Investigating the Relationship between Argumentation and Proof from a Representational Perspective

The purpose of this qualitative study was to analyze the relationship between argumentation and proof in terms of verbal, visual, and algebraic representations of mathematical concepts. We conducted task-based interviews based on geometric locus problems with six undergraduate mathematics teachers while they were working in pairs. We identified the mathematical arguments that the pairs produced in argumentation and proving by using Toulmin’s model. We examined the role of representations in the relationship between these two processes by performing an analysis considering the referential system and the structure dimensions. Data analysis revealed that students could transform the abductive and inductive arguments to deductive arguments in the process of proving if they could produce and utilize algebraic representations in the warrants and backings by relating visual and verbal representations.