1. Stephen Albone Diagnosing and Remediating Mathematical Problems Using InCAS Software

2. 2 Defining Maths Difficulties Low Attainment Under Attainment Lack of Progress

3. 3 Reasons for Maths Difficulties Institutional Motivational Neuropsychological

4. 4 Institutional Factors Learning Environment Suitability for Atypical Learners

5. 5 Motivational Factors Status of Mathematics in Society Effect of Low Achievement Perceived Control –Competence & Contingency afraid to make mistakes failure avoidance behaviour strong negative reactions associated with EBD, MLD & SLD

6. 6 Helping Motivation Well Structured Tasks Achievable Goals Immediate Feedback Cross-age Peer Tutoring

7. 7 Neuropsychological Factors Magnitude Representation –Internal Number Line –Number Sense –Approximate Number System (ANS) Symbolic Representation –Uses verbal systems to give semantic meaning to numerical quantities Spatial Representaion –Subitising?

8. 8 Dehaene et al. (2003) Cognitive Neuropsychology, vol. 20, pp. 487-506. Magnitude Representations Verbal Representations Visual/Spatial Representations

9. 9 Learning to Count Counting Word Sequence One-to-One Correspondance Cardinal Word Principle Order-Irrelevance Principle Abstractness Principle

10. 10 Early Arithmetic Calculation Strategies –count all –counting on from first –counting on from higher –recall

11. 11 The Role of Memory Working Memory Semantic (Long-Term) Memory

12. 12 Helping Arithmetic Instant feedback Evaluate reasons for incorrect responses Encourage new strategies Encourage answer checking using primitive strategies

13. 13 Helping Memory Use memory aids Literacy remediation strategies may help

14. 14 Verbal vs. Abstract Problems

15. 15 Verbal vs. Abstract Problems Proposed Developmental Sequence: 1.verbal single-reference 2.symbolic single reference 3.symbolic double-reference 4.verbal double-reference

16. 16 DD or MLD? Developmental Dyscalculia –Specific Impairment of Cognitive Function –Defective Number Module Hypothesis –Core Deficit Hypothesis Mathematical Learning Difficulties –Comorbidity with Other SENs

17. 17 Dehaene et al. (2003) Cognitive Neuropsychology, vol. 20, pp. 487-506. Intraparietal Sulchus (IPS) Left Angular Gyrus (AG) PSPL

18. 18 Proposed DD/MLD Framework Rubinsten & Henik (2009) TICS, vol. 13, pp. 92-99.

19. Stephen Albone Diagnosing and Remediating Mathematical Problems InCAS Feedback

20. Stephen Albone 20 Achievement Scores Table

21. Stephen Albone 21 Developed Ability Scores Table

22. Stephen Albone 22 General Maths Modules Scores Table

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51. Stephen Albone 51 CEM: Mountjoy Research Centre Durham University Stockton Road Durham, UK DH1 3UZ Tel: +44 (0) 191 334 4222 Email: stephen.albone@cem.dur.ac.ukstephen.albone@cem.dur.ac.uk www.cemcentre.org