A Pedagogical Framework for Distinguishing Mathematical Definitions in the Classroom

Abstract

Most students believe that definitions play an important role in the learning of mathematics. However, they struggle with transitioning from performing procedures to reasoning from definitions as they move into more sophisticated mathematics. Further, students tend to focus in on their experiences, examples, and intuition, especially the visual/mental images they hold for a concept, instead of the axiomatic assertions provided by a mathematical definition. This disconnect between approaches needs to be addressed at all levels of study. The goal of this paper is to present a pedagogical framework and some examples on how to address the role of definition in the study of mathematics for students at all levels