Mental Models and Deductive Inferences in Mathematics Education: An Exploratory Study for Didactic Purposes

Abstract

This article reports an exploratory study about conditional deductive inference in mathematics classes at the college level. The target was college students that had finished high school and were taking a leveling introductory course in the National University of General Sarmiento (UNGS).  Course topics were a high school review. We focused here on deductive conditional reasoning because in math classes a conclusion or answer is required for the student when a mathematical property or definition is applied and generally this conclusion is derived deductively.  We aimed to have guidelines for developing specific activities and situations that can promote deductive inference in mathematics classes, from a semantic point of view. To get this, we proposed to study students' responses to simple situations of deductive inference with mathematical content.  We take into account the Mental Models Theory for designing the test and interpreting the responses (Johnson-Laird and Byrne, 1991, Johnson-Laird, Byrne and Shaeken, 1992, Johnson-Laird and Byrne, 2002, Johnson-Laird, 2013, Johnson-Laird and Khemlani, 2013). The Mental Model Theory (hereinafter MMT) introduces a semantic and practical perspective of reasoning. It is a cognitive theory about human processes of deduction that point to the semantic procedure of searching for interpretations of the premises to conclude a valid statement, in the context of the information given by the premises.