SPELDKeynote_AnnaWilson_2008

8/12/2019 SPELDKeynote_AnnaWilson_2008

1/75

Dyscalculia: Why do numbersmake no sense to some people?

Dyscalculia: Why do numbersmake no sense to some people?

Dr. Anna J. WilsonResearch FellowDepartment of PsychologyUniversity of Auckland

Dr. Anna J. WilsonResearch FellowDepartment of PsychologyUniversity of Auckland


2/75

My backgroundMy background BSc, The University of Auckland (Psychology)

Exchange to University of California, Berkeley PhD, University of Oregon (Psychology)

Dissertation: Numerical & spatial cognition

BSc, The University of Auckland (Psychology)

Exchange to University of California, Berkeley PhD, University of Oregon (Psychology)

Dissertation: Numerical & spatial cognition

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)

Postdoctoral fellowship, INSERM U562, Paris Development & testing of remediation software for





3/75

www.aboutdyscalculia.orgwww.aboutdyscalculia.org PhD, University of Oregon

Dissertation: Numerical & spatial cognition Supporting area: Math learning disabilities

Postdoctoral fellowship, INSERM U562, Paris

PhD, University of Oregon

Dissertation: Numerical & spatial cognition Supporting area: Math learning disabilities

Postdoctoral fellowship, INSERM U562, Paris




www.aboutdyscalculia.org




www.aboutdyscalculia.org


4/75

Talk outlineTalk outline What is dyscalculia?

Numerical cognition Causes of dyscalculia

What is dyscalculia?


Identification Remediation

The future


The future


5/75

Severe difficulty in mathematics presumed to

be due to a specific impairment in brainfunction

Also called Mathematics Disorder (DSM-IV),

Severe difficulty in mathematics presumed to

be due to a specific impairment in brainfunction

Also called Mathematics Disorder (DSM-IV),

Developmental dyscalculiaDevelopmental dyscalculia

Prevalence: around 6% (same as dyslexia!)

Has genetic component (runs in families)

Understudied compared to dyslexia

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


6/75

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 symptoms 3 x 2 =3 x 3 =

3 x 4 =

Geary (1993, 2004) - review

Difficulties with story problems?

(e.g. Nancy Jordans research)- esp. when dyslexia present!

Geary (1993, 2004) - review

Difficulties with story problems?

(e.g. Nancy Jordans research)- esp. when dyslexia present!


7/75

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 & Nel, 2007;Rubinsten & Henik 2005)

Mental number line slow to develop

Number symbols processed less automatically

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

Mental number line slow to develop

7 9 7 9


8/75

Some examplesSome examples

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


9/75

Llanderl, Bevan & Butterworth, 2004.

7


10/75

Mental number line developmentMental number line development0 100"Put a mark where 64 goes"

Siegler & Booth, 2004 Individual differences on this task correlate

with maths achievement scores.


11/75

Mental number line in dyscalculiaMental number line in dyscalculia0 100"Put a mark where 64 goes"

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

80

100

i t u

d e

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

800

900

1000

t u d e

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

0

20

40

60

0 20 40 60 80 100Actual magnitude

M e a n e s

t i m a

t e d m a g

DyscalculicControl

0

100

200

300

400

500

600

0 100 200 300 400 500 600 700 800 900 1000

Actual magnitude

M e a n e s

t i m a t e d m a g n

i

DyscalculicControl


12/75


13/75

Blocked from certain professions (lower salary)

Difficulty managing money Difficulty understanding statistics/numbers (influence

on decision making)

Blocked from certain professions (lower salary)

Difficulty managing money Difficulty understanding statistics/numbers (influence

on decision making)

Consequences in adultsConsequences in adults

- , ,- , ,

I have always had difficulty with simpleaddition and subtraction since young,

always still have to count on my fingersquickly e.g. 5+7 without anyone knowing.Sometimes I feel very embarrassed!Especially under pressure I just panic.


14/75

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

Consequences in adultsConsequences in adults

English was one of my best subjects at school. I have no trouble whatsoever reading or writing,

understanding literary concepts and theories etc., butspend an hour sitting in the bank trying to work out how

much money is in my cheque account! Last year I returnedto University, attempting to avoid any papers containingmathematics, but hidden in nearly everything are formulasand calculations.

