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An APOS analysis of solving systems of equations using the inverse matrix method

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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.

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Authors and Affiliations

  1. School of Education, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, South Africa

    Cathrine Kazunga & Sarah Bansilal

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  1. Cathrine Kazunga
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  2. Sarah Bansilal
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Correspondence to Cathrine Kazunga.

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Kazunga, C., Bansilal, S. An APOS analysis of solving systems of equations using the inverse matrix method. Educ Stud Math 103, 339–358 (2020). https://doi.org/10.1007/s10649-020-09935-6

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