Date
Publisher
arXiv
The evolution of technology and education is driving the emergence of
Intelligent & Autonomous Tutoring Systems (IATS), where objective and
domain-agnostic methods for determining question difficulty are essential.
Traditional human labeling is subjective, and existing NLP-based approaches
fail in symbolic domains like algebra. This study introduces the Approach of
Passive Measures among Educands (APME), a reinforcement learning-based
Multi-Armed Bandit (MAB) framework that estimates difficulty solely from solver
performance data -- marks obtained and time taken -- without requiring
linguistic features or expert labels. By leveraging the inverse coefficient of
variation as a risk-adjusted metric, the model provides an explainable and
scalable mechanism for adaptive assessment. Empirical validation was conducted
on three heterogeneous datasets. Across these diverse contexts, the model
achieved an average R2 of 0.9213 and an average RMSE of 0.0584, confirming its
robustness, accuracy, and adaptability to different educational levels and
assessment formats. Compared with baseline approaches-such as regression-based,
NLP-driven, and IRT models-the proposed framework consistently outperformed
alternatives, particularly in purely symbolic domains. The findings highlight
that (i) item heterogeneity strongly influences perceived difficulty, and (ii)
variance in solver outcomes is as critical as mean performance for adaptive
allocation. Pedagogically, the model aligns with Vygotskys Zone of Proximal
Development by identifying tasks that balance challenge and attainability,
supporting motivation while minimizing disengagement. This domain-agnostic,
self-supervised approach advances difficulty tagging in IATS and can be
extended beyond algebra wherever solver interaction data is available
Study at a glance
- Question: Can a system accurately estimate math question difficulty using only student scores and completion time?
- Setting and data: Three datasets of solver performance data, including marks obtained and time taken.
- Method: Compares a new difficulty-estimation algorithm against baseline models (reinforcement learning-based Multi-Armed Bandit framework).
Why it matters
Intelligent and autonomous tutoring systems need objective ways to determine question difficulty. However, traditional human labeling is subjective, and existing natural language processing approaches fail in symbolic domains like algebra.
Key findings
- In diverse math assessments, an AI tool accurately estimated question difficulty using student scores and completion times, without needing question text or human labels.
- The AI tool consistently outperformed traditional text-based and statistical models, especially on purely symbolic algebra questions.
- Differences among test questions strongly influenced perceived difficulty, while variation in student outcomes was as critical as average performance.
Summary drafted with AI from the paper’s abstract and may contain errors. See the full paper for details.
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Study design
