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

ISBN-13: 9780367443955 / Angielski / Miękka / 2020 / 266 str.

Liping Ma

Opis

The 20^th anniversary edition of this groundbreaking and bestselling volume offers powerful examples for grasping the mathematical content necessary to understand and develop the thinking of school children.

Spis treści

A Note about the 20^th Anniversary Edition

Author's Preface to the 20^th 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 20^th Anniversary edition: A Critique of the Structure of U.S. Elementary School Mathematics

Index

O autorze

Liping Ma earned a Ph.D. from Stanford University, following a masters degree in education from East China Normal University. After a term as a senior scholar at the Carnegie Foundation for the Advancement of Teaching, she is now an independent scholar. She served as a member of the National Mathematics Advisory Panel from 2006 to 2008.