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

by Ma, Liping

• ISBN13: 9780805829099
• ISBN10: 0805829091
• Format: Paperback
• Copyright: 1999-05-01
• Publisher: Lawrence Erlbau

Summary

Although Chinese students typically outperform U.S. students on comparisons of mathematics competency, Chinese teachers receive far less education than U.S. teachers. This book describes the development of the profound understanding of fundamental mathematics that elementary teachers need.

Table of Contents

Foreword	ix
Acknowledgments	xiii
Introduction	xvii
Subtraction With Regrouping: Approaches To Teaching A Topic	1	(27)
The U.S. Teachers' Approach: Borrowing Versus Regrouping	2	(5)
The Chinese Teachers' Approach: ``Decomposing a Higher Value Unit''	7	(14)
Discussion	21	(5)
Summary	26	(2)
Multidigit Number Multiplication: Dealing With Students' Mistakes	28	(27)
The U.S. Teachers' Approach: Lining Up Versus Separating Into Three Problems	29	(9)
The Chinese Teachers' Approach: Elaborating the Concept of Place Value	38	(14)
Discussion	52	(2)
Summary	54	(1)
Generating Representations: Division By Fractions	55	(29)
The U.S. Teachers' Performance on Calculation	56	(2)
The Chinese Teachers' Performance on Calculation	58	(6)
The U.S. Teachers' Representations of Division by Fractions	64	(8)
The Chinese Teachers' Approach to the Meaning of Division by Fractions	72	(8)
Discussion	80	(2)
Summary	82	(2)
Exploring New Knowledge: The Relationship Between Perimeter And Area	84	(23)
How the U.S. Teachers Explored the New Idea	85	(5)
How the Chinese Teachers Explored the New Idea	90	(13)
Discussion	103	(3)
Summary	106	(1)
Teachers' Subject Matter Knowledge: Profound Understanding Of Fundamental Mathematics	107	(18)
A Cross-Topic Picture of the Chinese Teachers' Knowledge: What Is Its Mathematical Substance?	108	(5)
Knowledge Packages and Their Key Pieces: Understanding Longitudinal Coherence in Learning	113	(3)
Elementary Mathematics as Fundamental Mathematics	116	(2)
Profound Understanding of Fundamental Mathematics	118	(5)
Summary	123	(2)
Profound Understanding Of Fundamental Mathematics: When And How Is It Attained	125	(19)
When Is Profound Understanding of Fundamental Mathematics Attained?: What the Preteaching Groups Knew About the Four Topics	126	(3)
Profound Understanding of Fundamental Mathematics: How It Is Attained?	129	(13)
Summary	142	(2)
Conclusion	144	(10)
Address Teacher Knowledge and Student Learning at the Same Time	146	(1)
Enhance the Interaction Between Teachers' Study of School Mathematics and How to Teach It	147	(2)
Refocus Teacher Preparation	149	(1)
Understand the Role That Curricular Materials, Including Textbooks, Might Play in Reform	150	(1)
Understand the Key to Reform: Whatever the Form of Classroom Interactions Might Be, They Must Focus on Substantive Mathematics	151	(3)
Appendix	154	(2)
References	156	(5)
Author Index	161	(2)
Subject Index	163