Student Development in Logical Reasoning: Results of an Intervention Guiding Students Through Different Modes of Visual and Formal Representation

Abstract Due to growing interest in twenty-first-century skills, and critical thinking as a key element, logical reasoning is gaining increasing attention mathematics curricula secondary education. In this study, we report on an analysis of video recordings student discussions one class seven students who were taught with specially designed course for non-science (12th graders). During the 10 lessons, worked diversity tasks: both closed tasks where all premises provided everyday implicit premises. The structure focused linking different modes representation (enactive, iconic, symbolic), based model concreteness fading (Fyfe et al., 2014). Results show that easily link concrete situations certain iconic referents, such formal (letter) symbols, but need more practice others, Venn Euler diagrams. We also symbolic mode, i.e. interpretation general abstract models, not strong. This might be due limited time spent further practice. However, transition from via may take step back visual representation, which shows working links useful students. Overall, conclude can support education reasoning. One recommendation devote sufficient establishing between types referents representations.