Scalable and Equitable Math Problem Solving Strategy Prediction in Big
  Educational Data
Anup Shakya Vasile Rus Deepak Venugopal
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.