tallal, P., Miller, S. L., Bedi, G., Byma, G., Wang, X., Nagarajan, S. S., et al. (1996). Language comprehension in language-learning impaired children improved with acoustically modified speech. Science, 271(5245), 81-84.

Temple, E., Deutsch, G. K., Poldrack, R. A., Miller, S. L., Tallal, P., Merzenich, M. M., et al. (2003). Neural deficits in children with dyslexia ameliorated by behavioral remediation: Evidence from functional mri. Proc Natl Acad Sci U S A, 100(5), 2860-2865.

Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. In D. Coch, G. Dawson & K. Fischer (Eds.), Human behavior, learning and the developing brain: Atypical development. New York: Guilford Press.

Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006a). Principles underlying the design of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(19).

Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006b). An open trial assessment of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(20).

comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361-395.

Rubinsten, O., & Henik, A. (2005). Automatic Activation of Internal Magnitudes: A Study of Developmental Dyscalculia. Neuropsychology, 19(5), 641.

Shalev, R. S., & Gross-Tsur, V. (2001). Developmental dyscalculia. Pediatric Neurology, 24(5), 337-342.

Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.

Tallal, P., Miller, S. L., Bedi, G., Byma, G., Wang, X., Nagarajan, S. S., et al. (1996). Language comprehension in language-learning impaired children improved with acoustically modified speech. Science, 271(5245), 81-84.

Temple, E., Deutsch, G. K., Poldrack, R. A., Miller, S. L., Tallal, P., Merzenich, M. M., et al. (2003). Neural deficits in children with dyslexia ameliorated by behavioral remediation: Evidence from functional mri. Proc Natl Acad Sci U S A, 100(5), 2860-2865.

Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. In D. Coch, G. Dawson & K. Fischer (Eds.), Human behavior, learning and the developing brain: Atypical development. New York: Guilford Press.

Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006a). Principles underlying the design of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(19).

Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006b). An open trial assessment of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(20).

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