Math Majors' Visual Proofs in a Dynamic Environment: The Case of Limit of a Function and the ?-d Approach

Autor/in	Caglayan, Günhan
Titel	Math Majors' Visual Proofs in a Dynamic Environment: The Case of Limit of a Function and the ?-d Approach
Quelle	In: International Journal of Mathematical Education in Science and Technology, 46 (2015) 6, S.797-823 (27 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2015.1015465
Schlagwörter	Geometry; Computer Software; Technology Uses in Education; Teaching Methods; Undergraduate Study; College Mathematics; Visualization; Mathematical Concepts; Concept Formation; Mathematics Instruction; Calculus; Validity; Mathematical Logic; Problem Solving; Qualitative Research; Semi Structured Interviews; Equations (Mathematics) + Suchen Sie Ihr Suchwort? Geometrie; Technology enhanced learning; Technology aided learning; Technologieunterstütztes Lernen; Teaching method; Lehrmethode; Unterrichtsmethode; Grundstudium; Visualisation; Visualisierung; Concept learning; Begriffsbildung; Mathematics lessons; Mathematikunterricht; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Gültigkeit; Mathematical logics; Mathematische Logik; Problemlösen; Qualitative Forschung; Equations; Mathematics; Gleichungslehre
Abstract	Despite few limitations, GeoGebra as a dynamic geometry software stood as a powerful instrument in helping university math majors understand, explore, and gain experiences in visualizing the limits of functions and the ?-d formalism. During the process of visualizing a theorem, the order mattered in the sequence of constituents. Students made use of such rich constituents as finger-hand gestures and cursor gestures in an attempt to keep a record of visual demonstration in progress, while being aware of the interrelationships among these constituents and the transformational aspect of the visually proving process. Covariational reasoning along with interval mapping structures proved to be the key constituents in the visualizing and sense-making of a limit theorem using the delta-epsilon formalism. Pedagogical approaches and teaching strategies based on experimental mathematics--mindtool--consituential visual proofs trio would permit students to study, construct, and meaningfully connect the new knowledge to the previously mastered concepts and skills in a manner that would make sense for them. (As Provided).
Anmerkungen	Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01