Knot Theory for Preservice and Practicing Secondary Mathematics Teachers

Chico State Enterprises, Chico CA

Investigators

Abstract

Mathematical Sciences (21) This proof-of-concept (POC) project is developing and evaluating a set of curriculum modules in knot theory for use in courses that typically comprise a pre-service teacher program. The PIs aim to graduate teachers who "learn mathematics in a coherent fashion that emphasizes the interconnections among theory, procedures and applications," and who "develop the habits of mind of a mathematical thinker" (CBMS, 2000). Since knot theory draws on connections with diverse types of mathematics, it has the potential to integrate well into courses on geometry, topology, combinatorics, discrete mathematics, or graph theory. Java applications are being developed to illustrate the Jones polynomial in a dynamic and visual context. Additionally, the project team is conducting research that addresses the mathematical knowledge and the beliefs about mathematics of preservice and practicing secondary mathematics teachers.