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Stephen Albone Diagnosing and Remediating Mathematical Problems Using InCAS Software Defining Maths Difficulties • Low Attainment • Under Attainment • Lack of Progress 2 Reasons for Maths Difficulties • Institutional • Motivational • Neuropsychological 3 Institutional Factors • Learning Environment • Suitability for Atypical Learners 4 Motivational Factors • Status of Mathematics in Society • Effect of Low Achievement • Perceived Control – Competence & Contingency • • • • 5 afraid to make mistakes failure avoidance behaviour strong negative reactions associated with EBD, MLD & SLD Helping Motivation • • • • 6 Well Structured Tasks Achievable Goals Immediate Feedback Cross-age Peer Tutoring 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? 7 Magnitude Representations Verbal Representations Visual/Spatial Representations Dehaene et al. (2003) Cognitive Neuropsychology, vol. 20, pp. 487-506. 8 Learning to Count • • • • • 9 Counting Word Sequence One-to-One Correspondance Cardinal Word Principle Order-Irrelevance Principle Abstractness Principle Early Arithmetic • Calculation Strategies – count all – counting on from first – counting on from higher – recall 10 The Role of Memory • Working Memory • Semantic (Long-Term) Memory 11 Helping Arithmetic • Instant feedback • Evaluate reasons for incorrect responses • Encourage new strategies • Encourage answer checking using primitive strategies 12 Helping Memory • Use memory aids • Literacy remediation strategies may help 13 Verbal vs. Abstract Problems 14 Verbal vs. Abstract Problems Proposed Developmental Sequence: 1. verbal single-reference 2. symbolic single reference 3. symbolic double-reference 4. verbal double-reference 15 DD or MLD? • Developmental Dyscalculia – Specific Impairment of Cognitive Function – Defective Number Module Hypothesis – Core Deficit Hypothesis • Mathematical Learning Difficulties – Comorbidity with Other SEN’s 16 Intraparietal Sulchus (IPS) Left Angular Gyrus (AG) PSPL Dehaene et al. (2003) Cognitive Neuropsychology, vol. 20, pp. 487-506. 17 Proposed DD/MLD Framework Rubinsten & Henik (2009) TICS, vol. 13, pp. 92-99. 18 Stephen Albone Diagnosing and Remediating Mathematical Problems InCAS Feedback Stephen Albone Achievement Scores Table 20 Stephen Albone Developed Ability Scores Table 21 Stephen Albone General Maths Modules Scores Table 22 Stephen Albone 23 Stephen Albone 24 Stephen Albone 25 Stephen Albone 26 Stephen Albone 27 Stephen Albone 28 Stephen Albone 29 Stephen Albone 30 Stephen Albone 31 Stephen Albone 32 Stephen Albone 33 Stephen Albone 34 Stephen Albone 35 Stephen Albone 36 Stephen Albone 37 Stephen Albone 38 Stephen Albone 39 Stephen Albone 40 Stephen Albone 41 Stephen Albone 42 Stephen Albone 43 Stephen Albone 44 Stephen Albone 45 Stephen Albone 46 Stephen Albone 47 Stephen Albone 48 Stephen Albone 49 Stephen Albone 50 Stephen Albone CEM: Mountjoy Research Centre Durham University Stockton Road Durham, UK DH1 3UZ Tel: +44 (0) 191 334 4222 Email: [email protected] www.cemcentre.org 51