Analysis of Students' Errors and Misconceptions in Solving Linear Ordinary Differential Equations Using the Method of Laplace Transform

Autor/inn/en	Msomi, Alfred Mvunyelwa; Bansilal, Sarah
Titel	Analysis of Students' Errors and Misconceptions in Solving Linear Ordinary Differential Equations Using the Method of Laplace Transform
Quelle	In: International Electronic Journal of Mathematics Education, 17 (2022) 1, (10 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Zusatzinformation	ORCID (Msomi, Alfred Mvunyelwa) ORCID (Bansilal, Sarah)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1306-3030
Schlagwörter	Mathematics Instruction; Error Patterns; Misconceptions; Equations (Mathematics); Problem Solving; College Students; Mathematical Concepts; Mathematics Skills; Foreign Countries; Engineering Education; South Africa + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Fehlertyp; Missverständnis; Equations; Mathematics; Gleichungslehre; Problemlösen; Collegestudent; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Ausland; Ingenieurausbildung; Südafrika; Süd-Afrika; Republik Südafrika; Südafrikanische Republik
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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01