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

Joshua Chesler


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.


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