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Provides middle school teachers with a firm pedagogical foundation based on the manner in which students learn the mathematics being taught.
This book is written primarily for middle grade teachers who are discovering that they now want to teach in ways that create positive mathematical learning environments and instigate rich classroom discourse. Many of these teachers are finding that their mathematical preparation did not address the complexities underlying the mathematics they now want to teach.
In Part One, the authors provide a foundation for the mathematics of these grades, particularly the mathematics that grows out of concepts of number, quantity, and arithmetic operations. In Part Two, through three case studies, the authors demonstrate to teachers how a deeper understanding of the mathematics they teach can enhance classroom instruction.
The book interweaves research and classroom practice. Mathematics teacher educators, researchers, curriculum developers, textbook authors, and supervisors of mathematics programs will find this book to be useful. Teachers, both prospective and practicing, will benefit most from this book when the chapters are used as catalysts for discussion in classes or professional development programs.
Preface
1. Continuing the Mathematical Preparation of Middle-Grade Teachers: An Introduction
Judith T. Sowder
Part 1: Mathematics for the Middle Grades
2. Instructing for Rational Number Sense
Judith T. Sowder
3. Creating Spaces for Learning Fractions
Thomas E. Kieren
4. Critical Ideas, Informal Knowledge, and Understanding Fractions
Nancy K. Mack
5. Multiplication and Division of Fractions: The Search for Meaning
Barbara E. Armstrong Nadine Bezuk
6. Addressing the Story-Problem Problem
Larry Sowder
7. From Naive-Interpretist to Operation-Conserver
Guershon Harel
8. Ratio and Proportion: Elementary Didactical Phenomenology
Susan J. Lamon
9. Notation, Convention, and Quantity in Elementary Mathematics
Patrick W. Thompson
10. The Value of Interaction in Promoting Teaching Growth
Judith T. Sowder Randolph A. Philipp
Part II: Case Studies: Catalysts for Change
11. Instructional Effects of Knowledge Of and About Mathematics: A Case Study
Judith T. Sowder Randolph A. Philipp Alfinio Flores Bonnie P. Schappelle
12. Orchestrating, Promoting, and Enhancing Mathematical Discourse in the Middle Grades: A Case Study
Alfinio Flores Judith T. Sowder Randolph A. Philipp Bonnie P. Schappelle
13. A Responsible Mathematics Teacher and the Choices She Makes: A Case Study
Randolph A. Philipp Judith T. Sowder Alfinio Flores Bonnie P. Schappelle
List of Contributors
Index