Bridging the Gap

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

Argumentation theory · Epistemology · Logical reasoning · Mathematics education · Computer Science · Education and Critical Thinking Development · Educational Assessment and Pedagogy · Mathematics · Mathematics Education and Teaching Techniques · Philosophy

• The Theory of Conceptual Fields

  Open Access•Gérard Vergnaud•Human Development•2009

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• Intuitionistic Logic As Epistemic Logic

  Open Access•Jaakko Hintikka•Synthese•2001

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