From the Book - Anniversary ed.
Author's Preface to the Anniversary Edition
Series Editor's Introduction to the Anniversary Edition
A Note about the Anniversary Edition
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"
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
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
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
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
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
Address Teacher Knowledge and Student Learning at the Same Time
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
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"
New to the Anniversary Edition: Ma's Response to "Bridging Polarities"
