About dyscalculia:Causes, symptoms & remediationAbout dyscalculia:Causes, symptoms & remediation

Dr. Anna J. WilsonLecturer, Educational Studies and Human DevelopmentCollege of EducationUniversity of Canterburyanna.wilson@canterbury.ac.nz

Dr. Anna J. WilsonLecturer, Educational Studies and Human DevelopmentCollege of EducationUniversity of Canterburyanna.wilson@canterbury.ac.nz

• Severe difficulty in mathematics, not explained by general cognitive difficulties or educational opportunities

• Also called “mathematical learning disabilities”

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

• Has genetic component (runs in families)

• Understudied compared to dyslexia

• Severe difficulty in mathematics, not explained by general cognitive difficulties or educational opportunities

• Also called “mathematical learning disabilities”

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

• Has genetic component (runs in families)

• Understudied compared to dyslexia

Developmental dyscalculiaDevelopmental dyscalculia

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

Delay in acquisition of:

– Counting

– Addition strategies (e.g. counting on vs. counting all)

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

Geary (1993, 2004) - review

Difficulties with word problems

- Although may be linked to dyslexia

(Jordan & Hanich, 2000; Jordan et al., 2003; Jordan & Montani, 1997)

Delay in acquisition of:

– Counting

– Addition strategies (e.g. counting on vs. counting all)

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

Geary (1993, 2004) - review

Difficulties with word problems

- Although may be linked to dyslexia

(Jordan & Hanich, 2000; Jordan et al., 2003; Jordan & Montani, 1997)

Developmental symptomsDevelopmental symptoms

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)

– Slower counting speed

• Number symbols processed less automatically

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

• 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)

– Slower counting speed

• Number symbols processed less automatically

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

Core cognitive symptomsCore cognitive symptoms

7

9 7

9

Difficulty with:

• Using finger counting (slow, inaccurate, trouble recognising finger configurations – now clear evidence)

• 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

Difficulty with:

• Using finger counting (slow, inaccurate, trouble recognising finger configurations – now clear evidence)

• 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

Likely other symptomsLikely other symptoms

Both verbal and non-verbal:

• Dyslexia (50%)

• ADHD (30%)

• Dyspraxia

• Spatial difficulties

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

Both verbal and non-verbal:

• Dyslexia (50%)

• ADHD (30%)

• Dyspraxia

• Spatial difficulties

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

Co-occurring difficultiesCo-occurring difficulties

• 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

“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.”

Mathematical cognitionMathematical cognition

• Study of representation ofnumber in the brain

• Good introductory books:

• Study of representation ofnumber in the brain

• Good introductory books:

Stanislas Dehaene Brian

Butterworth

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!• 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

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

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

Mathematics is componentialMathematics is componential

• Non-verbal– number, approximation, comparison

• Verbal– number facts (multiplication, addition)

• Logical– problem solving, higher maths

• Spatial– geometry? Number line?

• Attentional / working memory

• Non-verbal– number, approximation, comparison

• Verbal– number facts (multiplication, addition)

• Logical– problem solving, higher maths

• Spatial– geometry? Number line?

• Attentional / working memory

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!• As can pre-verbal human infants...

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

• Animals can add, subtract, compare quantities!• As can pre-verbal human infants...

12 24

Ratio = 0.5

Dots: faster, more accurateDigits: the same!!

24 19

Ratio = 0.79

Dots: slower, less accurateDigits: the same!!

Approximate numberApproximate numberAbility to discriminate depends on ratio of the two numbers. This "distance effect" is found in animals, and human adults and children.

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

Number sense in adultsNumber sense in adults

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

Automatically activated by viewing numbers

Dehaene, Piazza, Pinel, & Cohen (2003)

z = 44 x = 39x = - 48

Left hemisphere Right hemisphere

50 %

22 %

z = 49

HIPS

Axial slice

Using number sense activates the intraparietal sulcus (IPS):

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

e.g. comparison

Brain imaging studies show that the angular gyrus (green) is involved in “verbal” aspects of mathematics such as multiplication, and retrieval of arithmetic facts. It increases activation with “drill” type training, with practice, and with development.

