Dyscalculia: Difficulty learning numeracy

1
DyscalculiaDifficulty learning numeracy

• Dr. Anna J. Wilson
• Lecturer, Educational Studies and Human
  Development
• College of Education, University of Canterbury
• anna.wilson_at_canterbury.ac.nz

2
My background

• BSc, University of Auckland
• PhD, University of Oregon (Cognitive
  neuroscience)
• 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)
• Lecturer, University of Canterbury
• Teaching/research on mind, brain and education,
  dyscalculia

3
Talk outline

• What is dyscalculia?
• Maths and the brain
• Causes of dyscalculia
• Dyscalculia and dyslexia
• Identification
• Remediation

4
Developmental dyscalculia

• Severe difficulty in mathematics, not explained
  by general cognitive difficulties or educational
  opportunities
• Also called Mathematics Disorder (DSM-IV), 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
5
Surface symptoms

• Delay in acquisition of
• Counting
• Addition strategies (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

2 5 ? Counting all1..2...
1...2...3...4..5..1...2...3...4...5...6...7 Coun
ting on2...3...4...5...6...7 Counting on
(max)5...6...7
6
Core cognitive symptoms

• Difficulty representing quantity (number
  sense).
• Slow to compare numbers (Llanderl et al., 2004)
• Slow to enumerate 1-3 objects (subitizing)(Reev
  e et al., in press)
• Number symbols processed less automatically
• Number stroop task(Rouselle Nöel,
  2007Rubinsten Henik 2005)
• Mental number line slow to develop

7 9
7 9
7
Mental number line development
"Put a mark where 64 goes"
0
100
Siegler Booth, 2004
Individual differences on this task correlate
with maths achievement scores.
8
Mental number line in dyscalculia
"Put a mark where 64 goes"
0
100
Wilson, Krinzinger, Nuerk, Dehaene Willmes, in
prep
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

10
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.
57 without anyone knowing. Sometimes I feel very
embarrassed! Especially under pressure I just
panic.
11
Talk outline

• What is dyscalculia?
• Maths and the brain
• Causes of dyscalculia
• Dyscalculia and dyslexia
• Identification
• Remediation

12
Numerical cognition

• Study of representation ofnumber in the brain
• Methods Animals, infants, cross-cultural
  linguistics, brain imaging, cognitive psychology
• Good introductory books

Stanislas Dehaene
13
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

14
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...

15
Approximate number Demonstration
Which side has more dots?
16

17
(No Transcript)
18

19
(No Transcript)
20

21
Ratio 0.5 Faster, more accurate
Ratio 0.79 Slower, less accurate
22

23
12
24
24

25
19
24
26

27
12
24
24
19
Ratio 0.5 Dots faster, more accurate Digits
the same!!
Ratio 0.79 Dots slower, less accurate Digits
the same!!
28
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
29
Approximate number

• Non-verbal
• Non-symbolic
• Present in animals / human infants
• Still accessed in skilled adults
• Used for representation and operations
• Next Has a specific brain basis

30
Number sense in adults
Using number sense activates the intraparietal
sulcus (IPS) (This same area is involved in
thinking about space.)
Dehaene, Piazza, Pinel, Cohen (2003)

• Tasks that activate this region
• ? Comparison of numbers
• ? Subtraction
• ? Approximation
• Estimation
• Non-symbolic tasks
• Automatically activated by viewing numbers

e.g. comparison
31
Number sense in children
Neural correlates the same as in adults.
Non symbolic tasks
Cantlon, Brannon, Carter Pelphrey 2006 fMRI
in 4 year olds
32
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

33
Verbal components in mathematics

• Angular gyrus (green) involved in verbal
  aspects of mathematics such as multiplication,
  and retrieval of arithmetic facts

34
Numerical cognition angular gyrus

• Angular gyrus increases activation with drill
  type training, with practice, and with
  development. Function linking non-symbolic to
  symbolic representations?

e.g. Ischebeck et al. (2007) Training by drill
increases AG activation
35
Mathematics is componential

• Non-verbal Intraparietal sulcus (IPS)
• number, approximation, comparison
• Verbal Perisylvian language network
• number facts (multiplication, addition)
• Logical Frontal lobes?
• problem solving, higher maths
• Spatial Parietal lobes?
• geometry? Number line?
• Attentional / working memory incl. Frontal

36
Talk outline

• What is dyscalculia?
• Maths and the brain
• Causes of dyscalculia
• Dyscalculia and dyslexia
• Identification
• Remediation

37
Brain bases of dyscalculia
Dyscalculic adults born pre-term less gray
matter in IPS(Isaacs, Edmonds Lucas, 2001)
Dyscalculic children - less grey matter in IPS
(Rotzer et al., 2008)
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.
38
Causes of dyscalculia
39
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)

40
Talk outline

• What is dyscalculia?
• Maths and the brain
• Causes of dyscalculia
• Dyscalculia and dyslexia
• Identification
• Remediation

41
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?

