Mathematical errors in differential calculus tasks in the Senior School Certificate Examinations in South Africa

The paper attempts to answer the research question: What is the nature of the errors that learners display in answering grade 12 mathematics examination questions on the topic of differential calculus? This quest is justified because calculus is a topic recently introduced in the Further Education and Training Band of the 'New Curriculum' in South Africa. Furthermore it is important to research on the errors learners make under the realistic tension of high stakes examinations such as those of the National Senior Certificate as this has not been done using similar instruments. The sample consisted of 1 000 randomly selected examination scripts from the 2008 Mathematics Paper 1 examination, written by school leaving learners of both sexes from varied socio-economic and academic backgrounds. Learners' responses to differential calculus tasks were analysed for their nature using the method of content analysis. The theoretical perspectives of Davis's (1984) cognitive frames of reference and Tall and Vinner's (1981) concept images and concept definitions made up the theoretical framework. Implications of the study to the South African and worldwide mathematics education community are highlighted.