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E-raamat: Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States 3rd edition [Taylor & Francis e-raamat]

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Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States 3rd editionSuurem pilt
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Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003009443

The 20th anniversary edition of this groundbreaking and bestselling volume offers powerful examples of the mathematics that can develop the thinking of elementary school children.

Studies of teachers in the U.S. 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 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.

Along with the original studies of U.S. and Chinese teachers’ mathematical understanding, this 20th anniversary edition includes a new preface and a 2013 journal article by Ma, "A Critique of the Structure of U.S. Elementary School Mathematics" that describe differences in U.S. and Chinese elementary mathematics. These are augmented by a new series editor’s introduction and two key journal articles that frame and contextualize this seminal work.

A Note about the 20th Anniversary Edition xiv
Author's Preface to the 20th Anniversary Edition xv
Series Editor's Introduction to the 20th Anniversary Edition: What Makes a Classic? xx
Author's Preface to the 2010 Edition xxii
Series Editors Introduction to the 2010 Edition xxvii
Foreword xxi
Acknowledgments xxxiii
Introduction 1(8)
1 Subtraction With Regrouping: Approaches To Teaching A Topic
9(26)
The U.S. Teachers' Approach: Borrowing Versus Regrouping
10(4)
The Chinese Teachers' Approach: "Decomposing a Higher Value Unit"
14(14)
Discussion
28(5)
Summary
33(2)
2 Multidigit Number Multiplication: Dealing With Students' Mistakes
35(27)
The U.S. Teachers' Approach: lining Up Versus Separating Into Three Problems
36(9)
The Chinese Teachers' Approach: Elaborating the Concept of Place Value
45(13)
Discussion
58(3)
Summary
61(1)
3 Generating Representations: Division By Fractions
62(29)
The U.S. Teachers' Performance on Calculation
62(3)
The Chinese Teachers' Performance on Calculation
65(6)
The U.S. Teachers' Representations of Division by Fractions
71(7)
The Chinese Teachers' Approach to the Meaning of Division by Fractions
78(9)
Discussion
87(2)
Summary
89(2)
4 Exploring New Knowledge: The Relationship Between Perimeter And Area
91(23)
How the U.S. Teachers Explored the New Idea
92(5)
How the Chinese Teachers Explored the New Idea
97(13)
Discussion
110(3)
Summary
113(1)
5 Teachers' Subject Matter Knowledge: Profound Understanding Of Fundamental Mathematics
114(17)
A Cross-Topic Picture of the Chinese Teachers' Knowledge: What Is Its Mathematical Substance?
114(5)
Knowledge Packages and Their Key Pieces: Understanding Longitudinal Coherence in Learning
119(2)
Elementary Mathematics as Fundamental Mathematics
121(2)
Profound Understanding of Fundamental Mathematics
123(5)
Summary
128(3)
6 Profound Understanding Of Fundamental Mathematics: When And How Is It Attained?
131(19)
When Is Profound Understanding of Fundamental Mathematics Attained?: What the Preteaching Groups Knew About the Four Topics
131(4)
Profound Understanding of Fundamental Mathematics: How It Is Attained
135(12)
Summary
147(3)
7 Conclusion
150(74)
Address Teacher Knowledge and Student Learning at the Same Time
152(1)
Enhance the Interaction Between Teachers' Study of School Mathematics and How to Teach It
153(2)
Refocus Teacher Preparation
155(1)
Understand the Role That Curricular Materials, Including Textbooks, Might Play in Reform
155(1)
Understand the Key to Reform: Whatever the Form of Classroom Interactions Might Be, They Must Focus on Substantive Mathematics
156(4)
Appendix
160(2)
References
162(6)
Bridging Polarities: How Liping Ma's Knowing and Teaching Elementary Mathematics Entered the U.S. Mathematics and Mathematics Education Discourses
168(24)
Response to "Bridging Polarities: How Liping Ma's Knowing and Teaching Elementary Mathematics Entered the U.S. Mathematics and Mathematics Education Discourses"
192(2)
New to the 20th Anniversary Edition: A Critique of the Structure of U.S. Elementary School Mathematics
194(30)
Index 224
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.
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