Analysis of errors in derivatives of trigonometric functions

Abstract

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 (1991) 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.

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

“…The mistakes of prospective teachers on the concept of multiplication operation of two matrices based on APOS analysis mostly occur in prior learning which is more concerned with rote and procedure without having to understand the concepts studied. This is in line with the results of Siyepu's research, which states that students' mistakes on trigonometric derivative functions based on APOS theory analysis are mostly derived from previous mathematical learning and more than generalizations of certain mathematical rules [10]. Rote learning routines or procedures dominate the student's previous learning without students understanding them.…”

Flipped Classroom Strategy Based on Critical Thinking Skills: Helping Fresh Female Students Acquiring Derivative Concept

“…On the other hand, studies described some procedures to fix the situation as Mehrage and wahge (2016) stated that the teaching implication should focus on representations and relevant connections as part of understanding a derivative concept. As Siyepu (2015) asserted that the identification of errors might assist lecturers and mathematics teachers to focus on the development of pedagogical techniques that may overcome students' difficulties in their learning of derivative concept.…”

Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills

“…Orhun (2010) further explains that the majority of students in calculus class have low performance in operating trigonometric expressions, for example when operating the multiplication between sin × sin . Siyepu (2013Siyepu ( , 2015 found that students were more likely to generalize the properties of ( * ) = ( ) * ( ) in all cases, so they frequently make mistakes when writing down sin( + ) = sin + sin . Kamber & Takaci (2018) found that students had difficulty understanding the periodic function of trigonometry when faced with inequality problems.…”