构建可识别错误概念的自适应学习框架，提升个性化教学效率
EDGE: A Theoretical Framework for Misconception-Aware Adaptive Learning
- 四阶段闭环：评估、诊断、生成、练习，融合认知诊断与智能题库
- 提出EdgeScore指标，证明其单调性与连续性，支持近优调度策略
- 生成反事实题目可加速纠正特定错误概念，理论有保障
我们提出EDGE，一种通用的、关注错误概念的自适应学习框架，包含四个阶段：评估（能力与状态估计）、诊断（错误概念后验推断）、生成（反事实题目合成）和练习（基于索引的检索调度）。该框架统一了心理测量学（IRT/贝叶斯状态空间模型）、认知诊断（从干扰项模式与反应时中发现错误概念）、对比题生成（最小扰动下破坏学习捷径但保持心理测量有效性）以及合理调度（休息随机博弈近似下的间隔检索）。我们形式化了一个复合就绪度指标EdgeScore，证明其单调性和Lipschitz连续性，并推导出在遗忘与学习增益假设较弱条件下近最优的索引策略。进一步建立了反事实题目能比传统方法更快降低目标错误概念后验概率的条件。本文聚焦理论分析与可实现伪代码；实证研究留待未来工作。
原文摘要 · Abstract (English)
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.
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