Dissertation Archive, WMU Graduate College

Dissertation Defense

Candidate: Jihwa Noh

Degree of: Doctor of Philosophy

Department: Mathematics

Title: An Investigation of Secondary Teachers' Knowledge of Rate of Change in the Context of Teaching a Standards-Based Curriculum

Date: Monday, July 19, 2004 4:00 p.m.-6:00 p.m.
Alavi Commons Room, 6625 Everett Tower

Committee: Drs. Kate Kline and Steven Ziebarth, Chairs
Dr. Christian Hirsch
Dr. Laura Van Zoest
Dr. Rebecca Walker

Abstract: This study investigated teachers' mathematical content and pedagogical content knowledge with respect to rate of change in the context of teaching a Standards-based high school mathematics curriculum that emphasizes rate of change as a central theme, the Core-Plus Mathematics Project (CPMP) materials. A framework was designed to provide a comprehensive guide for analyzing different aspects of rate of change knowledge incorporating existing frameworks relative to rate of change, NCTM recommendations described in Curriculum and Evaluation Standards for School Mathematics and Principles and Standards for School Mathematics (NCTM, 2000), and research related to pedagogical understanding of rate of change.

Data for this study were collected from thirteen teachers with a wide variety of CPMP teaching experience using survey, mathematical task-based interview and classroom observations. The results showed teachers' conception of rate of change differed based on experience with the CPMP curriculum. Teachers demonstrated a well-connected understanding and flexible use of different representations in situations involving constant rate of change. Teachers who had more experience with the CPMP curriculum were generally more successful in dealing with non-constant rates of change and recognizing similar and contrasting characteristics of different types of representations across contexts. Context played an important role in regard to teachers' ability to explore rate of change as more teachers were able to interpret situations involving non-constant rates of change when they were embedded in a context-rich setting. Teachers generally had more difficulty using graphical representations compared to numerical and symbolic representations. Understanding connections between finding the slope of a line and methods for estimating the rate of change for nonlinear functions proved to be challenging for most teachers, although more experienced teachers demonstrated a better understanding of these connections.

The findings of this study suggest that curriculum materials may support teachers as they learn ideas involving rate of change, but that a more thorough understanding of the concept may require additional resources.

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