Alice slowly develops self-efficacy with writing proof frameworks, but her initial progress and sense of self-efficacy evaporates when she encounters unfamiliar concepts: However, it eventually returns

PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION

2017

San Diego, California

Alice slowly develops self-efficacy with writing proof frameworks, but her initial progress and sense of self-efficacy evaporates when she encounters unfamiliar concepts: However, it eventually returns

Page: 398

• Annie Selden
• John Selden
• Ahmed Benkhalti

We document Alice’s progression with proof-writing over two semesters. We analyzed videotapes of her one-on-one sessions working through the course notes for our inquiry-based transition-to-proof course. Our theoretical perspective informed our work and includes the view that proof construction is a sequence of mental and physical, actions. It also includes the use of proof frameworks as a means of getting started. Alice’s early reluctance to use proof frameworks, after an initial introduction to them, is documented, as well as her subsequent acceptance of and proficiency with them by the end of the real analysis section of the course notes, along with a sense of self-efficacy. However, during the second semester, upon first encountering semigroups, with which she had no prior experience, her proof writing deteriorated, as she coped with understanding the new concepts. But later, she began using proof frameworks again and regained a sense of self-efficacy.