Pre-service Teachers’ Mental Constructions of Concepts in Matrix Algebra

Abstract

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers through a structured activity sheet. The aim was to explore their mental constructions of matrix algebra concepts and how they concur with a preliminary genetic decomposition. The study is underpinned by APOS theory (action–process–object–schema). The findings revealed that the mental constructions made by pre-service teachers in most cases concur with the preliminary genetic decomposition. In terms of APOS theory, the responses revealed that most pre-service teachers were operating at action and process stages, with few operating at the object stage. It was observed that the schemata for basic algebra and real number are necessary for the conceptual development of matrix algebra, and that familiarity of the correct use of terminology and notations promotes the earning of matrix algebra. On the basis of the detailed response analysis, modified genetic decompositions are proposed for the matrix order concept, matrix transpose concept and for matrix operations.

Keywords:

• APOS theory
• genetic decomposition
• matrix algebra

Acknowledgements

The first author would like to place on record her sincere gratitude to the organising team of the 12th Annual Research School hosted by SAARMSTE. The facilitators at this school made suggestions in the preparatory stages of the writing of this paper. We would also place on record our sincere appreciation to our colleague Mrs E. Dowlath for proofreading the manuscript.

Disclosure Statement

No potential conflict of interest was reported by the authors.