Virtual Mathematical Inquiry: Problem Solving at the Gestural — Symbolic Interface of Remote-Control Embodied-Interaction Design

Abstract

What, if any, are unique affordances of embodied-interaction (EI) design for mathematics learning? How, in turn, might engineering and testing such design aid us in building theory of learning? We draw on media studies to argue that activities situated at the hybrid intersection of two media, for example physical-virtual interfaces, enable both learners and their researchers to objectify important notions. We evoke cultural-historical psychology theory, which implicates gesture as the ontogenesis of inscription, to interpret instructional EI as offering analogous enactive-semiotic tension and resolution. We support our view with selected empirical data from a design-based research project investigating the emergence of mathematical concepts from mediated engagement in EI activity. Specifically, we present, analyze, and juxtapose two case studies respectively illustrating student success or failure to grope toward a conceptual system (proportions) embedded in a technological system (EI).