Students' Images of Two-Variable Functions and Their Graphs

Autor/inn/en	Weber, Eric; Thompson, Patrick W.
Titel	Students' Images of Two-Variable Functions and Their Graphs
Quelle	In: Educational Studies in Mathematics, 87 (2014) 1, S.67-85 (19 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-014-9548-0
Schlagwörter	Visual Aids; Abstract Reasoning; Learning Processes; Mathematics Instruction; Generalization; Graphs + Suchen Sie Ihr Suchwort? Anschauungsmaterial; Abstraktes Denken; Denken; Learning process; Lernprozess; Mathematics lessons; Mathematikunterricht; Grafische Darstellung
Abstract	This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of one-variable functions to graphs of two-variable functions. To evaluate the viability of this learning trajectory, we use data from two teaching experiments based on tasks intended to support development of the schemes in the HLT. We focus on the schemes that two students developed in these teaching experiments and discuss their relationship to the original HLT. We close by considering the role of covariational reasoning in generalization, consider other ways in which students might come to conceptualize graphs of two-variable functions, and discuss implications for instruction. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10