An investigation of secondary teachers' knowledge of rate of change in the context of teaching a standards-based curriculum.

摘要

This study investigated teachers' mathematical content knowledge 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 experience teaching CPMP using a survey, a mathematical task-based interview and classroom observations and follow-up interviews. The results showed that teachers demonstrated a well-connected understanding and flexible use of different representations in situations involving constant rate of change. Context played an important role with 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 were generally less able to use 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.;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. Teachers' conception of rate of change also differed based on experience with the CPMP curriculum. The findings of this study suggest that Standards-based 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.