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<p>Automating mathematical proficiency assessment remains challenging due to the lack of adaptive, psychometrically consistent mechanisms in both traditional and machine-learning approaches. Rule-based and supervised models evaluate performance without modeling conceptual dependencies or accounting for varying difficulty across curricula. This study introduces an adaptive assessment framework that integrates Graph Neural Networks (GNNs) and Deep Q-Networks (DQNs) to infer mathematical proficiency and dynamically optimize question selection. The GNN captures structural relations between mathematical concepts, while the reinforcement learning agent adjusts the difficulty trajectory in real time. A hybrid calibration process inspired by Item Response Theory ensures that difficulty levels are comparable across heterogeneous datasets. Experimental results show that the model achieves high sensitivity, with recall between 85 and 90% and F1-scores up to 90.8%, outperforming DNN and logistic regression baselines. These results highlight the system’s capacity to detect learning difficulties, maintain scalability under high concurrency, and provide pedagogically meaningful feedback. The integration of graph-based knowledge representation, reinforcement learning, and psychometric calibration establishes a robust foundation for scalable, explainable, and adaptive assessment, particularly within mathematics and other domains characterized by well-defined conceptual structures.</p>

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Adaptive mathematical competency assessment using graph neural networks and reinforcement learning

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月11日

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  • Rommel Gutierrez,
  • Alexandra Maldonado,
  • William Villegas-Ch

摘要

Automating mathematical proficiency assessment remains challenging due to the lack of adaptive, psychometrically consistent mechanisms in both traditional and machine-learning approaches. Rule-based and supervised models evaluate performance without modeling conceptual dependencies or accounting for varying difficulty across curricula. This study introduces an adaptive assessment framework that integrates Graph Neural Networks (GNNs) and Deep Q-Networks (DQNs) to infer mathematical proficiency and dynamically optimize question selection. The GNN captures structural relations between mathematical concepts, while the reinforcement learning agent adjusts the difficulty trajectory in real time. A hybrid calibration process inspired by Item Response Theory ensures that difficulty levels are comparable across heterogeneous datasets. Experimental results show that the model achieves high sensitivity, with recall between 85 and 90% and F1-scores up to 90.8%, outperforming DNN and logistic regression baselines. These results highlight the system’s capacity to detect learning difficulties, maintain scalability under high concurrency, and provide pedagogically meaningful feedback. The integration of graph-based knowledge representation, reinforcement learning, and psychometric calibration establishes a robust foundation for scalable, explainable, and adaptive assessment, particularly within mathematics and other domains characterized by well-defined conceptual structures.