Brain imaging studies show that the angular gyrus (green) is involved in “verbal” aspects of mathematics such as multiplication, and retrieval of arithmetic facts. It increases activation with “drill” type training, with practice, and with development.

Verbal components in mathematicsVerbal components in mathematicsVerbal components in mathematicsVerbal components in mathematics

Adapted from Dehaene et al. 2003

Brain bases of dyscalculiaBrain bases of dyscalculia

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

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

verbal"six"

quantity

visual6

visual6

quantity

"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)

• 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?

• 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)

• 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?

• 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)

Subtypes of dyscalculia?Subtypes of dyscalculia?Subtypes of dyscalculia?Subtypes of dyscalculia?

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)• Dyslexia, ADHD, spatial difficulties, dyspraxia if

suspected

Important to rule out:educational experiences, motivation

Test for:• Mathematics level (standardised test)

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

• Profile of performance in different components• 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)•TEMA-3 (3-8 yrs)•CMAT (7-19 yrs)•Diagnostic mathematics profiles (AUS)•Booker Profiles? (AUS)

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

Computerised, for use in schools– Number stroop– Subitizing / Counting– Mental arithmetic

Administration time: 30 minutesAdvantages: Precise measures including reaction time,

standardised, fastDisadvantages: Assumes dyscalculia caused by core

deficit in number sense

Brian Butterworth, University College Londonwww.mathematicalbrain.com

Computerised, for use in schools– Number stroop– Subitizing / Counting– Mental arithmetic

Administration time: 30 minutesAdvantages: Precise measures including reaction time,

standardised, fastDisadvantages: Assumes dyscalculia caused by core

deficit in number sense

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!)• Provide lots of practice• Reduce need for memorisation• Ask a lot of questions to get the individual

engaged and thinking• Make learning active and fun

• Focus on understanding (esp. quantity) • Drilling of facts only useful up to a point• Use concrete materials• Start at an easy level (success important!)• Provide lots of practice• Reduce need for memorisation• Ask a lot of questions to get the individual

engaged and thinking• Make learning active and fun

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 adult is good at multiplication but has trouble with subtraction, focus on number sense.

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

Note that this necessitates a componential assessment

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 adult is good at multiplication but has trouble with subtraction, focus on number sense.

If adult 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 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).

SoftwareSoftware

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

Bubble Reefby ICDC

Bubble Reefby ICDC

Knowsley Woodsby ICDC

Knowsley Woodsby ICDC

Number Sharkby White SpaceNumber Shark

by White Space

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, copy, distribute, modify)

• Programmed by myself

Wilson et al. 2007a,b

Languages:

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, copy, distribute, modify)

• Programmed by myself

Wilson et al. 2007a,b

Languages:

www.aboutdyscalculia.orgwww.aboutdyscalculia.org

• PhD, University of Oregon– Dissertation: Numerical & spatial cognition– 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.org

• PhD, University of Oregon– Dissertation: Numerical & spatial cognition– 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.org

AcknowledgementsAcknowledgementsSupervisors / Collaborators

Stanislas Dehaene, Laurent Cohen (INSERM U562)Karen Waldie, Mike Thomas (University of Auckland)

CollaboratorsMonique Plaza, David Cohen, Philippe Pinel

Pekka Räsänen, Alex Masloff, Andry Vertiy, Dan Schwartz, Joan DavisKlaus Willmes, Helga Krinzinger, Michel Fayol

Research assistants, studentsSusannah Revkin, Céline Amy, Marie Gambert, Séverine Frédonie

Stuart Andrewes, Veema Lodhia, Lucy PatstonRajna Bogdanovic, Helena Struthers, Phil Light, Janine Keir, Kimberley Maskell

FundingFyssen Foundation, McDonnell Foundation & Institut de France (S. Dehaene), OECD

The University of Auckland (K. Waldie, M. Thomas), University of Canterbury