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ERIC Number: EJ1041567
Record Type: Journal
Publication Date: 2014-Nov
Pages: 27
Abstractor: As Provided
Reference Count: 44
ISBN: N/A
ISSN: ISSN-0013-1954
Analyzing the Teaching of Advanced Mathematics Courses via the Enacted Example Space
Fukawa-Connelly, Timothy Patrick; Newton, Charlene
Educational Studies in Mathematics, v87 n3 p323-349 Nov 2014
Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the concept of an example space (Mason & Watson, 2008) and variation theory (Runesson in "Scandinavian Journal of Educational Research" 50:397-410, 2006) to create a lens to study how examples are used for pedagogical purposes in undergraduate proof-based instruction. We adapted the construct of an example space and extended its application to the constructs of example neighborhood, methods of example construction, and the functions of examples. We explained how to use our new lens to analyze the collection of examples and non-examples that the students had access to. We then demonstrate our method by analyzing the collection of examples and non-examples of a mathematical group the professor of an abstract algebra class presented during lectures or assigned to students in problem sets or exams.
Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A