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Dyscalculia: Difficulty learning numeracy

Dyscalculia: Difficulty learning numeracy. Dr. Anna J. Wilson Lecturer, Educational Studies and Human Development College of Education, University of Canterbury anna.wilson@canterbury.ac.nz. My background. BSc, University of Auckland PhD, University of Oregon (Cognitive neuroscience)

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Dyscalculia: Difficulty learning numeracy

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  1. Dyscalculia:Difficulty learning numeracy Dr. Anna J. Wilson Lecturer, Educational Studies and Human Development College of Education, University of Canterbury anna.wilson@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 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”

  6. 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) • Number symbols processed less automatically • Number stroop task(Rouselle & Nöel, 2007;Rubinsten & Henik 2005) • Mental number line slow to develop 7 9 79

  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. 5+7 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. +

  18. +

  19. Ratio = 0.5 Faster, more accurate Ratio = 0.79 Slower, less accurate

  20. +

  21. 12 24

  22. +

  23. 19 24

  24. +

  25. 12 24 24 19 Ratio = 0.5 Dots: faster, more accurate Digits: the same!! Ratio = 0.79 Dots: slower, less accurate Digits: the same!!

  26. Approximatenumber 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

  27. Approximatenumber • 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

  28. 50 % 22 % Axial slice Right hemisphere Left hemisphere z = 44 z = 49 x = 39 x = - 48 HIPS 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

  29. Number sense in children Neural correlates the same as in adults. Non symbolic tasks Cantlon, Brannon, Carter & Pelphrey 2006 fMRI in 4 year olds

  30. 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

  31. Verbal components in mathematics Angular gyrus (green) involved in “verbal” aspects of mathematics such as multiplication, and retrieval of arithmetic facts Numerical comparison (1 digit) Exact subtraction > Comparison Exact subtraction > Multiplication Approximate addition Numerosity estimation Numerical distance effect (1 digits) Number subliminal perception Complex > Simple addition Numerical distance effect (2 digits) Multiplication > Comparison Multiplication > Subtraction Exact > Approximate calculation Subtraction ∩ Phoneme detection Simple addition > Complex addition Adapted from Dehaene et al. 2003

  32. 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

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

  34. Talk outline • What is dyscalculia? • Maths and the brain • Causes of dyscalculia • Dyscalculia and dyslexia • Identification • Remediation

  35. Superimposed images of sulci Controls Turner subjects 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) 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.

  36. "Access" hypothesis : Deficit in link between number sense and symbols (Rouselle & Nöel, 2007) "Core deficit" hypothesis: Deficit in number sense(Butterworth, 1999; Gersten & Chard, 1999; Wilson & Dehaene, 2007) left hemisphere right hemisphere quantity quantity  verbal "six"   visual 6 visual 6 Dehaene, S. (1992). Cognition, 44, 1-42. Dehaene, S., & Cohen, L. (1995). Mathematical Cognition, 1, 83-120. Causes of dyscalculia

  37. 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)

  38. Talk outline • What is dyscalculia? • Maths and the brain • Causes of dyscalculia • Dyscalculia and dyslexia • Identification • Remediation

  39. 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?

  40. 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)

  41. Dyscalculia & dyslexia comorbidity 1. Overlap in networks involved in mathematics and reading Numerical comparison (1 digit) Exact subtraction > Comparison Exact subtraction > Multiplication Approximate addition Numerosity estimation Numerical distance effect (1 digits) Number subliminal perception Complex > Simple addition Numerical distance effect (2 digits) Multiplication > Comparison Multiplication > Subtraction Exact > Approximate calculation Subtraction ∩ Phoneme detection Simple addition > Complex addition Adapted from Dehaene et al. 2003

  42. 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

  43. 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

  44. 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 (n=80) – battery of 14 tasks • fMRI (n=48) • Genetics (n=48)

  45. Symbolic Arithmetic: Multiplication 3 x 7 Give answer out loud

  46. Symbolic Arithmetic: Subtraction 9 - 5 42 - 38 Give answer out loud

  47. Enumeration How many dots?

  48. Symbolic number comparison 2 8 Press key on same side as biggest number

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