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Knowing and Teaching Elementary Mathematics

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The 20th anniversary edition of this groundbreaking and bestselling volume offers powerful examples of the mathematics that can d... Weiterlesen
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Beschreibung

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.



Autorentext

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.



Inhalt

A Note about the 20th Anniversary Edition

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

Index

Produktinformationen

Titel: Knowing and Teaching Elementary Mathematics
Untertitel: Teachers' Understanding of Fundamental Mathematics in China and the United States
Autor:
EAN: 9781000023084
Digitaler Kopierschutz: frei
Format: E-Book (epub)
Hersteller: Taylor & Francis Ltd.
Genre: Pädagogik
Anzahl Seiten: 266
Veröffentlichung: 06.01.2020
Dateigrösse: 2.4 MB