Proving in Geometry As an Embodied Process: the Case of Proofs Without Words

We investigate proving activities from a monistic embodied perspective, namely the functional dynamic systems (FDS) approach. Using proofs without words, we focus on proving activities that can be conceptualized as identifying and filling gaps. Using a microethnographic methodology enhanced by eye-tracking, we investigate sensory-motor processes in proving and theorize their roles. Findings reveal five theoretical roles of sensory-motor processes: Exploring the environment, Appropriating artifacts, Connecting artifacts, Blocking out the environment for enrichment, and Expanding the environment. Through nonlinear iterative activations of sensory-motor processes serving these roles, a student forms a coherent FDS that constitutes the proof.