Concept Maps as Research Tools in Mathematics

By: Williams, Carol G.

Reform efforts in mathematics aim to increase conceptual understanding, an aim that can be supported through concept maps. This study compared the conceptual knowledge of function held by college students in reform and traditional calculus sections at a large state university. Fourteen students from reform sections and 14 from traditional sections served as subjects. A primary task was the construction of a concept map of function. Four instructors of reform sessions and four from traditional sections also completed concept maps. Quantitative analyses of the concept maps showed that the core contents from both student groups matched poorly with instructors’ core concepts. Qualitative analysis of the student maps revealed differences between the student groups, with the reform group using terminology common in the reform text and using fewer algorithmic references than the traditional group. The traditional group’s maps contained more algorithmic references to hand-graphing techniques. Maps of both groups were considerably less well-structured than experts’ maps and lacked their higher level categories. (Contains 9 figures, 10 tables, and 35 references.)

Paper presented at the Annual Meeting of the American Educational Research Association (San Francisco, CA, April 18-22, 1995).

Download the Paper at ERIC (PDF, 55 Pages, 2.62 MB)