English was one of my best subjects at school. I have no trouble whatsoever reading or writing,

understanding literary concepts and theories etc., butspend an hour sitting in the bank trying to work out how

much money is in my cheque account! Last year I returnedto University, attempting to avoid any papers containingmathematics, but hidden in nearly everything are formulasand calculations.


15/75

Both verbal and non-verbal:

Dyslexia (50%) ADHD (30%)

Both verbal and non-verbal:

Dyslexia (50%) ADHD (30%)

Co-morbid difficultiesCo-morbid difficulties

Spatial difficulties

Why is there such a high association betweenthese disorders?? What is the implication forremediation?

Spatial difficulties

Why is there such a high association betweenthese disorders?? What is the implication forremediation?


16/75

What causes dyscalculia?

How can it be indentified early?Can it be prevented?



The big questionsThe big questions

Why does it co-occur so often with otherlearning disabilities?

Are there subtypes; if so do they need differentremediation approaches?

In order to answer these we need to know about

how maths works in the brain.


Are there subtypes; if so do they need differentremediation approaches?

In order to answer these we need to know about

how maths works in the brain.


17/75






The future


The future


18/75

Numerical cognitionNumerical cognition Study of representation of

number in the brain

Methods: Animals, infants, cross-cultural

Study of representation of

number in the brain

Methods: Animals, infants, cross-cultural, ,

Good introductory books:

, ,

Good introductory books:

Stanislas

Dehaene


19/75

Mathematics is componentialMathematics is componential Non-verbal

number, approximation, comparison Verbal

Non-verbal

number, approximation, comparison Verbal

,

Logical problem solving, higher maths

Spatial geometry? Number line?

,

Logical problem solving, higher maths

Spatial geometry? Number line?


20/75

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!

As can pre-verbal human infants... As can pre-verbal human infants...

Platt & Johnson (1971).

Rats taught to press buttona certain number of timesfor reward.Mode at the right value, but

responses approximate .

Platt & Johnson (1971).

Rats taught to press buttona certain number of timesfor reward.Mode at the right value, but

responses approximate .


21/75

Approximate number: Demonstration

Which side has more dots?


22/75


23/75


24/75


25/75


26/75


27/75

Ratio = 0.5

Faster, more accurate

Ratio = 0.79

Slower, less accurate


28/75

Approximate numberApproximate numberAbility to discriminate depends on ratio of the twonumbers. This "distance effect" is found in

animals, and human adults and children.

Ability to discriminate depends on ratio of the twonumbers. This "distance effect" is found in


e.g. see Brannon (2003) for review


29/75


30/75


31/75


32/75


33/75


34/75

12 24

Ratio = 0.5

Dots: faster, more accurateDigits: the same!!

24 19

Ratio = 0.79

Dots: slower, less accurateDigits: the same!!


35/75

Approximate numberApproximate numberAbility to discriminate depends on ratio of the twonumbers. This "distance effect" is found in


Ability to discriminate depends on ratio of the twonumbers. This "distance effect" is found in


e.g. see Brannon (2003) for review


36/75

Approximate arithmeticApproximate arithmeticBarth (2005) Five year old childrenBarth (2005) Five year old children


37/75

Approximate numberApproximate numberWhat have we learned about it so far?

Non-verbal Non-symbolic

What have we learned about it so far?

Non-verbal Non-symbolic

resen n an ma s uman n an s Still accessed in skilled adults Used for representation and operations

Next: Has a specific brain basis

resen n an ma s uman n an s Still accessed in skilled adults Used for representation and operations

Next: Has a specific brain basis


38/75


39/75

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


40/75

Neurons & approximate numberNeurons & approximate number

Areas that respond to a change of numerosity

The distance effect shows up in responses

of neurons

The 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 aftera adaptation period

% d

a c t

i v a

t i o n

Ratio / target Ratio / target

Weberfraction

Weberfraction

Piazza, 2004

Nieder &Miller,2004


41/75

Number sense in childrenNumber sense in childrenNeural correlates the sameas in adults.

