Liping Ma earned a Ph.D. from Stanford University, following a masters degree in education from East China Normal
University. After a term as a senior scientist at the Carnegie Foundation for the Advancement of Teaching, she
is now an independent scholar.
Summary
Documents differences between Chinese & US teachers' knowledge of mathematics for teaching & suggests how Chinese teachers' understanding contributes to their teaching competence and their students' success.
Table of Contents
Author's Preface to the Anniversary Edition xi
Series Editor's Introduction to the Anniversary Edition xvi
A Note about the Anniversary Edition xviii
Foreword xix
Acknowledgments xxiii
Introduction xxvi
1 Subtraction With Regrouping: Approaches To Teaching A Topic 1
The U. S. Teachers' Approach: Borrowing Versus Regrouping 2
The Chinese Teachers' Approach: "Decomposing a Higher Value Unit" 7
Discussion 21
Summary 26
2 Multidigit Number Multiplication: Dealing with Students' Mistakes 28
The U.S. Teachers' Approach: Lining Up Versus Separating Into Three Problems 29
The Chinese Teachers' Approach: Elaborating the Concept of Place Value 38
Discussion 52
Summary 54
3 Generating Representations: Division By Fractions 55
The U.S. Teachers' Performance on Calculation 56
The Chinese Teachers' Performance on Calculation 58
The U.S. Teachers' Representations of Division by Fractions 64
The Chinese Teachers' Approach to the Meaning of Division by Fractions 72
Discussion 80
Summary 82
4 Exploring New Knowledge: The Relationship Between Perimeter And Area 84
How the U. S. Teachers Explored the New Idea 85
How the Chinese Teachers Explored the New Idea 90
Discussion 103
Summary 106
5 Teachers' Subject Matter Knowledge: Profound Understanding of Fundamental Mathematics 107
A Cross-Topic Picture of the Chinese Teachers' Knowledge: What Is Its Mathematical Substance" 108
Knowledge Packages and Their Key Pieces: Understanding Longitudinal Coherence in Learning 113
Elementary Mathematics as Fundamental Mathematics 116
Profound Understanding of Fundamental Mathematics 118
Summary 123
6 Profound Understanding Of Fundamental Mathematics: When And How Is It Attained" 125
When Is Profound Understanding of Fundamental Mathematics Attained": What the Preteaching Groups Knew About
the Four Topics 126
Profound Understanding of Fundamental Mathematics: How It Is Attained 129
Summary 142
7 Conclusion 144
Address Teacher Knowledge and Student Learning at the Same Time 146
Enhance the Interaction Between Teachers' Study of School Mathematics and How to Teach It 147
Refocus Teacher Preparation 149
Understand the Role That Curricular Materials, Including Textbooks, Might Play in Reform 150
Understand the Key to Reform: Whatever the Form of Classroom Interactions Might Be, They Must Focus on Substantive
Mathematics 151
Appendix 154
References 156
New to the Anniversary Edition: Fang and Paine's "Bridging Polarities: How Liping Ma's Knowing and Teaching
Mathematics Entered the U. S. Mathematics and Mathematics Education Discourses" 161
New to the Anniversary Edition: Ma's Response to "Bridging Polarities" 186
