Expert Mathematics' Approach to Understanding Definitions

Autor/in	Parameswaran, Revathy
Titel	Expert Mathematics' Approach to Understanding Definitions
Quelle	In: Mathematics Educator, 20 (2010) 1, S.43-51 (9 Seiten) PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1062-9017
Schlagwörter	Definitions; Mathematical Concepts; Mathematics Instruction; Cognitive Processes; Research; Mathematical Logic; Validity; Teaching Methods; Questionnaires; Concept Formation; Comprehension; Professional Personnel + Suchen Sie Ihr Suchwort? Begriffsbestimmung; Mathematics lessons; Mathematikunterricht; Cognitive process; Kognitiver Prozess; Forschung; Mathematical logics; Mathematische Logik; Gültigkeit; Teaching method; Lehrmethode; Unterrichtsmethode; Fragebogen; Concept learning; Begriffsbildung; Verstehen; Verständnis; Personalbestand
Abstract	In this article I report on a study of the cognitive tools that research mathematicians employ when developing deep understandings of abstract mathematical definitions. I arrived at several conclusions about this process: Examples play a predominant role in understanding definitions. Equivalent reformulations of definitions enrich understanding. Evoked conflicts and their resolutions result in improved understanding. The primary role of definitions in mathematics is in proving theorems. And there are several stages in developing understandings of mathematical definitions (Manin, 2007; Tall & Vinner, 1981; Thurston, 1994). I also include some suggestions for pedagogy that are found in the data. (Contains 1 figure.) (As Provided).
Anmerkungen	Mathematics Education Student Association, University of Georgia. 105 Aderhold Hall, Athens, GA 30602. Tel: 706-542-4194; Fax: 706-542-4551; e-mail: mesaprez@gmail.com; Web site: http://math.coe.uga.edu/Mesa/MESA.html
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10