Abstract
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 (1991) APOS Theory (Actions, Processes, Objects, and Schemas) to classify errors into categories and analyse the data collected. 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. 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.
Highlights
Introduction and backgroundThis paper is part of a doctoral study conducted to explore students’ errors in derivatives of trigonometric functions
This study focuses on errors displayed by students in derivatives of trigonometric functions
Arnon et al (2014) explain that: Action Process Object Schema (APOS) Theory focuses on models of what might be going on in the mind of an individual when he or she is trying to learn a mathematical concept and uses these models to design instructional materials and/or to evaluate student successes and failures in dealing with mathematical problem situations. (p.1) This study focuses on errors displayed by students in derivatives of trigonometric functions
Summary
This paper is part of a doctoral study conducted to explore students’ errors in derivatives of trigonometric functions This was to enable the researcher to establish causes and origins of such errors to develop a means of eliminating displayed errors. Siyepu International Journal of STEM Education (2015) 2:16 students’ prior learning, either in the classroom (especially for mathematics) or from their interaction with the physical and social world” (p.10) They further elaborate that misconceptions can be stable and widespread among students and such misconceptions can be strongly held and resistant to change Orton (1983a) asserts that students have problems in understanding the meaning of the derivative when it is written as a fraction His findings include different types of errors displayed by students in a calculus classroom. This study used Dubinsky’s (1991) APOS Theory (Actions, Processes, Objects, and Schemas) to classify errors into categories and analyse the data collected
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