Exploring Errors and Misconceptions in Differentiation: A Case Study of Advanced Level Students in Zimbabwe

Abstract

Students’ errors help teachers to tease out misconceptions and decide on what intervention strategies to adopt and use to challenge these alternative conceptions. The purpose of the study was to explore A-Level students’ errors and misconceptions when solving problems in differentiation. A largely qualitative case study strategy was adopted. The case was made up of Two A-Level teachers and 25 students. After covering the topic differentiation, a test was administered. Qualitative data was collected using the test scripts and syllabus documents, questionnaire and focus group discussions. Content analysis was used to reveal errors and misconceptions when solving problems in differentiation. The common errors and misconceptions displayed by A-Level students were largely procedural when they failed to use the quotient rule, chain rule and power rule in finding derivatives. Our study found out that errors and misconceptions when using the power rule were adding a one to the power part instead of subtracting, bringing down the power and mistakenly adding a one to the power, failure to integrate functions, failure to separate variables correctly, failure to find the required derivative and using wrong laws to solve problems in differentiation. These errors and misconceptions were, possibly originating from students’ lack of prior knowledge of differentiation, laws of logarithms, proportionality and integration and rate of change. We recommend further research using larger population and samples.