The Development of Arithmetic Concepts and Skills: Constructive Adaptive Expertise

by Baroody, Arthur J.; Dowker, Ann; Bryant, Peter; Carpenter, Thomas P.

• ISBN13: 9780805831559
• ISBN10: 080583155X
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Lawrence Erlbau

Summary

This volume focuses on two related questions that are central to both the psychology of mathematical thinking and learning and to the improvement of mathematics education: What is the nature of arithmetic expertise? How can instruction best promote it? Contributors from a variety of specialities, including cognitive, developmental, educational, and neurological psychology; mathematics education; and special education offer theoretical perspectives and much needed empirical evidence about these issues. As reported in this volume, both theory and research indicate that the nature of arithmetic expertise and how to best promote it are far more complex than conventional wisdom and many scholars, past and present, have suggested. The results of psychological, educational, and clinical studies using a wide range of arithmetic tasks and populations (including "normally" and atypically developing children, non-injured and brain-injured adults, and savants) all point to the same conclusion: The heart of arithmetic fluency, in general, and the flexible and creative use of strategies, in particular, is what is termed "adaptive expertise" (meaningful or conceptually based knowledge). The construction of adaptive expertise in mathematics is, for the first time, examined across various arithmetic topics and age groups. This book will be an invaluable resource for researchers and graduate students interested in mathematical cognition and learning (including mathematics educators, developmental and educational psychologists, and neuropsychologists), educators (including teachers, curriculum supervisors, and school administrators), and others interested in improving arithmetic instruction (including officials in national and local education departments, the media, and parents).

Table of Contents

Foreword	xi
Giyoo Hatano
Preface	xv
Arthur J. Baroody
Ann Dowker
The Development of Adaptive Expertise and Flexibility: The Integration of Conceptual and Procedural Knowledge	1	(34)
Arthur J. Baroody
Does It All Add Up? Changes in Children's Knowledge of Addition Combinations, Strategies, and Principles	35	(40)
Richard Cowan
Two Perspective on Addition Development	75	(52)
Arthur J. Baroody
Sirpa H. Tiilikainen
The Development of Children's Understanding of Additive Commutativity: From Protoquantitative Concept to General Concept?	127	(34)
Arthur J. Baroody
Jesse L. M. Wilkins
Sirpa Tiilikainen
``You've Got to Carefully Read the Math Sentence . . .'': Classroom Context and Children's Interpretations of the Equals Sign	161	(28)
Kyoung-Hye Seo
Herbert P. Ginsburg
Basic Multiplication Combinations: Passive Storage or Dynamic Reorganization?	189	(14)
Brian Butterworth
Noemi Marschesini
Luisa Girelli
Young Adults' Strategic Choices in Simple Arithmetic: Implications for the Development of Mathematical Representations	203	(26)
Jo-Anne LeFevre
Brenda L. Smith-Chant
Karen Hiscock
Karen E. Daley
Jason Morris
Language Supports for Mathematics Understanding and Performance	229	(14)
Irene T. Miura
Yukari Okamoto
Young Children's Estimates for Addition: The Zone of Partial Knowledge and Understanding	243	(24)
Ann Dowker
Multidigit Addition and Subtraction Methods Invented in Small Groups and Teacher Support of Problem Solving and Reflection	267	(38)
Karen C. Fuson
Birch H. Burghardt
Children's Invention of Multidigit Multiplication and Division Algorithms	305	(32)
Rebecca Ambrose
Jae-Meen Baek
Thomas P. Carpenter
The Early Numeracy of Children With Specific Language Impairments	337	(22)
Chris Donlan
Mathematical Thinking and Learning Difficulties	359	(26)
Nancy Jordan
Laurie B. Hanich
Heather Z. Uberti
Neuropsychological Findings on Conceptual Knowledge of Arithmetic	385	(24)
Margarete Delazer
Arithmetical Savants	409	(56)
Lisa Heavey
Arithmetical Development: Commentary on Chapters 1 through 8 and Reflections on Directions	435	(18)
Jeffrey Bisanz
Arithmetical Development: Commentary on Chapters 9 through 15 and Future Directions	453	(12)
David C. Geary
Glossary of Abbreviations	465	(2)
Author Index	467	(16)
Subject Index	483