



Knowing and Teaching Mathematics describes the nature and development of the "profound understanding of fundamental mathematics" that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.
"This is indeed a valuable, enlightening book. It attests to the talent of its author, and to the Chinese and American learning environments that have nurtured that talent. It attests to the value of welcoming scholars from other nations to study in the United States. I urge all those who are seriously concerned about the quality of mathematics education in the United States to read this book, and to take its lessons seriously."
 From the Foreword by Lee Shulman, President, Carnegie Foundation for the Advancement of Teaching
"Liping Ma's work has given me hope about what can be done to improve mathematics education. She illustrates what 'profound understanding of fundamental mathematics' is for elementary school teachers and has some useful suggestions about what we can do to help more teachers acquire this knowledge."
 Richard Askey, John Bascom Professor of Mathematics, University of WisconsinMadison
Above is an extract from Knowing and Teaching Elementary Mathematics.
Knowing and Teaching Elementary Mathematics
Contents
Author's Preface to the Anniversary Edition
Series Editor's Introduction to the Anniversary Edition
A Note about the Anniversary Edition
Foreword
Acknowledgments
Introduction
 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
 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
 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
 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
 Teachers' Subject Matter Knowledge: Profound Understanding of Fundamental Mathematics
 A CrossTopic 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
 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 Is It Attained?
Summary
 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
Author Index
Subject Index
Samples
Sample 1
Sample 2
Sample 3
Sample 4













Our recommendation:
Knowing and Teaching Elementary Mathematics is a good book for those who are interested in and concerned with mathematics education.








