A Case Study of Undergraduates' Proving Behaviors and Uses of Visual Representations in Identification of Key Ideas in Topology

Autor/inn/en	Gallagher, Keith; Infante, Nicole Engelke
Titel	A Case Study of Undergraduates' Proving Behaviors and Uses of Visual Representations in Identification of Key Ideas in Topology
Quelle	In: International Journal of Research in Undergraduate Mathematics Education, 8 (2022) 1, S.176-210 (35 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Gallagher, Keith) ORCID (Infante, Nicole Engelke)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2198-9745
DOI	10.1007/s40753-021-00149-6
Schlagwörter	Undergraduate Students; Mathematical Logic; Problem Solving; Visual Aids; Student Behavior; Topology; Visualization + Suchen Sie Ihr Suchwort? Mathematical logics; Mathematische Logik; Problemlösen; Anschauungsmaterial; Student behaviour; Schülerverhalten; Topologie; Visualisation; Visualisierung
Abstract	Visual representations, such as diagrams, are known to be valuable tools in problem solving and proof construction. However, previous studies have shown that simply having access to a diagram is not sufficient to improve students' performance on mathematical tasks. Rather, students must actively extract information about the problem scenario from their diagrams for them to be useful. Furthermore, several studies have described the behaviors of mathematicians and students when solving problems and writing proofs, but few have discussed students' behaviors in the context of proof writing in introductory point-set topology. We present a case study of an undergraduate, Stacey, enrolled in a general topology course. Throughout a semester, we presented Stacey with several proof-related tasks and examined how and why Stacey used diagrams when working on these tasks. Based on our analysis, we concluded that Stacey's diagram creation and subsequent use during the construction of a given proof was an effort to identify the key idea of the proof. We describe Stacey's overall proving behaviors through the lens of a problem-solving framework and present Stacey's use of diagrams as an aid to discovering the key ideas of proofs in topology. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01