The Nature and Origins of Mathematical Skills

Jamie I.D. Campbell (Eds.)978-0-444-89014-6, 0444890149

A broad range of current experimental research on numerical cognition and the acquisition of mathematical skills is covered in this volume. The individual chapters provide in-depth analysis of specific issues, methodologies, phenomena, and theory. The book is divided into two parts. In the first part the focus is on the acquisition and development of numerical skills. Part 2 of the book contains research on the information-processing basis of numerical skills, focusing on the mechanisms of perception, attention, and memory that support number skills.

The range of theoretical and methodological orientations represented in the volume captures both the diversity and coherence of contemporary research into mathematical skills. The research of educational psychologists, cognitive psychologists, and cognitive neuropsychologists mutually informs and reinforces theoretical developments within each area. The multidisciplinary interest in mathematics skills reflects the pervasiveness and importance of mathematics in education, technology, and science, and also indicates that questions about mathematical competence address important issues in diverse areas of psychology and cognitive science.

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Table of contents :
Content:
Edited by
Page iii

Copyright page
Page iv

Introduction
Pages vii-ix

Acknowledgements
Page x

Chapter 1 What A Number is: Mathematical Foundations and Developing Number Concepts Original Research Article
Pages 3-38
Kevin F. Miller

Chapter 2 Relationships Children Construct Among English Number Words, Multiunit Base-Ten Blocks, And Written Multidigit Addition Original Research Article
Pages 39-112
Karen C. Fuson, Judith L. Fraivillig, Birch H. Burghardt

Chapter 3 Understanding Elementary Mathematics Original Research Article
Pages 113-136
Jeffrey Bisanz, Jo-Anne LeFevre

Chapter 4 Mathematical Misunderstandings: Qualitative Reasoning About Quantitative Problems Original Research Article
Pages 137-153
Richard E. Mayer, Anne Bovenmyer Lewis, Mary Hegarty

Chapter 5 The Role Of Expertise In Solving Arithmetic And Algebra Word Problems By Analogy Original Research Article
Pages 155-188
Laura R. Novick

Chapter 6 The Development Of Skill In Mental Arithmetic: An Individual Differences Perspective Original Research Article
Pages 189-253
Keith F. Widaman, Todd D. Little

Chapter 7 A Theory Of Enumeration That Grows Out Of A General Theory Of Vision: Subitizing, Counting, And Finsts Original Research Article
Pages 257-299
Lana M. Trick

Chapter 8 Working Memory, Automaticity, And Problem Difficulty Original Research Article
Pages 301-329
Mark H. Ashcraft, Rick D. Donley, Margaret A. Halas, Mary Vakali

Chapter 9 Representation And Retrieval Of Arithmetic Facts: A Network-Interference Model And Simulation Original Research Article
Pages 331-364
Jamie I.D. Campbell, Michael Oliphant

Chapter 10 Mathnet: Preliminary Results From A Distributed Model Of Arithmetic Fact Retrieval Original Research Article
Pages 365-409
Michael McCloskey, A. Margrethe Lindemann

Chapter 11 Inhibitory Mechanisms In Normal And Dysfunctional Number Processing Original Research Article
Pages 411-455
James M. Clark

Chapter 12 Cognitive Number Processing: An Encoding-Complex Perspective Original Research Article
Pages 457-491
Jamie I.D. Campbell, James M. Clark

Chapter 13 The Functional Architecture Of Numerical Processing Mechanisms: Defending The Modular Model Original Research Article
Pages 493-537
Michael McCloskey, Paul Macaruso, Tony Whetstone

Chapter 14 In Defense Of The Encoding-Complex Approach: Reply To Mccloskey, Macaruso, & Whetstone Original Research Article
Pages 539-556
Jamie I.D. Campbell

Author Index
Pages 557-565

Subject Index
Pages 567-569