What Makes Actions Matter in Virtual Reality? Examining the Effects of Conceptual Congruence and Sensorimotor Engagement on Geometric Reasoning

Abstract

While virtual reality adoption accelerates in mathematics education, we lack an understanding of what makes physical actions in VR environments effective for learning. This dissertation examines how body movements influence geometric reasoning through two complementary studies grounded in Grounded and Embodied Mathematical Cognition theory. According to the action-cognition transduction hypothesis, directed actions drive cognitive states toward valid geometric reasoning by activating spatial-motoric simulations that reveal invariant mathematical properties. Study 1 synthesizes nine randomized controlled experiments (N=774) using integrative data analysis to establish baseline mechanisms. Employing Item Response Theory for measure harmonization, the study uses structural equation modeling to test pathways from task-relevant/irrelevant actions through cognitive mechanisms to reasoning outcomes. Preliminary analysis reveals dual pathways: imagery formation (β*=.392) and sensori-motor simulation (β*=.159), with task-relevant actions showing positive indirect effects while task-irrelevant actions impair performance. Study 2 employs a 2×2 between-subjects experimental design (N=200), manipulating conceptual congruence (alignment between virtual actions and mathematical properties) and sensorimotor engagement (active manipulation versus passive observation) in VR. Participants interact with virtual geometric shapes through hand-tracking in CurioXR, with multimodal data capturing verbal proofs (intuition, insight, generality, logic, operationality), and gesture production (dynamic/non-dynamic). This work advances embodied learning theory for immersive environments and methodological approaches for cross-study data harmonization, while providing evidence-based design principles specifying when and how virtual actions enhance mathematical learning.