Non symbolictasks

Cantlon, Brannon,Carter & Pelphrey 2006

fMRI in 4 year olds


42/75

Mathematics is componentialMathematics is componential Non-verbal Intraparietal sulcus (IPS)

number, approximation, comparison Verbal Perisylvian language network

Non-verbal Intraparietal sulcus (IPS)

number, approximation, comparison Verbal Perisylvian language network

,

Logical Frontal lobes? problem solving, higher maths

Spatial Parietal lobes? geometry? Number line?

,

Logical Frontal lobes? problem solving, higher maths

Spatial Parietal lobes? geometry? Number line?


43/75

Supramarginalgyrus

Angular gyrus

Superior Frontal Gyrus

Middle FrontalGyrus

Intraparietalsulcus

InferiorFrontal Gyrus

Middle Temporal Gyrus

Inferior temporal Gyrus


44/75






The future


The future


45/75

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


46/75

Brain bases of dyscalculiaBrain bases of dyscalculia

D scalculic adults born re-term D scalculic children - less re matter inless gray matter in IPS

(Isaacs, Edmonds & Lucas, 2001)

Superimposed images of sulciTurnersubjects

Controls

Molko, Cachia and Riviere (2004) Turners subjects -structural and functional alternations in IPS.

IPS (Rotzer et al., 2008)

Dyscalculic children less activation inIPS during magnitude tasks (Kucian etal., 2006)


47/75

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 betweennumber sense and symbols

(Rouselle & Nel, 2007)

Dehaene, S. (1992). Cognition, 44 , 1-42.Dehaene, S., & Cohen, L. (1995). Mathematical Cognition, 1 , 83-120.

verbal"six"

quantity

visual6

visual6

quantity


48/75

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

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

Associated with dyslexia?

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)

Associated with dyslexia?

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)


49/75






The future


The future


50/75





The big questionsThe big questions


Are there subtypes ; if so do they need differentremediation approaches?


Are there subtypes ; if so do they need differentremediation approaches?


51/75

Auckland comorbidity projectAuckland comorbidity projectPostdoctoral fellowship with KarenWaldie, funded by Univ. of Auckland.

Phase I:

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

Phase I: , ,

both or neither (20 per group)

Cognitive testing (symptoms, subtypes)

Brain imaging (fMRI; neural markers)

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

, ,both or neither (20 per group)

Cognitive testing (symptoms, subtypes)

Brain imaging (fMRI; neural markers)

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


52/75


53/75


54/75

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

S ecific Lan ua e Im airment D slexia

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

Temple et al. 2003


55/75






The future


The future


56/75

IdentificationIdentificationTest for: Mathematics level (standardised test)

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

Profile of performance in different components

Test for: Mathematics level (standardised test)

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

Profile of performance in different components ru e ou genera cu es

Dyslexia, ADHD, spatial difficulties, dyspraxia ifsuspected

Important to rule out:educational experiences, motivation

ru e ou genera cu es Dyslexia, ADHD, spatial difficulties, dyspraxia if

suspected

Important to rule out:educational experiences, motivation


57/75

Profiling testsProfiling testsIdeally: Measurements of response time as

well as accuracy. Separate breakdowns fordifferent operations and components KeyMath (5-22 yrs)

Ideally: Measurements of response time as

well as accuracy. Separate breakdowns fordifferent operations and components KeyMath (5-22 yrs)

TEMA-3 (3-8 yrs) CMAT (7-19 yrs) Diagnostic mathematics profiles (AUS) Booker Profiles? (AUS)

TEMA-3 (3-8 yrs) CMAT (7-19 yrs) Diagnostic mathematics profiles (AUS) Booker Profiles? (AUS)

ff


58/75

Dyscalculia Screener (nferNelson)Dyscalculia Screener (nferNelson)

Brian Butterworth, University College Londonwww.mathematicalbrain.com

Computerised, for use in schools Number stroop

Brian Butterworth, University College Londonwww.mathematicalbrain.com

Computerised, for use in schools Number stroop

u z ng oun ng Mental arithmetic

Administration time: 30 minutes

Advantages: Precise measures including reaction time,standardised, fastDisadvantages: Assumes dyscalculia caused by core

deficit in number sense

u z ng oun ng Mental arithmetic

Administration time: 30 minutes

Advantages: Precise measures including reaction time,standardised, fastDisadvantages: Assumes dyscalculia caused by core

deficit in number sense


59/75





Identification Remediation The future



60/75

Individual remediationIndividual remediation Focus on understanding (esp. quantity)

