Understanding a student's problem-solving strategy can have a significant impact on effective math learning using Intelligent Tutoring Systems (ITSs) and Adaptive Instructional Systems (AISs). For instance, the ITS/AIS can better personalize itself to correct specific misconceptions that are indicated by incorrect strategies, specific problems can be designed to improve strategies and frustration can be minimized by adapting to a student's natural way of thinking rather than trying to fit a standard strategy for all. While it may be possible for human experts to identify strategies manually in classroom settings with sufficient student interaction, it is not possible to scale this up to big data. Therefore, we leverage advances in Machine Learning and AI methods to perform scalable strategy prediction that is also fair to students at all skill levels. Specifically, we develop an embedding called MVec where we learn a representation based on the mastery of students. We then cluster these embeddings with a non-parametric clustering method where we progressively learn clusters such that we group together instances that have approximately symmetrical strategies. The strategy prediction model is trained on instances sampled from these clusters. This ensures that we train the model over diverse strategies and also that strategies from a particular group do not bias the DNN model, thus allowing it to optimize its parameters over all groups. Using real world large-scale student interaction datasets from MATHia, we implement our approach using transformers and Node2Vec for learning the mastery embeddings and LSTMs for predicting strategies. We show that our approach can scale up to achieve high accuracy by training on a small sample of a large dataset and also has predictive equality, i.e., it can predict strategies equally well for learners at diverse skill levels.

翻译：理解学生的解题策略对于利用智能辅导系统（ITS）和自适应教学系统（AIS）实现高效数学学习具有重要影响。例如，ITS/AIS可以更好地针对错误策略所指示的具体误解进行个性化调整，设计特定问题以改进策略，并通过适应学生自然的思维方式而非试图采用统一标准策略来减少挫败感。虽然人类专家可能在课堂环境中通过充分的学生互动手动识别策略，但这无法扩展到大数据规模。因此，我们利用机器学习和人工智能方法的进展来实现可扩展的策略预测，同时确保该方法对所有技能水平的学生公平。具体而言，我们开发了一种名为MVec的嵌入表示，基于学生的能力水平学习表征。随后，我们采用非参数聚类方法对这些嵌入进行聚类，逐步学习聚类结果，使得同一聚类中的实例具有近似对称的策略。策略预测模型基于从这些聚类中采样的实例进行训练，这确保了模型在多样化策略上进行训练，同时避免特定群体的策略对深度神经网络（DNN）模型产生偏差，从而使其能够优化所有群体上的参数。利用来自MATHia的真实大规模学生交互数据集，我们使用Transformer和Node2Vec学习能力嵌入，并使用LSTM预测策略。实验表明，我们的方法能够通过对大数据集的小样本训练实现高精度可扩展性，同时具备预测公平性，即能够对不同技能水平的学习者同等准确地预测其策略。