Exploring the causes of the poor performance by Grade 12 learners in Calculus-based tasks

Abstract

The study attempted to determine the causes of poor performance among Grade 12 learners in tasks involving calculus, especially in cubic graphs and the application of differential calculus. The study was conducted in three schools of the Msukaligwa 1 Circuit in the Gert Sibande District, Mpumalanga Province in South Africa. Differential calculus is a branch of mathematics that is concerned mainly with the study of the rate of change of functions with respect to their variables especially through the use derivatives and differentials. Students have difficulties in learning and mastering this section of calculus as is revealed by examiners’ and moderators’ reports year after year. The purpose of this study was to investigate the possible reasons for the poor performance by Grade 12 learners in calculus-based tasks, especially in cubic graphs and the application in optimisation. The study sought to investigate the causes of the poor performance by Grade 12 learners in tasks based on these two subtopics of calculus. Three schools were selected by means of purposive sampling: one former model C, one Mathematics, Science and Technology Academy (MSTA) and one other school that does not fall in either of these two categories. This enabled the study to have participants from diverse backgrounds. A qualitative research design was used. Data was collected using learners’ scripts for the three formal tasks: May common test, June (midyear) and Trial (preparatory) examinations. Only the questions involving cubic graphs and the application of calculus were part of the study. Analysis was done in order to determine learners’ challenges, common mistakes, and misconceptions, but also of good responses given by learners.