Bridging the Gap: An Epistemic Logical Model for Analysing Students’ Argumentation and Proof in Mathematics Education Research

Abstract

In this theoretical paper, an epistemic logical model for analysis of students’ argumentation and proof processes is presented. The model is conceived as a methodological tool addressed to the researcher in mathematics education that aims to shed light on the relations between argumentation and proof, highlighting the continuities and discontinuities within and between them. It reconciles the epistemic logic approach, which takes into account the exploratory phases of a statement, linked to argumentative processes, and the deductive logic approach, which takes into account the phases linked to proof in a classical sense. The model is based on Vergnaud’s concepts- and theorems-in-action, on Duval’s distinction between the epistemic and logical value of verbalised propositions, and on elements of Oostra’s intuitionistic existential graphs, a kind of graphical topological logic rooted in Peircean thought, adapted to mathematics education research by considering also shifts in the classical existential graphs. After exposing the theoretical grounding the model is based on, some examples taken from the literature are examined to exemplify how it works.

Keywords

• logical tools and methods of inquiry
• epistemic logic
• intuitionistic logic
• classical logic
• argumentation and proof
• continuity and discontinuity between argumentation and proof