Mathematical Modeling of Embodied Cognition and Personalized Learning in Interactive Virtual Reality: A Nonlinear Systems Approach

Abstract

This study develops a mathematical model of embodied cognition integrated with personalized learning within an interactive Virtual Reality (VR) environment, employing nonlinear systems theory to optimize educational outcomes.The study mathematically formulates the interactions between learners' cognitive states, bodily actions, and environmental inputs by applying state-space models and multi-modal data analysis.The framework incorporates real-time affective feedback and dynamic adjustment mechanisms, improving mental performance and reducing cognitive load.A randomized controlled trial validates the model, demonstrating significant enhancements in learning satisfaction and knowledge retention.This research provides a novel quantitative basis for integrating nonlinear mathematical methods into the design and optimization of personalized learning systems in VR.