Misconceptions and Errors Among Grade 12 Students When Learning Differentiation Rules: A Case Study

t is an established fact that some grade 12 students learning differentiation in calculus are found struggling with the rule of differentiation and these rules include power rule, quotient rule, chain rule and product rule. Because of these, some students came up with some misconceptions which eventually resulted to the students having multiple errors when learning rules of differentiation. The reason associated with these common errors are not far from their failure to model some prerequisite knowledge in the laws of logarithm into their learning of the laws of differentiation. And this has resulted to the poor performance of some students in mathematics (calculus) since calculus carries about 40% in the overall grade in mathematics as a subject at grade 12 level. On this note, this paper presents an analysis of students’ errors and misconceptions in learning differentiation rule. The study was conducted among grade 12 students preparing for NSC examination in a high school in Limpopo province in South Africa. And the data was initially collected using 35 test scripts of grade 12 on the topic of differentiation and differentiation rule. A qualitative approach was considered, and the data collected was analysed, focusing on product rules, quotient rules and chain rules and the errors committed. The result of the study indicated that some grade 12 students make some errors and misconceptions in differentiation rules. And these were because of poor conceptual understanding, poor mathematics language understanding, and some other error. It was confirmed that the results of this study highlight the common mistakes and errors students make when learning differentiation rules, and these errors are; conceptual, systemic, language, and generalization errors.