ERIC Number: EJ1427943
Record Type: Journal
Publication Date: 2024-Apr
Pages: 23
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-2198-9745
EISSN: EISSN-2198-9753
Students' Thinking about the Structure of Constructive Existence Proofs
Kristen Vroom; Tenchita Alzaga Elizondo
International Journal of Research in Undergraduate Mathematics Education, v10 n1 p34-56 2024
Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural error while the second was a valid argument of the claim. We found that the students often considered the logical structures of the arguments when validating them. They provided reasons for their evaluations, including why they thought the structure of the first argument functioned to prove the claim and why they thought the structure of the second argument did not function to prove the claim. We discuss how these reasons provide insights into why constructive existence proofs might be challenging for students. We end the paper with implications for the teaching and learning of constructive existence proofs and their proof frameworks.
Descriptors: Mathematics Instruction, Validity, Mathematical Logic, Student Attitudes, Persuasive Discourse, Teaching Methods, Learning Processes, Error Patterns, Undergraduate Students, Problem Solving
Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://bibliotheek.ehb.be:2123/
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: 1916490