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ERIC Number: EJ1035911
Record Type: Journal
Publication Date: 2014
Pages: 7
Abstractor: As Provided
Reference Count: N/A
ISBN: N/A
ISSN: ISSN-0228-0671
When Proofs Reflect More on Assumptions than Conclusions
Dawkins, Paul Christian
For the Learning of Mathematics, v34 n2 p17-23 2014
This paper demonstrates how questions of "provability" can help students engaged in reinvention of mathematical theory to understand the axiomatic game. While proof demonstrates how conclusions follow from assumptions, "provability" characterizes the dual relation that assumptions are "justified" when they afford proof of appropriate results. I provide examples of students' learning in teaching experiments connected to an advanced, undergraduate, neutral axiomatic geometry course. Students used "provability" relations to choose definitions, develop the notion of independence, and understand the relationship between axioms and theorems. I argue that provability promotes cognitive need for systematization, allaying concerns that geometric proof lacks illuminative value.
FLM Publishing Association. 382 Education South, University of Alberta, Edmonton, Alberta T6G 2G5, Canada. e-mail: flm2@ualberta.ca; Web site: http://flm.educ.ualberta.ca
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A