Coming to Understand the Formal Definition of Limit: Insights Gained from Engaging Students in Reinvention

Autor/inn/en	Swinyard, Craig; Larsen, Sean
Titel	Coming to Understand the Formal Definition of Limit: Insights Gained from Engaging Students in Reinvention
Quelle	In: Journal for Research in Mathematics Education, 43 (2012) 4, S.465-493 (29 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0021-8251
Schlagwörter	Mathematics Education; Learner Engagement; Models; Experiments; Teaching Methods; Calculus; College Mathematics; Mathematics Instruction; Higher Education; Intervals; Cognitive Processes; Cognitive Development; Logical Thinking + Suchen Sie Ihr Suchwort? Mathematische Bildung; Analogiemodell; Erprobung; Teaching method; Lehrmethode; Unterrichtsmethode; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Hochschulbildung; Hochschulsystem; Hochschulwesen; Cognitive process; Kognitiver Prozess; Kognitive Entwicklung
Abstract	The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding a definition of limit. The 1st construct relates to the need for students to move away from their tendency to attend first to the input variable of the function. The 2nd construct relates to the need for students to overcome the practical impossibility of completing an infinite process. Together, these 2 theoretical constructs build on Cottrill et al.'s work, resulting in a revised conceptual framework of limit. (Contains 7 figures, 3 tables and 13 footnotes.) (As Provided).
Anmerkungen	National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10