About dyscalculia:
Causes, symptoms &
remediation
Dr. Anna J. Wilson
Lecturer, Educational Studies and Human Development
College of Education
University of Canterbury
anna.wilson@canterbury.ac.nz
Developmental dyscalculia
• 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
Kosc, 1974; Shalev & Gross-Tsur, 2001; Geary, 1993, 2004; Badian, 1983;
Lewis, Hitch, & Walker, 1994
Developmental symptoms
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
2+5=?
Difficulties with word problems
- Although may be linked to dyslexia
(Jordan & Hanich, 2000; Jordan et al., 2003
; Jordan & Montani, 1997)
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”
Core cognitive symptoms
• 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)
7
9 7
9
Likely other symptoms
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
Co-occurring difficulties
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?
Consequences in adults
• Blocked from certain professions (lower salary)
• Difficulty managing money
• Difficulty understanding statistics/numbers (influence
on decision making)
• 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.”
Mathematical cognition
• Study of representation of
number in the brain
• Good introductory books:
Stanislas
Dehaene
Brian
Butterworth
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
Mathematics 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 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...
12
24
24
19
Ratio = 0.5
Ratio = 0.79
Dots: faster, more accurate
Digits: the same!!
Dots: slower, less accurate
Digits: the same!!
Approximate 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
Number sense in adults
Using number sense activates the intraparietal sulcus (IPS):
(This same area is involved in thinking about space.)
Axial slice
Left hemisphere
x = - 48
z = 44
Right hemisphere
z = 49
x = 39
50 %
HIPS
22 %
Dehaene, Piazza, Pinel, & Cohen (2003)
Tasks that activate this region:
 Comparison of numbers
 Subtraction
 Approximation
 Estimation
e.g. comparison
 Non-symbolic tasks
Automatically activated by viewing numbers
Verbal components in mathematics
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.
Adapted from Dehaene et al. 2003
Brain bases of dyscalculia
Dyscalculic children - less grey matter in
IPS (Rotzer et al., 2008)
Dyscalculic adults born pre-term –
less gray matter in IPS
(Isaacs, Edmonds & Lucas, 2001)
Superimposed images of sulci
Controls
Turner
subjects
Dyscalculic children – less activation in
IPS during magnitude tasks (Kucian et
al., 2006)
Molko, Cachia and Riviere (2004) Turners subjects structural and functional alternations in IPS.
Causes of dyscalculia
"Access" hypothesis :
Deficit in link between
number sense and symbols
(Rouselle & Nöel, 2007)
left hemisphere
quantity
verbal
"six"


visual
6
"Core deficit" hypothesis:
Deficit in number sense
(Butterworth, 1999; Gersten & Chard,
1999; Wilson & Dehaene, 2007)
right hemisphere
quantity

visual
6
Dehaene, S. (1992). Cognition, 44, 1-42.
Dehaene, S., & Cohen, L. (1995). Mathematical Cognition, 1, 83-120.
Subtypes of dyscalculia?
• 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)
Identification
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 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)
Dyscalculia Screener (nferNelson)
Brian Butterworth, University College London
www.mathematicalbrain.com
Computerised, for use in schools
– Number stroop
– 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
Individual 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
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
Remediation 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).
Software
Bubble Reef
by ICDC
Number Shark
by White Space
To Market, To Market
by Learning in Motion
The Number Race
by myself and Stan
Dehaene
Knowsley Woods
by ICDC
The 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:
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
Acknowledgements
Supervisors / Collaborators
Stanislas Dehaene, Laurent Cohen (INSERM U562)
Karen Waldie, Mike Thomas (University of Auckland)
Collaborators
Monique Plaza, David Cohen, Philippe Pinel
Pekka Räsänen, Alex Masloff, Andry Vertiy, Dan Schwartz, Joan Davis
Klaus Willmes, Helga Krinzinger, Michel Fayol
Research assistants, students
Susannah Revkin, Céline Amy, Marie Gambert, Séverine Frédonie
Stuart Andrewes, Veema Lodhia, Lucy Patston
Rajna Bogdanovic, Helena Struthers, Phil Light, Janine Keir, Kimberley Maskell
Funding
Fyssen Foundation, McDonnell Foundation & Institut de France (S. Dehaene), OECD
The University of Auckland (K. Waldie, M. Thomas), University of Canterbury