Analysis of Mathematics Student Teachers’ Conceptions of the Limit of a Function: An Autoethnographic Perspective

Abstract

The initial teacher education is the focal point for developing student teachers’ content knowledge and the pedagogy that goes with it. The limit concept, amongst other concepts, allowed us to model what it means to teach mathematical concepts for understanding. The concept of a limit plays a significant role in the study of calculus. Although there is extensive research that focuses on students’ difficulties related to the limit of a function, the literature is scarce on students' conceptions of this important topic. As a result, the study analyses the mathematics student teachers’ conceptions of the limit of a function. An autoethnographic research design was to foreground the conceptions of three student teachers through a limit test based on the intuitive definition of a limit, its application using a table of values, its graphical determination, and its algebraic determination. The thematic analysis procedure was used to analyze student teachers’ test scripts. The findings of the study revealed that student teachers have underdeveloped conceptions of the intuitive definition of the limit concept. It was also revealed that some possess conceptions of the algebraic representations, as compared to other forms of representations. It is concluded that mathematics student teachers should develop different representations of the limit concept to create meaningful learning opportunities for their prospective learners.