Symbolizing While Solving Linear Systems

Autor/inn/en	Zandieh, Michelle; Andrews-Larson, Christine
Titel	Symbolizing While Solving Linear Systems
Quelle	In: ZDM: The International Journal on Mathematics Education, 51 (2019) 7, S.1183-1197 (15 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Zandieh, Michelle)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1863-9690
DOI	10.1007/s11858-019-01083-3
Schlagwörter	Problem Solving; Equations (Mathematics); Algebra; College Mathematics; Undergraduate Students; Introductory Courses; Matrices; Symbols (Mathematics) + Suchen Sie Ihr Suchwort? Problemlösen; Equations; Mathematics; Gleichungslehre; Einführungskurs; Matrizenrechnung
Abstract	Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory undergraduate linear algebra course at a large public research university in the United States. Based on our analysis, we expanded our framework (Larson & Zandieh, 2013) for interpretations of matrix equations to include augmented matrices and symbolic forms commonly used in solving linear systems. We document considerable variation in students' symbolization processes, which broadly occurred along two primary trajectories: systems trajectories and row reduction trajectories. Row reduction trajectories included at least five symbolic shifts, two of which students executed with a great deal of success and uniformity. Students' symbolizing processes varied more in relation to the other three shifts, and these variations were often linked to trends of variable renaming, variable creation, or imagined parameter reasoning. Students were more flexible in their solution strategies when solving systems involving lines than for systems involving planes. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01