Young Children Reinvent Arithmetic: Implications of Piaget's Theory (Early Childhood Education Series (Teachers College Pr))

Based on the constructivist Jean Piaget's theories on how children develop logico-mathematical thinking, this text describes and develops a programme for teaching arithmetic to young primary school children. The authors provide a theoretical foundation and an explanation of goals and objectives. In this fully revised second edition of the classic Young Children Reinvent Arithmetic , Constance Kamii describes and develops an innovative program of teaching arithmetic in the early elementary grades. Kamii bases her educational strategies on renowned constructivist Jean Piaget's scientific ideas of how children develop logico-mathematical thinking. Written in collaboration with a classroom teacher, and premised upon the conviction that children are capable of much more than teachers and parents generally realize, the book provides a rich theoretical foundation and a compelling explanation of educational goals and objectives. Kamii calls attention to the ways in which traditional textbook-based teaching can be harmful to children's development of numerical reasoning, and uses extensive research and classroom-tested studies to illuminate the efficacy of the approach. This book is full of practical suggestions and developmentally appropriate activities that can be used to stimulate numerical thinking among students of varying abilities and learning styles, both within and outside of the classroom. In this new edition of her important book, Connie Kamii demonstrates scholarship not just in what she has written, but in her willingness to incorporate new ideas and findings. Many people update their books; few assiduously revise them, confronting what they believe to be past errors or gaps in their thinking. Such intellectual honesty, along with consistent connections between theory and practice, make this book a solid contribution to mathematics education of young children. -- Douglas Clements , State University of New York at Buffalo The development of young childrens logico-mathematical knowledge is at the heart of this text. Similar to the first edition, this revision of Young Children Reinvent Implications of Piagets Theory provides a rich theoretical foundation as well as child-centered activities and principles of teaching that support problem solving, communicating, reasoning, making connections, and representing mathematical ideas. In this great resource for preservice and in-service elementary teachers, Professor Kamii continues to help us understand the implications of Piagetian theory. -- Frances R. Curcio , New York University Contents Acknowledgments Introduction Part I: THEORETICAL FOUNDATION Chapter 1. How Do Children Acquire Number Concepts? Chapter 2. Representation Chapter 3. The Importance of Social Interaction Part II: GOALS AND OBJECTIVES Chapter 4. Autonomy: The Aim of Education for Piaget Chapter 5. Addition as an Objective Chapter 6. Subtraction as an Objective Chapter 7. Multiplication and Division as Objectives Part III: ACTIVITIES AND PRINCIPLES OF TEACHING Chapter 8. The Use of Situations Outside the Math Hour Chapter 9. Word Problems Chapter 10. Games Involving Logic, Spatio-Temporal Reasoning,Small Numbers, and Numerals Chapter 11. Games and Other Activities Involving Addition and Subtraction Chapter 12. General Principles of Teaching Chapter 13. Principles of Teaching with Games Chapter 14. Evaluation Part IV: RESULTS Appendix: Resources References Index About the Author This book describes and develops an innovative program of teaching arithmetic in the early elementary grades. The educational strategies employed are based on Jean Piaget's constructivist scientific ideas of how children develop logico-mathematical thinking. The book is written in collaboration with a classroom teacher and premised on the conviction that children are capable of much more than teachers and parents generally realize. It provides a theoretical foundation and an explanation of educational goals and objectives. The book also contains practical suggestions and developmentally appropriate activities that can be used to stimulate numerical thinking among students of varying abilities and learning styles inside and outside of the classroom. (MM) 1. How Do Children Acquire Number Concepts? -- 2. Representation -- 3. The Importance Of Social Interaction -- 4. Autonomy: The Aim Of Education For Piaget -- 5. Addition As An Objective -- 6. Subtraction As An Objective -- 7. Multiplication And Division As Objectives -- 8. The Use Of Situations Outside The Math Hour / Leslie Baker Housman -- 9. Word Problems -- 10. Games Involving Logic, Spatio-temporal Reasoning, Small Numbers, And Numerals -- 11. Games And Other Activities Involving Addition And Subtraction -- 12. General Principles Of Teaching -- 13. Principles Of Teaching With Games -- 14. Evaluation. Includes Bibliographical References (p. 231-235) And Index. During the past 20 years, I (CK) have been asking educators in audiences all over the United States and abroad how they think children acquire number concepts, such as the idea (not the word) of "eight."