Knowing and Teaching Elementary Mathematics : Teachers' Understanding of Fundamental Mathematics in China and the United States (Hardcover, 3 ed)

A Note about the 20th Anniversary Edition Author's Preface to the 20th Anniversary Edition Series Editor's Introduction to the 20th Anniversary Edition: What Makes a Classic? Author’s Preface to the 2010 Edition Series Editor’s Introduction to the 2010 Edition　 Foreword Acknowledgments Introduction 1. Subtraction With Regrouping: Approaches To Teaching A Topic　　 The U.S. Teachers' Approach: Borrowing Versus Regrouping 　　 The Chinese Teachers' Approach: "Decomposing a Higher Value Unit" 　　 Discussion　　 Summary 2. Multidigit Number Multiplication: Dealing With Students' Mistakes　　 The U.S. Teachers' Approach: Lining Up Versus Separating Into Three Problems　　 The Chinese Teachers' Approach: Elaborating the Concept of Place Value 　　 Discussion　　 Summary 3. Generating Representations: Division By Fractions　　 The U.S. Teachers' Performance on Calculation 　　 The Chinese Teachers' Performance on Calculation The U.S. Teachers' Representations of Division by Fractions 　　 The Chinese Teachers' Approach to the Meaning of Division by Fractions 　　 Discussion 　　 Summary 4. Exploring New Knowledge: The Relationship Between Perimeter And Area　　 How the U.S. Teachers Explored the New Idea 　　 How the Chinese Teachers Explored the New Idea 　　 Discussion 　　 Summary 5. Teachers' Subject Matter Knowledge: Profound Understanding Of Fundamental Mathematics　　 A Cross-Topic Picture of the Chinese Teachers' Knowledge: What Is Its Mathematical Substance?　　 Knowledge Packages and Their Key Pieces: Understanding Longitudinal Coherence in Learning　　 Elementary Mathematics as Fundamental Mathematics 　　 Profound Understanding of Fundamental Mathematics 　　 Summary 6. Profound Understanding Of Fundamental Mathematics: When And How Is It Attained?　　 When Is Profound Understanding of Fundamental Mathematics Attained?: What the Preteaching Groups Knew About the Four Topics　　 Profound Understanding of Fundamental Mathematics: How It Is Attained　　 Summary 7. Conclusion　　 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　　 Refocus Teacher Preparation　　 Understand the Role That Curricular Materials, Including Textbooks, Might Play in Reform　　 Understand the Key to Reform: Whatever the Form of Classroom Interactions Might Be, They Must Focus on Substantive Mathematics Appendix References Fang and Paine's "Bridging Polarities: How Liping Ma's Knowing and Teaching Mathematics Entered the U.S. Mathematics and Mathematics Education Discourses" Liping Ma's Response to "Bridging Polarities" New to the 20th Anniversary edition: A Critique of the Structure of U.S. Elementary School Mathematics Index