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

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

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by Liping Ma
     
 

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ISBN-10: 0805829083

ISBN-13: 9780805829082

Pub. Date: 03/01/1999

Publisher: Taylor & Francis

Studies of teachers in the United States often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development

Overview

Studies of teachers in the United States often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U. S. counterparts.

The anniversary edition of this bestselling volume includes the original studies that compare U.S. and Chinese elementary school teachers' mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author's work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

Product Details

ISBN-13:
9780805829082
Publisher:
Taylor & Francis
Publication date:
03/01/1999
Series:
Studies in Mathematical Thinking and Learning Series
Pages:
192
Product dimensions:
6.10(w) x 9.00(h) x 0.70(d)
Lexile:
1190L (what's this?)

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

Author Index 189

Subject Index 191

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Knowing and Teaching Elementary Mathematics 3.8 out of 5 based on 0 ratings. 4 reviews.
Guest More than 1 year ago
I found this book to be very enlightening on the subject of Math education and the differences in understanding of elementary math education between Asian, specifically China, and the US. She gives detailed examples of various elementary/basic math concepts that students must learn and discusses how the different teachers approached problems and understood the mathematical concepts. Frankly, I have had a college level class on math for elementary teachers which I found helpful in filling in the gaps of my own understanding of math and ways to teach it. However, I found the many detailed explanations given by the chinese teachers to be much better at connecting all the concepts and previous knowledge. I highly recommend this book to any US teachers whether in public/private schools or in home schools.
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