On the construction of set-based meanings for the truth of mathematical conditionals

Abstract

This paper presents a case study of Hugo’s construction of Euler diagrams to develop set-based meanings for the truth of mathematical conditionals. We use this case to set forth a framework of three stages of activity in students’ guided reinvention of mathematical logic: reading activity, connecting activity, and fluent activity. The framework also categorizes various forms of connecting activity by which students may reflect on their reading activity: connecting tasks, connecting representations, and connecting conditions for truth and falsehood (which we call meanings). We argue that coordinating such connections is necessary to justify logical equivalences, such as why contrapositive statements share truth-values. Through the case study, we document the representations and meanings that Hugo called upon to assign truth-values to conditionals. The framework should help clarify and advance future research on the teaching and learning of logic rooted in students’ mathematical activity.