Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction

A Research Monograph

By Judith Sowder, Randolph A. Philipp, Barbara E. Armstrong, and Bonnie P. Schappelle

Subjects: Education
Series: SUNY series, Reform in Mathematics Education
Paperback : 9780791438428, 227 pages, July 1998
Hardcover : 9780791438411, 227 pages, July 1998

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Table of contents

1. Introduction

2. Conceptual Framework

3. Methodology

4. Results: Effects of Seminars on Teachers' Knowledge

5. Linda: Coming to Appreciate the Role of Mathematics in Professional Development

6. Shey: Teaching Mathematics to Children of Diversity

7. Darota: Ideals Collide With Reality

8. Tom: Mathematics as Concepts Versus Mathematics as Procedures: Finding a Balance

9. Cynthia: The Pain of Change

10. Student Learning

11. Reflections and Conclusions




A. Test of Teachers' Pedagogical Content Understanding
B. Initial Interviews With Teachers
C. Reflections of Teachers at Conclusion of Year 1
D. Teacher Observation Form
E. Teacher/Teacher Observation Form
F. Fraction Understanding and Proporational Reasoning Text



Investigates how middle grade teachers' deeper understanding of the mathematics of number, quantity, and proportion influences the way they teach and the way students learn.


The outcome of a two-year investigation, this book shows how teachers' understanding of the mathematics of number, quantity, and proportion influences how they teach and what their students learn of the concepts, skills, and reasoning associated with this mathematical domain of knowledge. It grew out of the recognition of the need to understand the complexities of helping teachers reconceptualize the mathematics they teach and the resulting effects in their classrooms. The book includes case studies of five teachers, from different types of school settings, illustrating changes in the teachers' teaching methods, expectations of students, and beliefs about the role of professional development.

At the Center for Research in Mathematics and Science Education, San Diego State University, Judith T. Sowder is Professor of Mathematical Sciences, Randolph A. Philipp and Barbara E. Armstrong are Assistant Professors of Teacher Education, and Bonnie P. Schappelle is a Research Associate.


"What I like most about the this book is that it brings together in one study many aspects of research in mathematics education–it marries what we know about the meaningful learning of multiplicative structures with what we know about effective teacher training. It incorporates elements of the research base on what it takes to change teachers' beliefs and teaching practices. It is longitudinal and qualitative in nature—and thus gives some badly needed depth to this confluence of various areas of study in mathematics education. " — Vicky L. Kouba, University at Albany, State University of New York

"This book represents sound and important scholarship in the field of mathematics education, particularly in mathematics teacher education. The authors have conducted a good study, one that is of the long term nature that can serve as a model to be emulated by researchers and those interested in professional development. " — Doug Jones, University of Kentucky