Analysis of Students’ Errors and Misconceptions in Solving Linear Ordinary Differential Equations Using the Method of Laplace Transform
Alfred Mvunyelwa Msomi 1 2 * , Sarah Bansilal 1 2
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1 Mangosuthu University of Technology, SOUTH AFRICA2 University of KwaZulu Natal, SOUTH AFRICA* Corresponding Author

Abstract

Laplace transform (LT) is an essential mathematical tool for solving linear ordinary differential equations (ODE) with boundary values, by transforming differential equation into algebraic equations which are easier to manipulate. In this article, we analyse the errors students make and misconceptions they have in solving linear ODE using LT method. The study participants were 81 students enrolled in an engineering mathematics course at a University of Technology in South Africa. The students’ responses to an item based on LT which formed part of an assessment, were analysed. The analysis identified three stages of working that were necessary to reach a solution (introduction of LT and simplification; resolution of expressions using partial fractions (PF); carrying out the inverse LT and manipulations). Within each stage, we distinguished between three types of errors (conceptual, procedural and technical). The results showed that students experienced most problems when working in the PF layer because of the poor background in manipulation of algebraic expressions. It is recommended that students are given opportunities to develop fluency in pre-requisite concepts, so that their efforts at solving problems using LT or other advanced mathematics techniques can be less stressful.

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2022, Volume 17, Issue 1, Article No: em0670

https://doi.org/10.29333/iejme/11474

Publication date: 03 Jan 2022

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Article Downloads: 799

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