EDGE: A Theoretical Framework for Misconception-Aware Adaptive Learning

Abstract: We present EDGE, a general-purpose, misconception-aware adaptive learning framework composed of four stages: Evaluate (ability and state estimation), Diagnose (posterior infer-ence of misconceptions), Generate (counterfactual item synthesis), and Exercise (index-based retrieval scheduling). EDGE unifies psychometrics (IRT/Bayesian state space models), cog-nitive diagnostics (misconception discovery from distractor patterns and response latencies), contrastive item generation (minimal perturbations that invalidate learner shortcuts while pre-serving psychometric validity), and principled scheduling (a restless bandit approximation to spaced retrieval). We formalize a composite readiness metric, EdgeScore, prove its monotonicity and Lipschitz continuity, and derive an index policy that is near-optimal under mild assumptions on forgetting and learning gains. We further establish conditions under which counterfactual items provably reduce the posterior probability of a targeted misconception faster than standard practice. The paper focuses on theory and implementable pseudocode; empirical study is left to future work.