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

Abstract

Continuous and non-continuous functions as school topics are dealt with in grades 10 to 12 at South African high schools 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 the Action-Process-Object-Schema (APOS) and Three Worlds of Mathematics (TWM) theories developed in a previous article (Brijlall and Maharaj 2011). 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 an analysis of their responses to examination questions. The four pre-service teachers in the study specialised in the teaching of mathematics for the Further Education and Training (FET) high school curriculum at an education faculty in a South African university. One of the rationales for assessment was to obtain informed feedback on the effect of instructional treatments. The pre-service teachers' responses in their final examination were analysed using a modified framework for reflective abstraction (MFRA). The current article is follow-up to a two-tiered concurrent approach which engaged pre-service teacher with an instructional design worksheet and collaborations in order to develop mathematical understandings of the concept of continuity. In the study it was found that the mathematics pre-service teachers worked in a symbolic world of the MFRA. There was no clear demarcation between the embodied and symbolic worlds of the MFRA. The pre-service teachers either used either one or the other, or moved flexibly between them when offering their explanations.