PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Novice and expert evaluation of generic proofs
Page: 897
Mathematics education researchers do not yet agree on a shared characterization of proof, or generic proof; neither do mathematicians. Weber's "clustered concept" (2014) isolates six properties that, to personally varying degrees, comprise a valid proof. A generic proof consists of a sufficiently complicated example that illustrates the underlying structures of a generalized argument. Such arguments can be utilized to support student learning of proof. We examine students' and experts' perceptions about proof, explicitly generic proofs. Our findings support Weber's "clustered concept," and extend its utility by showing commensurate properties are also valued by students. In short, we observed that all participants in our study valued an array of psychological and social factors while determining a proof's validity. In addition, our findings suggest that experts do not consider generic arguments to be a proof.