Who's There? A Study of Students' Reasoning about a Proof of Existence

Autor/in	Brown, Stacy A.
Titel	Who's There? A Study of Students' Reasoning about a Proof of Existence
Quelle	In: International Journal of Research in Undergraduate Mathematics Education, 3 (2017) 3, S.466-495 (30 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2198-9745
DOI	10.1007/s40753-017-0053-6
Schlagwörter	Mathematical Logic; Abstract Reasoning; Logical Thinking; Concept Formation; Students + Suchen Sie Ihr Suchwort? Mathematical logics; Mathematische Logik; Abstraktes Denken; Denken; Concept learning; Begriffsbildung; Student; Schüler; Schülerin; Studentin
Abstract	Drawing on prior research on indirect proof, this paper reports on a series of exploratory studies that examine the extent to which findings on students' ways of reasoning about contradiction and contraposition characterize students' views of indirect existence proofs. Specifically, Study 1 documents students' comparative selections and selection rationales when asked to choose the "most convincing" proof, given a constructive and nonconstructive existence proof. Study 2 further examines findings from Study 1 by documenting novices' levels of conviction and interpretations of a nonconstructive existence proof. Findings show that when presented with a nonconstructive proof, students tended to not only find the proof convincing but also interpreted the proof constructively. Moreover, the data indicate students who exhibit an awareness of the nonconstructive structure were divided in terms of their views of which form--constructive or non-constructive--was the most convincing. The discussion considers students' reactions to the disjunctive structure of nonconstructive existence proofs and use of pragmatic and theoretical modes of thought. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01