From Classroom Observation to Computational Inference: A Cross-Disciplinary Cognitive Diagnosis Method Based on Variation Theory

Adaptive learning systems typically diagnose student knowledge within individual subjects, treating mathematics and physics as independent diagnostic targets. This subject-silo approach suffers from two fundamental limitations: data sparsity in low-engagement environments, and inability to capture domain-general cognitive traits such as carelessness propensity or guessing tendency. We propose a cross-disciplinary cognitive diagnosis framework grounded in Variation Theory, which posits that learning occurs through the discernment of critical features across varying contexts. Our framework operationalizes Variation Theory’s three modes—separation, generalization, and fusion—into a three-layer cognitive state machine (Standard, Reverse, Adaptive), and defines a quantitative cross-disciplinary cognitive distance metric D_cross. Through defect-injection simulation with 21 virtual students across four subjects (mathematics, physics, chemistry, biology) and 6,732 answer events, we demonstrate that: (1) BKT-estimated mastery values correctly separate subject-specific knowledge while maintaining domain-general cognitive parameter consistency; (2) students with identical overall scores exhibit fundamentally different cognitive profiles, distinguishable only through the three-layer state machine; and (3) cross-disciplinary parameter fusion enables cold-start transfer in sparse-data scenarios. We discuss the implications for adaptive learning deployments and the broader significance of computationally operationalizing qualitative educational theory.