Mastery Guided Non-parametric Clustering to Scale-up Strategy Prediction

Predicting the strategy (sequence of concepts) that a student is likely to use in problem-solving helps Adaptive Instructional Systems (AISs) better adapt themselves to different types of learners based on their learning abilities. This can lead to a more dynamic, engaging, and personalized experience for students. To scale up training a prediction model (such as LSTMs) over large-scale education datasets, we develop a non-parametric approach to cluster symmetric instances in the data. Specifically, we learn a representation based on Node2Vec that encodes symmetries over mastery or skill level since, to solve a problem, it is natural that a student's strategy is likely to involve concepts in which they have gained mastery. Using this representation, we use DP-Means to group symmetric instances through a coarse-to-fine refinement of the clusters. We apply our model to learn strategies for Math learning from large-scale datasets from MATHia, a leading AIS for middle-school math learning. Our results illustrate that our approach can consistently achieve high accuracy using a small sample that is representative of the full dataset. Further, we show that this approach helps us learn strategies with high accuracy for students at different skill levels, i.e., leveraging symmetries improves fairness in the prediction model.