Pre-service teachers understanding of continuity of functions in the context of assessment items

Abstract

Continuous and non-continuous functions are dealt with in the grades 10 to 12 South African high schools topics as prescribed by the Curriculum and Assessment Policy Statement. This article reports on the use of a combined framework for mathematical thinking that incorporated the ideas of APOS (action-process-object-schema) and the TWM (three worlds of mathematics) theories developed in a previous paper. The present study is qualitative in that it reports on those pre-service teachers’ mental constructions of the concept of continuity of single-valued functions, obtained from analysis of their responses to examination questions. The four pre-service teachers in this study specialised in the teaching of mathematics for the FET high school curriculum at an education faculty in a South African university. One of the rationales for assessment is to get informed feedback on the effect of instructional treatments. These pre-service teachers’ responses in their final examination were analysed using a modified framework for reflective abstraction (MFRA). This paper is follow-up to a two-tiered concurrent approach which engaged pre-service teacher with an instructional design worksheet and collaborations, to develop mathematical understandings of the concept of continuity. In this study it was found that the mathematics pre-service teachers worked in a symbolic world of MFRA. There was no clear demarcation between the embodied and symbolic worlds of MFRA. These pre-service teachers either used one or the other, or moved flexibly between them when offering their explanations