Pre-service Secondary Mathematics Teachers Making Sense of Definitions of Functions

Abstract

Definitions play an essential role in mathematics. As such, mathematics teachers and students need to flexibly and productively interact with mathematical definitions in the classroom. However, there has been little research about mathematics teachers’ understanding of definitions. At an even more basic level, there is little clarity about what teachers must know about mathematical definitions in order to support the development of mathematically proficient students. This paper reports on a qualitative study of pre-service secondary mathematics teachers choosing, using, evaluating, and interpreting definitions. In an undergraduate capstone course for mathematics majors, these future teachers were assigned three tasks which required them to (1) choose and apply definitions of functions, (2) evaluate the equivalence of definitions of functions, and (3) interpret and critique a secondary school textbook’s definition of a specific type of function. Their performances indicated that many of these pre-service mathematics teachers had deficiencies reasoning with and about mathematical definitions. The implications of these deficiencies are discussed and suggestions for teacher educators are proposed.