Stephen Albone Diagnosing and Remediating Mathematical Problems Using InCAS Software.
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Transcript of Stephen Albone Diagnosing and Remediating Mathematical Problems Using InCAS Software.
Stephen Albone
Diagnosing and Remediating Mathematical Problems
Using InCAS Software
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Defining Maths Difficulties
• Low Attainment
• Under Attainment
• Lack of Progress
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Reasons for Maths Difficulties
• Institutional
• Motivational
• Neuropsychological
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Institutional Factors
• Learning Environment
• Suitability for Atypical Learners
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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
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Helping Motivation
• Well Structured Tasks
• Achievable Goals
• Immediate Feedback
• Cross-age Peer Tutoring
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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?
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Dehaene et al. (2003) Cognitive Neuropsychology,
vol. 20, pp. 487-506.
Magnitude Representations
Verbal Representations
Visual/Spatial Representations
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Learning to Count
• Counting Word Sequence
• One-to-One Correspondance
• Cardinal Word Principle
• Order-Irrelevance Principle
• Abstractness Principle
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Early Arithmetic
• Calculation Strategies– count all– counting on from first– counting on from higher– recall
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The Role of Memory
• Working Memory
• Semantic (Long-Term) Memory
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Helping Arithmetic
• Instant feedback
• Evaluate reasons for incorrect responses
• Encourage new strategies
• Encourage answer checking using primitive strategies
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Helping Memory
• Use memory aids
• Literacy remediation strategies may help
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Verbal vs. Abstract Problems
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Verbal vs. Abstract Problems
Proposed Developmental Sequence:
1. verbal single-reference
2. symbolic single reference
3. symbolic double-reference
4. verbal double-reference
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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
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Dehaene et al. (2003) Cognitive Neuropsychology,
vol. 20, pp. 487-506.
Intraparietal Sulchus (IPS)
Left Angular Gyrus (AG)
PSPL
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Proposed DD/MLD Framework
Rubinsten & Henik (2009) TICS, vol. 13, pp. 92-99.
Stephen Albone
Diagnosing and Remediating Mathematical Problems
InCAS Feedback
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Achievement Scores Table
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Developed Ability Scores Table
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General Maths Modules Scores Table
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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