PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Mathematicians’ ideas when proving
Page: 1016
This study sought to describe the ideas professional mathematicians’ find useful in moving their arguments forward while constructing mathematical proof and the context surrounding the development of these ideas. Three research mathematicians completed real analysis tasks while thinking aloud in interview and independent settings recorded through Livescribe technology. Follow-up interviews were also conducted. Data were analyzed for perceived useful ideas and coded based on Dewey’s inquiry framework and Toulmin’s argumentation model. Toulmin argumentation diagrams were implemented to describe the evolution of the arguments, whereas Dewey’s inquiry framework helped to describe the context surrounding the development of the ideas. Preliminary findings show an active inquiry into forming a geometric understanding to develop warrants based on intuition and examples and then working to find backing that can be rendered into a formal argument.