Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Table of Contents
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
	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
Bridging Polarities: How Liping Ma’s Knowing and Teaching Elementary
Mathematics Entered the U.S. Mathematics and Mathematics
Education Discourses
Response to “Bridging Polarities: How Liping Ma’s Knowing and
Teaching Elementary Mathematics Entered the U.S. Mathematics and
Mathematics Education Discourses”
New to the 20th Anniversary Edition: A Critique of the Structure of U.S. Elementary School Mathematics
Index