PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Mathematicians’ ideas when formulating proof in real analysis
Page: 1348
This report presents some findings from a study that investigated the ideas professional mathematicians find useful in developing mathematical proofs in real analysis. This research sought to describe the ideas the mathematicians developed that they deemed useful in moving their arguments toward a final proof, the context surrounding the development of these ideas in terms of Dewey’s theory of inquiry, and the evolving structure of the personal argument utilizing Toulmin’s argumentation scheme. Three research mathematicians completed tasks in real analysis thinking aloud in interview and at-home settings and their work was captured via video and Livescribe technology. The results of open iterative coding as well as the application of Dewey’s and Toulmin’s frameworks were three categories of ideas that emerged through the mathematicians’ purposeful recognition of problems to be solved and their reflective and evaluative actions to solve them.