PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Mathematicians’ proof repertoires: The case of proof by contradiction
Page: 699
This paper reports findings from task-based interviews with 6 mathematicians, conducted to document mathematicians’ in situ application of their orientations towards proof by contradiction; that is, their reflective dispositions towards proof by contradiction. However, analyses suggest that when engaging in situated analyses mathematicians’ behaviors are better characterized as proof repertoires: sets of action-based dispositions tacitly codified into relationally-determined proving routines and best thought of as replicable agent-tool interactions. This theoretical report introduces these constructs (i.e., orientations and repertoires), and illustrates the utility of the latter when interpreting mathematician’s ways of reasoning about proofs by contradiction in situ.