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Argumentation and Proof: Continuity or distance? Bettina Pedemonte (Click name for speaker's biography) Today, only a few research works in mathematics deal with the relationship between argumentation and proof. In addition, the existing educational researches, analyzing this subject from a cognitive point of view, seem to be in disaccord. In this seminar, I propose my position in this debate. On the base of the contemporary linguistic theories, I put forward the hypothesis that proof is a particular argumentation and I propose Toulmin's model as a methodological tool to compare them. Through this model, the importance of a structural analysis between argumentation and proof is presented. Besides clear cases of continuity, the analysis shows the structural distance between the argumentation supporting the conjecture and its proof (from an abductive argumentation to a deductive proof, from an inductive argumentation to a mathematical inductive proof and so on) in the geometrical domain. On the contrary, this structural distance seems not to be present in solving algebraic problems. Algebraic proof is characterized by a strong deductive structure and abductive steps in the argumentation activity can be useful in linking the meaning of the letters used in the algebraic proof with numbers used in the argumentation. Co-sponsored by the Mathematics Education program of the Mathematics, Computer Science, and Statistics Dept. Please contact Mara Martinez (mara.martinez@mac.com) if you would like to meet with Dr. Pedemonte.
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