COGNITIVE LINKS IN UNDERSTANDING DERIVATIVE: THE CASE OF HELEN

Sally Jacobs

Arizona State University

sally.jacobs@mcmail.maricopa.edu

In this session, I will present a theoretical framework for analyzing aspects of the cognitive linkages between conceptual knowledge and procedural knowledge (hereinafter referred to as CK and PK). This framework builds on previous research regarding CK and PK of topics in arithmetic (e.g., Hiebert & Carpenter, 1992; Hiebert & Lefevre, 1986; Silver, 1986) and extends these studies by examining relationships between one calculus student's CK and PK of derivative.

My theoretical model consists of 3 components: Associativity, Stability, and Directionality. The first two components address the number and strength of the linkages between CK and PK, respectively. The third component addresses Silver's (1986) view that in some settings CK is constructed from a foundation of PK, but in other settings, PK rests on a base of CK.

I will present a method of diagram analysis for interpreting data. I will also explain how my model is a useful analytic and descriptive tool for examining three attributes of the cognitive connections between conceptual and procedural understanding of derivative.

References

Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Lawrence Erlbaum.

Hiebert, J. & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Macmillan.

Silver, E. A. (1986). Using conceptual and procedural knowledge: A focus on relationships. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 181-198). Hillsdale, NJ: Lawrence Erlbaum.