Students' Understanding of the General Notion of a Function of Two Variables

Autor/inn/en	Martinez-Planell, Rafael; Trigueros Gaisman, Maria
Titel	Students' Understanding of the General Notion of a Function of Two Variables
Quelle	In: Educational Studies in Mathematics, 81 (2012) 3, S.365-384 (20 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-012-9408-8
Schlagwörter	Calculus; Mathematics Education; Interviews; Theories; Educational Research + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematische Bildung; Interviewing; Interviewtechnik; Theory; Theorie; Bildungsforschung; Pädagogische Forschung
Abstract	In this study we analyze students' understanding of two-variable function; in particular we consider their understanding of domain, possible arbitrary nature of function assignment, uniqueness of function image, and range. We use APOS theory and semiotic representation theory as a theoretical framework to analyze data obtained from interviews with thirteen students who had taken a multivariable calculus course. Results show that few students were able to construct an object conception of function of two variables. Most students showed difficulties finding domains of functions, in particular, when they were restricted to a specific region in the "xy" plane. They also showed that they had not fully coordinated their R[superscript 3], set, and function of one variable schemata. We conclude from the analysis that many of the interviewed students' notion of function can be considered as pre-Bourbaki. (As Provided).
Anmerkungen	Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10