Argumentation and Proof in the Mathematics Classroom

Abstract

Studying the relationships between argumentation and proof could help teachers and students deal with the tension between the process by which a student develops a proof and the requirements the teacher places on the final product. This tension results from the need for students to experience freedom and flexibility during an initial exploratory phase whilst ultimately producing a proof that conforms to specific cultural constraints involving both logical and communicative norms. The chapter explores the issue of whether the activity of developing proofs under a teacher’s guidance can be used to introduce students to meta-mathematical concepts such as proof, definition, theorem, axiom, and theory. It also tries to clarify the perspectives underlying its specific proposals, to give insight into their richness, and to provide a basis for further research and innovation. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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