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: stephen.albone@cem.dur.ac.uk

www.cemcentre.org