42
Dyscalculia dyslexia comorbidity

• 1. Overlap in networks involved in mathematics
  and reading

LH areas involved in reading, and implicated in
dyslexia
Démonet, Taylor Chaix (2004)
43
Dyscalculia dyslexia comorbidity

• 1. Overlap in networks involved in mathematics
  and reading

Numerical comparison (1 digit) Exact subtraction
gt Comparison Exact subtraction gt
Multiplication Approximate addition Numerosity
estimation Numerical distance effect (1
digits) Number subliminal perception Complex gt
Simple addition Numerical distance effect (2
digits) Multiplication gt Comparison Multiplication
gt Subtraction Exact gt Approximate
calculation Subtraction n Phoneme
detection Simple addition gt Complex addition
44
Dyscalculia dyslexia comorbidity

• 1. Overlap in networks involved in mathematics
  and reading
• Different neural impairments underlie
  dyscalculia in presence/absence of comorbidity

Predictions Mathematics and reading disabilities
(MDRD) ? more impairment on verbal mathematical
tasks Mathematics disability only (MD) ? more
impairment on non-verbal mathematical tasks
45
Dyscalculia dyslexia comorbidity

• 2. Diffuse neural impairment
• Same neural impairment underlies dyscalculia in
  presence/absence of comorbidity
• Susceptibility genes for dyslexia (e.g. DYX1C1,
  DCDC2, KIAA0319) involved in neural migration,
  and expressed over wide areas of cortex. (Ramus,
  2006)

Predictions Mathematics and reading disabilities
(MDRD) and Mathematics disability only (MD) ?
either similar profiles across all mathematical
tasks, OR more impairment for MDRD across all
tasks
46
Auckland comorbidity project

• Aims
• Symptoms of dyscalculia in adults
• Core deficit(s) in dyscalculia
• Cause of co-morbidity with dyslexia
• Subtypes of dyscalculia and dyslexia
• Methods
• Four groupsof subjects
• Cognitive profiling (n80) battery of 14 tasks
• fMRI (n48)
• Genetics (n48)

Control Dyscalculia only Dyslexia only Dyscalculia dyslexia
Control MD RD MDRD
47
Symbolic Arithmetic Multiplication
3 x 7
Give answer out loud
48
Symbolic Arithmetic Subtraction
Give answer out loud
49
Enumeration
How many dots?
50
Symbolic number comparison
2 8
Press key on same side as biggest number
51
Non-symbolic addition
n 46
52
Other tasks
53
MULTIPLICATION
54
Control group
Behaviouralresults (all groups)
MULTIPLICATION
Left hemisphere verbal network active same areas
involved in reading in these subjects.
Control MD
RD MDRD
55
Dyscalculia (MD) group
MULTIPLICATION
More activity in RH homologs of SMG,
STG. Suggests greater use of verbal network?
56
Dyslexia (RD) group
MULTIPLICATION
More activity in typical nonverbal areas (hIPS,
SPL). Suggests greater reliance on nonverbal
representation of quantity?
57
Comorbid (MDRD) group
MULTIPLICATION
Similar posterior pattern to RD (more activity in
non-verbal areas) plus anterior DLPFC activity.
58
Talk outline

• What is dyscalculia?
• Maths and the brain
• Causes of dyscalculia
• Dyscalculia and dyslexia
• Identification
• Remediation

59
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 outeducational experiences,
  motivation

60
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)

61
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

62
Talk outline

• What is dyscalculia?
• Maths and the brain
• Causes of dyscalculia
• Dyscalculia and dyslexia
• Identification
• Remediation

63
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 child engaged
  and thinking
• Make learning active and fun

64
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 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

65
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).

66
Software
Number Sharkby White Space
Bubble Reef by ICDC

• To Market, To Marketby Learning in Motion

The Number Race by myself and Stan Dehaene
Knowsley Woods by ICDC
67
The Number Race

• http//www.unicog.org/main/pages.php?pageNumberRa
  ce
• 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

68
(No Transcript)
69
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

70
Acknowledgements
Supervisors / Collaborators Stanislas Dehaene,
Laurent Cohen (INSERM U562) Karen Waldie, Mike
Thomas (University of Auckland) Collaborators Mon
ique 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