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Author's Preface to the Anniversary Edition | |
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Series Editor's Introduction to the Anniversary Edition | |
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A Note about the Anniversary Edition | |
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Foreword | |
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Acknowledgments | |
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Introduction | |
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Subtraction With Regrouping: Approaches To Teaching A Topic | |
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The U. S. Teachers' Approach: Borrowing Versus Regrouping | |
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The Chinese Teachers' Approach: "Decomposing a Higher Value Unit" | |
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Discussion | |
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Summary | |
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Multidigit Number Multiplication: Dealing with Students' Mistakes | |
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The U.S. Teachers' Approach: Lining Up Versus Separating Into Three Problems | |
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The Chinese Teachers' Approach: Elaborating the Concept of Place Value | |
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Discussion | |
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Summary | |
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Generating Representations: Division By Fractions | |
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The U.S. Teachers' Performance on Calculation | |
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The Chinese Teachers' Performance on Calculation | |
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The U.S. Teachers' Representations of Division by Fractions | |
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The Chinese Teachers' Approach to the Meaning of Division by Fractions | |
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Discussion | |
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Summary | |
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Exploring New Knowledge: The Relationship Between Perimeter And Area | |
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How the U. S. Teachers Explored the New Idea | |
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How the Chinese Teachers Explored the New Idea | |
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Discussion | |
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Summary | |
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Teachers' Subject Matter Knowledge: Profound Understanding of Fundamental Mathematics | |
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A Cross-Topic Picture of the Chinese Teachers' Knowledge: What Is Its Mathematical Substance? | |
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Knowledge Packages and Their Key Pieces: Understanding Longitudinal Coherence in Learning | |
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Elementary Mathematics as Fundamental Mathematics | |
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Profound Understanding of Fundamental Mathematics | |
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Summary | |
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Profound Understanding Of Fundamental Mathematics: When And How Is It Attained? | |
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When Is Profound Understanding of Fundamental Mathematics Attained?: What the Preteaching Groups Knew About the Four Topics | |
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Profound Understanding of Fundamental Mathematics: How It Is Attained | |
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Summary | |
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Conclusion | |
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Address Teacher Knowledge and Student Learning at the Same Time | |
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Enhance the Interaction Between Teachers' Study of School Mathematics and How to Teach It | |
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Refocus Teacher Preparation | |
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Understand the Role That Curricular Materials, Including Textbooks, Might Play in Reform | |
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Understand the Key to Reform: Whatever the Form of Classroom Interactions Might Be, They Must Focus on Substantive Mathematics | |
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Appendix | |
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References | |
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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" | |
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New to the Anniversary Edition: Ma's Response to "Bridging Polarities" | |
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Author Index | |
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Subject Index | |