Knowing and teaching elementary mathematics teachers' understanding of fundamental mathematics in China and the United States

Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.

The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers' mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author's work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

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Prior to her graduate study in China and in the US, Ma taught elementary school in China. She completed this book as part of her postdoctoral work at Berkeley. Building on work by D. Ball and Michigan State University's Teacher Education and Learning to Teach Study (TELT), Ma examined how elementary school teachers in the US and China as well as preservice elementary teachers and ninth graders in China understand mathematics. She found that the Chinese teachers had a greater "profound understanding of fundamental mathematics" (PFUM) than did the American teachers. And, while both the Chinese preservice teachers and ninth graders had greater conceptual understanding of elementary mathematics than the American teachers, data suggest that teachers in China acquire PFUM during their years of teaching. Ma argues that teacher education must define and teach a new "solid and substantive school mathematics." She identifies conditions and attitudes that hamper American teachers from developing PFUM while teaching. Readers may increase their PFUM by examining Ma's descriptions of teachers' understanding of topics. Must reading for those who call for more mathematics and those who champion reform pedagogy in teacher education. Upper-division undergraduates, graduate students, and faculty. A. O. Graeber; University of Maryland College Park

Foreword	p. ix
Acknowledgments	p. xiii
Introduction	p. xvii
Chapter 1 Subtraction with Regrouping: Approaches to Teaching a Topic	p. 1
Chapter 2 Multidigit Number Multiplication: Dealing with Students' Mistakes	p. 28
Summary	p. 54
Chapter 3 Generating Representations: Division by Fractions	p. 55
Summary	p. 82
Chapter 4 Exploring New Knowledge: the Relationship Between Perimeter and Area	p. 84
Summary	p. 106
Chapter 5 Teachers' Subject Matter Knowledge: Profound Understanding of Fundamental Mathematics	p. 107
Summary	p. 123
Chapter 6 Profound Understanding of Fundamental Mathematics: When and How is It Attained	p. 125
Summary	p. 142
Chapter 7 Conclusion	p. 144
Appendix	p. 154
References	p. 156
Author Index	p. 161
Subject Index	p. 163

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