Mathematical Difficulties

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ISBN: 9780123736291 | 0123736293
Cover: Hardcover
Copyright: 6/18/2008

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This book examines the mathematical difficulties in typical and atypical populations. It discusses the behavioural, educational and neuropsychological characteristics of people with mathematical difficulties, and educational interventions to prevent, diagnose, treat or ameliorate such difficulties. The book brings together studies from different disciplines, including developmental psychology, neuroscience and education, and includes perspectives from practicing teachers. The book is divided into three major sections. The first includes chapters about the nature and characteristics of mathematical difficulties in the population as a whole, in relation to both psychology and education. The second deals with mathematical difficulties in children with other problems such as specific language impairment and dyslexia. The third discusses methods of interventions aimed at preventing, treating or ameliorating mathematical difficulties, and will include discussions of assessment and diagnosis.

List of contributors	p. XV
Introduction	p. XVII
Neural Correlates of Number Processing and Calculation: Developmental Trajectories and Educational Implications
Introduction	p. 1
Neuroanatomical Correlates of Number Processing and Calculation: Are They Identical in Developing and Mature Brain Systems?	p. 2
Are Neuroimaging Studies Apt to Have Any Educational Implications?	p. 6
Pros and cons Regarding a Modular View of Numerical Skills	p. 7
Synopsis	p. 9
Toward a Developmental Cognitive Neuroscience Approach to the Study of Typical and Atypical Number Development
Introduction	p. 13
Number Processing in the Adult Brain	p. 15
Numerical Magnitude Processing in the Adult Brain	p. 15
Calculation in the Adult Brain	p. 20
Number Processing in the Typically Developing Brain	p. 25
Number Processing in the Atypically Developing Brain	p. 30
Future Directions	p. 34
Conceptual Challenges	p. 34
Methodological Challenges	p. 35
Conclusions	p. 38
Acknowledgments	p. 39
A Number Sense Assessment Tool for Identifying Children at Risk for Mathematical Difficulties
What Is Number Sense?	p. 46
Components of Number Sense	p. 47
Predictability of Number Sense	p. 48
Developing a Number Sense Battery	p. 49
Counting and Number Recognition	p. 49
Number Knowledge	p. 49
Number Operations	p. 50
Key Findings from the Children's Math Longitudinal Study	p. 50
Streamlining the Number Sense Screening Tool	p. 51
Instructional Implications	p. 53
Acknowledgments	p. 53
Appendix	p. 57
The Essence of Early Childhood Mathematics Education and the Professional Development Needed to Support It
Social, Political, and Research Influences	p. 60
The Content of Early Mathematics	p. 63
The Different Components of Early Mathematics	p. 64
What is Good Early Mathematics Teaching?	p. 66
Teachers' Conceptions about EME	p. 67
How Good is Early Mathematics Teaching? Are Teachers Ready for it?	p. 68
The Status of EME Professional Development	p. 69
An Example: Big Math for Little Kids	p. 71
Big Math for Little Kids - An Overview	p. 71
Professional Development Workshops for BMLK	p. 72
What we have Learned about Professional Development	p. 74
Assessing the Success of Our Workshops	p. 76
Needed Support for an EME Program	p. 78
Top-level Administration	p. 78
Supervisory Staff	p. 78
Program Supervisors	p. 79
Parents	p. 79
Conclusion	p. 80
Progression in Numeracy Ages 5-11: Results from the Leverhulme Longitudinal Study
Background and Aims	p. 85
Methods and Data Sources	p. 86
Sample	p. 86
Test Design	p. 87
Case-study Methods	p. 91
Results and Discussion	p. 92
Conclusions	p. 106
An Analysis of Children's Numerical Difficulties with the Aid of a Dyscalculia Test Battery and a Presentation of Remedial Approaches to Facilitate Aspects of Numerical Development
Introduction	p. 109
A Dyscalculia Test Battery	p. 117
Numeral Processing Tasks	p. 117
Calculation Tasks	p. 118
A Multisensory Remedial Approach for Learning the Multiplication Tables	p. 120
Child A.	p. 121
Dyscalculia Test Battery Assessment	p. 122
Numeral Processing Tasks	p. 122
Calculation Tasks	p. 124
Child M.	p. 125
Dyscalculia Test Battery Assessment	p. 125
Numeral Processing Tasks	p. 125
Calculation Tasks	p. 129
Child L.	p. 130
Dyscalculia Test Battery Assessment	p. 131
Numeral Processing Tasks	p. 131
Calculation Tasks	p. 132
General Discussion and Conclusion	p. 133
Acknowledgments	p. 136
Children With and Without Mathematics Difficulties: Aspects of Learner Characteristics in a Developmental Perspective
Results and Discussion	p. 146
Educational Implications and Recommendations	p. 150
Number Development and Children with Specific Language Impairment
Introduction	p. 155
Monetary Value	p. 156
Ordinality	p. 157
Small Number Quantification	p. 157
Method	p. 158
Participants	p. 158
Experimental Tasks	p. 158
Results	p. 160
Discussion	p. 161
Monetary Value	p. 162
Ordinality	p. 164
Small Number	p. 164
Acknowledgments	p. 165
The Performance of Dyslexic and Non-Dyslexic Boys at Division Sums
Introduction	p. 167
Participants, Apparatus and Method	p. 168
Results	p. 170
Discussion	p. 177
Some Practical Implications	p. 179
Concluding Remarks	p. 179
Numeracy Recovery with Children with Arithmetical Difficulties: Intervention and Research
Numeracy Recovery Scheme	p. 182
Components that Are the Focus of the Project	p. 183
Evaluation of Effectiveness	p. 189
Further Development	p. 190
Study of Children with Arithmetical Difficulties	p. 190
Method and Techniques	p. 191
Derived Fact Strategy Task (Use of Arithmetical Principles)	p. 191
Estimation Task	p. 193
Translation Task	p. 193
Classification of Responses to Translation Task	p. 194
Lack of Gender Differences	p. 195
Relationships between Different Measures	p. 196
Factors Contributing to Scores on Components of Arithmetical Performance	p. 196
Discussion	p. 198
Acknowledgments	p. 200
Mathematics Recovery: An Early Number Program Focusing on Intensive Intervention
An Anecdote: The Case of Kim	p. 203
The Learning Framework in Number	p. 205
Five Aspects of the LFIN	p. 207
Using LFIN to Profile Student's Knowledge	p. 208
Some Important Features of the LFIN	p. 209
Pedagogical Tools	p. 215
Assessment Schedules	p. 215
Assessment And Instruction	p. 216
The General Approach Instruction	p. 217
The Case of Kim: Conclusion	p. 219
Teacher Development	p. 219
Brief History	p. 221
Sources of Additional Information	p. 222
Making Intervention in Numeracy More Effective in Schools
Introduction	p. 225
Current Intervention Programmes	p. 226
The Difficulty with Maths	p. 228
Making Intervention More Effective	p. 229
Professional Development	p. 230
Intervention as an Integral Part of the Maths Curriculum	p. 230
Effective Equipment	p. 231
Conclusion	p. 240
Afterword: Helping Children with Numeracy Difficulties in School: A Teacher's Notes
Index	p. 245
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Mathematical Difficulties

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