PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
What are the Functions of Proof in Introduction to Proof Textbooks
Page: 1644
The role of proof in mathematics is multifaceted. de Villiers (1990) argues students should be exposed to at least five essential roles: verifying, explaining, systematizing, discovering, and communicating. We analyzed six commonly-used Introduction to Proof (ITP) textbooks for their treatment of the function of proof. We used a thematic analysis approach leveraging de Villiers categorizations. We found that verification was heavily emphasized, while discovery was almost excluded. However, the textbooks emphasized verifying, explaining, systematizing, discovering, and communication in ways that de Villiers did not. For example, de Villiers focused on the global view of systematizing, where the books were more likely to emphasize the local structure of proof.