Consequential implications of mathematics student teachers’ definitions of the function concept

Abstract

This article reports consequential implications of mathematics student teachers’ definitions of the function concept. The implications emanated from scrutiny of written definitions, and exploration of demonstrated ability to identify functions and translate them into different representations. A qualitative study characterized by a case study design was conducted. Four student teachers of mathematics education at a public university constitute the sample. Whereas the study site was conveniently chosen, the participants were a sub-sample in the principal study selected using extreme case strategy. Data were collected through semi-structured interviews preceded by student teachers’ written definitions of the function concept. Explorations of the written work and interview transcripts suggest that the student teachers’ definitions of a function were dominated by a narrow view that all functions are one-to-one relations. Notwithstanding, the participants’ conception of one-to-one functions was superficial. The student teachers’ flawed definitions of a function influenced their inability to correctly identify functions. Likewise, those definitions were consistent with the student teachers’ incapacity to translate functions accurately from one kind of representation into another. These findings underscore the necessity for mathematics teacher educators to facilitate student teachers’ development of correct definitions and appropriate concept images of the function concept.