Undergraduates' Example Use in Proof Construction: Purposes and Effectiveness

Autor/inn/en	Alcock, Lara; Weber, Keith
Titel	Undergraduates' Example Use in Proof Construction: Purposes and Effectiveness
Quelle	In: Investigations in Mathematics Learning, 3 (2010) 1, S.1-22 (22 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1947-7503
Schlagwörter	Mathematics Instruction; College Mathematics; Mathematical Logic; Validity; Undergraduate Students + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Gültigkeit
Abstract	In this paper, we present data from an exploratory study that aimed to investigate the ways in which, and the extent to which, undergraduates enrolled in a transition-to-proof course considered examples in their attempted proof constructions. We illustrate how some undergraduates can and do use examples for specific purposes while successfully constructing proofs, and that these purposes are consistent with those described by mathematicians. We then examine other cases in which students used example ineffectively. We note that in these cases, the purposes for which the students attempted to use examples are again appropriate, but the implementation of their strategies is inadequate in one of two specific ways. On this basis we identify points that should be borne in mind by a university teacher who wishes to teach students to use examples effectively in proof-based mathematics courses. (As Provided).
Anmerkungen	Research Council on Mathematics Learning. Web site: http://www.unlv.edu/RCML
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10