EDGE: A Theoretical Framework for Misconception-Aware Adaptive Learning
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913982872289280 |
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| author | Verma, Ananda Prakash |
| author_facet | Verma, Ananda Prakash |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_07224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | EDGE: A Theoretical Framework for Misconception-Aware Adaptive Learning Verma, Ananda Prakash Machine Learning Artificial Intelligence 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. |
| title | EDGE: A Theoretical Framework for Misconception-Aware Adaptive Learning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2508.07224 |