Component-Wise Reasoning as a Mechanism of Sense-Making in Real Analysis

Autor/in	Reed, Zackery
Titel	Component-Wise Reasoning as a Mechanism of Sense-Making in Real Analysis
Quelle	In: International Journal of Research in Undergraduate Mathematics Education, 9 (2023) 2, S.217-242 (26 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Reed, Zackery)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2198-9745
DOI	10.1007/s40753-022-00198-5
Schlagwörter	Mathematical Concepts; Undergraduate Students; Mathematics Instruction; Mathematical Logic; Thinking Skills; Mathematics Education; College Mathematics + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Denkfähigkeit; Mathematische Bildung
Abstract	Undergraduate concepts are often first introduced in a single-dimensional setting and then extended to multiple dimensions. For instance, many undergraduate real analysis students will first learn of the metric topology on [set of real numbers] before being exposed to more general metric spaces. I conducted a paired teaching experiment (Steffe & Thompson, 2000) with introductory real analysis students that explored their learning of the general metric function. In this experiment, I was able to observe the students' mathematical activity as they made sense of analytic ideas in increasingly general settings. I present a construct, called component-wise reasoning, that offers an explanatory mechanism for the ways that the students leveraged their understandings of phenomena on [set of real numbers] to construct new schemes for similar phenomena in other metric spaces. I discuss how component-wise reasoning can offer explanatory power for students' sense-making in abstract spaces across the undergraduate curricula. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01