An APOS Analysis of Solving Systems of Equations Using the Inverse Matrix Method

Autor/inn/en	Kazunga, Cathrine; Bansilal, Sarah
Titel	An APOS Analysis of Solving Systems of Equations Using the Inverse Matrix Method
Quelle	In: Educational Studies in Mathematics, 103 (2020) 3, S.339-358 (20 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Kazunga, Cathrine) ORCID (Bansilal, Sarah)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-020-09935-6
Schlagwörter	Foreign Countries; Mathematical Concepts; Mathematical Applications; Mathematics Teachers; Algebra; Matrices; Problem Solving; Equations (Mathematics); Zimbabwe + Suchen Sie Ihr Suchwort? Ausland; Angewandte Mathematik; Innermathematische Anwendung; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Matrizenrechnung; Problemlösen; Equations; Gleichungslehre; Simbabwe
Abstract	The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a Zimbabwean university as part of a first course in linear algebra. The purpose of the study was to explore the role of prerequisite concepts of determinant and matrix inverse in solving systems of equations using the inverse matrix method. The Action-Process-Object-Schema (APOS) theoretical framework was used to analyse the 116 participants' written responses to a questionnaire together with interview responses of 13 of the participants. Across the group of participants, it was found that only a small number had constructed prerequisite concepts of determinant and that of matrix inverse as Objects. The difficulties they had with prerequisite concepts prevented them from working more efficiently with the higher level concept of solving systems of equations using the inverse matrix method. These results suggest that instructors should help students consolidate their understanding of prerequisite concepts so that they are better placed to work with applications of these concepts. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01