Analysis of errors in derivatives of trigonometric functions. (English)

Int. J. STEM Educ. 2, No. 1, Paper No. 16, 16 p., electronic only (2015).

Summary: Background: This article reports on an analysis of errors that were displayed by students who studied mathematics in Chemical Engineering in derivatives of mostly trigonometric functions. The poor performance of these students triggered this study. The researcher (lecturer) works in a mathematics support programme to enhance students’ understanding of mathematics. The purpose of this study was to identify errors and their origins when students did calculations in derivatives of trigonometric functions. The participants of this study were a group of thirty students who were registered for Mathematics in a university of technology in Western Cape, South Africa. The researcher used a qualitative case study approach and collected data from students’ written work. This study used Dubinsky’s APOS Theory (Actions, Processes, Objects, and Schemas) to classify errors into categories and analyse the data collected. Results: Errors displayed by students were conceptual and procedural; there were also errors of interpretation and linear extrapolation. Conceptual errors showed a failure to grasp the concepts in a problem and a failure to appreciate the relationships in a problem. Procedural errors occurred when students failed to carry out manipulations or algorithms, even if concepts were understood. Interpretation errors occurred when students wrongly interpreted a concept due to over-generalisation of the existing schema. Linear extrapolation errors occurred when students over-generalised the property $f(a+b)=f(a)+f(b)$, which applies only when $f$ is a linear function, to the form $f(a*b)=f(a)*f(b)$, where $f$ is any function and $*$ any operation. The findings revealed that the participants were not familiar with basic operational signs such as addition, subtraction, multiplication and division of trigonometric functions. The participants demonstrated poor ability to simplify once they had completed differentiation. Conclusions: This study recommends the strategy of focusing on elimination of errors to develop students’ understanding of derivatives of trigonometric functions. This can be done through learning activities that lead to identification and analyses of students’ errors in classroom discussions.