Drilling of facts only useful up to a point Use concrete materials

Focus on understanding (esp. quantity)

Drilling of facts only useful up to a point Use concrete materials

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

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

H h l i h lH h l i h l


61/75

How to help in the classroomHow to help in the classroom

Give children their own set of work, attheir level

Allow extra time

Give children their own set of work, attheir level

Allow extra time

questions Extra scaffolding, especially for multi-step

procedures

Reduce opportunity for comparison withpeers

questions Extra scaffolding, especially for multi-step

procedures

Reduce opportunity for comparison withpeers

Wh t b t bt ?Wh t b t bt ?


62/75

What about subtypes?What about subtypes?

In the absence of a verdict from research a goodway to approach subtypes is by using acomponential analysis to plan remediation.

In the absence of a verdict from research a goodway to approach subtypes is by using acomponential analysis to plan remediation.

. .

with number sense, focus on number sense!

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

Note that this necessitates a componentialassessment

. .

with number sense, focus on number sense!

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

Note that this necessitates a componentialassessment

R di ti kb kR di ti kb k


63/75

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 Glynis

Hannell. (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 Glynis

Hannell. (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).

Soft areSoft are


64/75

SoftwareSoftware

Bubble Reef

Bubble Reef

Number Sharkby White Space

Number Sharkby White Space

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

The Number Raceby myself and Stan

Dehaene

The Number Raceby myself and Stan

Dehaene

Knowsley Woods

by ICDC

Knowsley Woods

by ICDC

The Number RaceThe Number Race


65/75

The Number RaceThe Number Race

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

Adaptive game to remediate/teach early numbersense

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

Adaptive game to remediate/teach early numbersense

on-pro mo e open source = ree o o a n,copy, distribute, modify)

Programmed by myself

Wilson et al. 2007a,b

Languages:

on-pro mo e open source = ree o o a n,copy, distribute, modify)

Programmed by myself

Wilson et al. 2007a,b

Languages:


66/75

Research based instructional principlesResearch based instructional principles


67/75

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

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 & symbolicnum ers

encourage increasing reliance on symbols Conceptualise and automatise arithmetic

concrete representations of operations speed deadline

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

num ers

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


68/75

Adaptive algorithmAdaptive algorithm

AI (artificial intelligence) module builds a modelof children's "knowledge space"

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

AI (artificial intelligence) module builds a modelof children's "knowledge space"

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

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

10

0.2

0.4

0.6

0.8

n o t a t i o n

speeddistance

Talk outlineTalk outline


69/75

Talk outlineTalk outline







Future goalsFuture goals


70/75


Identify children as young as possible andprovide preventative intervention

Why? " "

Identify children as young as possible andprovide preventative intervention

Why? " "

Maths is highly cumulative Avoid negative experiences associated

with failure

Quicker and cheaper

Maths is highly cumulative Avoid negative experiences associated

with failure

Quicker and cheaper

Early identificationEarly identification


71/75

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 kindergarten (e.g. Mazzocco & Thompson, 2005)

But still have many false positives

More work needed to develop measures

(e.g. Mazzocco & Thompson, 2005)

But still have many false positives

More work needed to develop measures



72/75


Identify genetic markers so we know whichkids are at risk.Need to: find genes

Identify genetic markers so we know whichkids are at risk.Need to: find genes

Identify neural markers .Need to: develop inexpensive and quickbrain imaging techniques.

Identify neural markers .Need to: develop inexpensive and quickbrain imaging techniques.

A copy of this presentationA copy of this presentation


73/75

A copy of this presentationA copy of this presentation

...Can be found on:

My website:

...Can be found on:

My website:. .

(look under news)

Contact information:[email protected]

. .

(look under news)

Contact information:[email protected]


74/75


75/75

Documents

SPELDKeynote_AnnaWilson_2008