ERIC Number: EJ1417529
Record Type: Journal
Publication Date: 2024
Pages: 30
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0020-739X
EISSN: EISSN-1464-5211
Available Date: N/A
Experienced Provers' Uses of Contexts While Engaging in Combinatorial Proof of Binomial Identities
Sarah Erickson; Elise Lockwood
International Journal of Mathematical Education in Science and Technology, v55 n4 p946-975 2024
Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely the kinds of contexts that experienced provers used to establish combinatorial proofs of binomial identities. Our findings show that overall, our participants used a variety of contexts in their work; we also demonstrate ways in which previous experiences influenced the contexts they chose, and we offer some instances in which features of a context supported their combinatorial proof production. We offer some theoretical implications of our work, and we conclude with a discussion of limitations and avenues for future work.
Descriptors: Mathematics Instruction, Validity, Mathematical Logic, Advanced Courses, Undergraduate Students, Problem Solving
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: 1650943; 1920538
Author Affiliations: N/A