Pre-Service Teachers' Mental Constructions of Concepts in Matrix Algebra

Autor/inn/en	Ndlovu, Zanele; Brijlall, Deonarain
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 Verfügbarkeit
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 + Suchen Sie Ihr Suchwort? 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).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01