Prospective Mathematics Teachers’ Choice and Use of Representations in Teaching Limit Concept

Abstract

The purpose of this case study was to examine prospective mathematics teachers’ lessons in the context of choice and use of representations while teaching limit. The participants were four senior prospective mathematics teachers. The data were obtained from the participants’ lessons plans, the video recordings of their lessons, and the semi-structured interviews. We categorized the representations used by the participants as real number line, tabular, figural, graphical, algebraic and verbal. While the participants mostly used the verbal representations during their lessons, they used real number line least. They used the graphical representations sometimes by means of mathematical software. The participants mostly used tabular representations in their first lessons to make an introduction to limit, however two participants also used them in their last lessons to make students comprehend the limits at infinity. They used the algebraic representations to express the limit algebraically, to present the properties of limit and to solve examples. They performed the conversions among the real number line, tabular, figural, graphical, algebraic and verbal representations. The conversions were mostly from the algebraic representation to the verbal representation and vice versa.