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ERIC Number: EJ892418
Record Type: Journal
Publication Date: 2010
Pages: 9
Abstractor: As Provided
Reference Count: 14
ISBN: N/A
ISSN: ISSN-1062-9017
Expert Mathematics' Approach to Understanding Definitions
Parameswaran, Revathy
Mathematics Educator, v20 n1 p43-51 2010
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.)
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
Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A