A Characterization of a Unified Notion of Mathematical Function: The Case of High School Function and Linear Transformation

Autor/inn/en	Zandieh, Michelle; Ellis, Jessica; Rasmussen, Chris
Titel	A Characterization of a Unified Notion of Mathematical Function: The Case of High School Function and Linear Transformation
Quelle	In: Educational Studies in Mathematics, 95 (2017) 1, S.21-38 (18 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Zandieh, Michelle)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-016-9737-0
Schlagwörter	Mathematics Instruction; Algebra; Mathematical Concepts; Problem Solving; Secondary School Mathematics; High School Students; College Mathematics; College Students; Mathematical Formulas + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Problemlösen; High school; High schools; Student; Students; Oberschule; Schüler; Schülerin; Studentin; Collegestudent; Mathematische Formel
Abstract	As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear transformation as related to high school function. Analysis of these data led to a characterization of student responses into three categories of mathematical structures used to discuss function: properties, computations, and a series of five interrelated clusters of metaphorical expressions. In this paper, we use this analytic framing for exploring the question: to what extent does each of the students in this study have a unified concept image of function across two mathematical contexts, high school algebra and their study of linear algebra? We found that students who expressed a unified notion of function used metaphorical language to bridge any gaps between the notion of function from high school and the notion of linear transformation from linear algebra. We conjecture that the framing of computations, properties, and metaphorical clusters could be extended to discussions of functions in contexts with other mathematical domains. Future research that further examines the extent to which undergraduate students develop a unified concept image of function could then lead to various design research efforts aimed at explicitly fostering such a unified understanding. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01