This was a qualitative study carried out with learners from a grade twelve Standard Grade mathematics class from a South Durban school in the province of KwaZulu-Natal, South Africa. The main purpose of this study was to explore learners‟ understanding of the concept of the derivative. The participants comprised one class of twenty seven learners who were enrolled for Standard Grade mathematics at grade twelve level. Learners‟ responses to May and August examinations were examined. The examination questions that were highlighted were those based on the concept of the derivative. Additionally semi-structured interviews were carried out with a smaller sample of four of the twenty seven learners to gauge their perceptions of the derivative. The learners‟ responses to the examination questions and semi-structured interviews were exhaustively analysed. Themes that ran across the data were identified and further categorised in a bid to provide answers to the main research question. It was found that most learners‟ difficulties with the test items were grounded in their difficulties with algebraic manipulation skills. A further finding was that learners overwhelmingly preferred working out items that involved applying the rules. Although the Higher and Standard grade system of assessing learners‟ mathematical abilities has been phased out, with the advent of the new curriculum, the findings of this study is still important for learners, teachers, curriculum developers and mathematics educators because calculus forms a large component of the new mathematics curriculum.

Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2008.