One Approach to Mathematical E-Learning Systems Content Generation
摘要
Most existing e-learning systems have tools for creating an individual learning trajectory. These tools select the next task or test using student performance and task difficulty levels as initial data. This article attempts to complement such technologies. Specifically, the goal is to learn how to generate sets of computational questions for exam papers. Unlike individual tests, less formalized concepts should be used to characterize such sets. The exam paper is expected to be balanced in complexity and diversified in content. No models exist for such concepts, but appropriate data sets enable their creation. We used a set of exam papers from the university course on complex analysis prepared for us by experts. They composed exam papers utilizing a set of computational questions labeled with a topic, difficulty level, and set of competencies. The new methodology should leverage expert knowledge embedded in the exam papers. We propose and compare two generation methods. The first one is based on the classical probabilistic model and uses only frequency characteristics. The second one is based on generative-adversarial neural networks. The experimental results show that generative models are applicable for exam papers composing even in the presence of issues of poor convergence and partial mode collapse.