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About dyscalculia: Causes, symptoms & remediation Dr. Anna J. Wilson Lecturer, Educational Studies and Human Development College of Education University of Canterbury [email protected] 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