Addition and Subtraction
A Cognitive Perspective
A hallmark of much of the research on children’s thinking in the 1970s had been the focus on explicit content domains. Much of this research had been represented by an eclectic collection of studies sampled from a variety of disciplines and content areas. However, in the few years before this publication, research in several content domains has begun to coalesce into a coherent body of knowledge. Originally published in 1982, the chapters in this work represent one of the first attempts to bring together the perspectives of a variety of different researchers investigating a specific, well defined content domain.
This book presents theoretical views and research findings of a group of international scholars who are investigating the early acquisition of addition and subtraction skills by young children. Together, the contributors bring a blend of psychology, educational psychology, and mathematics education to this topic. Fields of interest such as information processing, artificial intelligence, early childhood, and classroom teaching and learning are included in this blend.
Table of Contents
Preface. 1. An Emerging Paradigm for Research on Addition and Subtraction Skills Thomas A. Romberg 2. The Development of Addition and Subtraction Problem-Solving Skills Thomas P. Carpenter and James M. Moser 3. Levels of Description in the Analysis of Addition and Subtraction Word Problems Pearla Nesher 4. A Classification of Cognitive Tasks and Operations of Thought Involved in Addition and Subtraction Problems Gérard Vergnaud 5. Interpretations of Number Operations and Symbolic Representations of Addition and Subtraction J. Fred Weaver 6. An Analysis of the Counting-On Solution Procedure in Addition Karen C. Fuson 7. Children’s Counting in Arithmetical Problem Solving Leslie P. Steffe, Patrick W. Thompson and John Richards 8. The Development of Addition and Subtraction Abilities Prior to Formal Schooling in Arithmetic Prentice Starkey and Rochel Gelman 9. Towards a Generative Theory of "Bugs" John Seely Brown and Kurt VanLehn 10. Syntax and Semantics in Learning to Subtract Lauren B. Resnick 11. General Developmental Influences on the Acquisition of Elementary Concepts and Algorithms in Arithmetic Robbie Case 12. The Structure of Learned Outcomes: A Refocusing for Mathematics Learning Kevin Collis 13. Type 1 Theories and Type 2 Theories in Relationship to Mathematical Learning Richard R. Skemp 14. The Development of Addition in Contexts of Culture, Social Class, and Race Herbert P. Ginsburg 15. Learning to Add and Subtract: A Japanese Perspective Giyoo Hatano 16. The Psychological Characteristics of the Formation of Elementary Mathematical Operations in Children V. V. Davydov. Author Index. Subject Index.
Thomas P. Carpenter, James M. Moser, Thomas A. Romberg