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Autor/inn/en | Ndlovu, Zanele; Brijlall, Deonarain |
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Titel | Pre-Service Teachers' Mental Constructions of Concepts in Matrix Algebra |
Quelle | In: African Journal of Research in Mathematics, Science and Technology Education, 19 (2015) 2, S.156-171 (16 Seiten)
PDF als Volltext |
Sprache | englisch |
Dokumenttyp | gedruckt; online; Zeitschriftenaufsatz |
ISSN | 1029-8457 |
DOI | 10.1080/10288457.2015.1028717 |
Schlagwörter | Preservice Teachers; Mathematics Instruction; Algebra; Teaching Methods; Learning Activities; Cognitive Processes; Foreign Countries; Theories; Qualitative Research; Problem Solving; Mathematical Concepts; Computation; Mathematical Logic; Matrices; South Africa Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Lernaktivität; Cognitive process; Kognitiver Prozess; Ausland; Theory; Theorie; Qualitative Forschung; Problemlösen; Mathematical logics; Mathematische Logik; Matrizenrechnung; Südafrika; Süd-Afrika; Republik Südafrika; Südafrikanische Republik |
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. (As Provided). |
Anmerkungen | Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals |
Erfasst von | ERIC (Education Resources Information Center), Washington, DC |
Update | 2020/1/01 |