Cognitive-Uncertainty Guided Knowledge Distillation for Accurate Classification of Student Misconceptions

TL;DR

This paper introduces a two-stage knowledge distillation framework guided by cognitive uncertainty to improve student misconception classification, achieving high accuracy with limited data and small models.

Contribution

It proposes a novel dual-layer marginal selection mechanism based on cognitive uncertainty for effective sample mining in knowledge distillation.

Findings

Achieved 0.9585 MAP@3 on MAP-Charting dataset with only 10.30% filtered samples.

Attained 84.38% accuracy on middle school algebra misconceptions with a 4B model.

Significantly outperformed state-of-the-art LLM and fine-tuned models.

Abstract

Accurately identifying student misconceptions is crucial for personalized education but faces three challenges: (1) data scarcity with long-tail distribution, where authentic student reasoning is difficult to synthesize; (2) fuzzy boundaries between error categories with high annotation noise; (3) deployment parado-large models overlook unconventional approaches due to pretraining bias and cannot be deployed on edge, while small models overfit to noise. Unlike traditional methods that increase diversity through large-scale data synthesis, we propose a two-stage knowledge distillation framework that mines high-value samples from existing data. The first stage performs standard distillation to transfer task capabilities. The second stage introduces a dual-layer marginal selection mechanism based on cognitive uncertainty, identifying four types of critical samples based on teacher model uncertainty and confidence differences. For different data subsets, we design difficulty-adaptive mechanism to balance hard/soft label contributions, enabling student models to inherit inter-class relationships from teacher soft labels while distinguishing ambiguous error types. Experiments show that with augmented training on only 10.30% of filtered samples, we achieve MAP@3 of 0.9585 (+17.8%) on the MAP-Charting dataset, and using only a 4B parameter model, we attain 84.38% accuracy on cross-topic tests of middle school algebra misconception benchmarks, significantly outperforming sota LLM (67.73%) and standard fine-tuned 72B models (81.25%). Our code is available at https://github.com/RoschildRui/acl2026_map.