Data Driven Prediction for the Difficulty of Mathematical Items
Tong Wei, Wang Fei, Liu Qi, Chen Enhong
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The construction of item banking system is an important guarantee for the reform and development of educational examination, and meanwhile, is also an essential means to promote the modernization of examination. In such a system, item difficulty is one of the most important parameters, which has a direct influence on item designing, test paper organization, result report and even the fairness guarantee. Unfortunately, due to the unique education background and test characteristics in China, it is difficult to evaluate item difficulty through pre-test organization like some foreign countries. Thus, traditional efforts usually refer to the manual evaluation by expertise (e.g., experienced teachers). However, this way tends to be laborious, time-consuming and subjective in some way. Therefore, it is of great value to automatically judge the difficulty of items by information technology. Along this line, in this paper, we aim to propose a data-driven solution to predict the item difficulty in mathematics leveraged by the historical test logs and the corresponding item materials. Specifically, we propose a C-MIDP model and a R-MIDP model, which are based on CNN and RNN respectively, and further a hybrid H-MIDP model combined with both C-MIDP and R-MIDP. In the models, we directly learn item sematic representation from its text and train its difficulty with the statistic score rates among tests, where the whole modeling do not need any expertise, such as knowledge labeling. Then, we adopt a context-dependent training strategy considering the incomparability between different groups. Finally, with the trained models, we can predict each item difficulty only with its text input. Extensive experiments on a real-world dataset demonstrate that the proposed models perform very well.