  Recent advances in artificial intelligence for education leverage generative
large language models, including using them to predict open-ended student
responses rather than their correctness only. However, the black-box nature of
these models limits the interpretability of the learned student knowledge
representations. In this paper, we conduct a first exploration into
interpreting latent student knowledge representations by presenting InfoOIRT,
an Information regularized Open-ended Item Response Theory model, which
encourages the latent student knowledge states to be interpretable while being
able to generate student-written code for open-ended programming questions.
InfoOIRT maximizes the mutual information between a fixed subset of latent
knowledge states enforced with simple prior distributions and generated student
code, which encourages the model to learn disentangled representations of
salient syntactic and semantic code features including syntactic styles,
mastery of programming skills, and code structures. Through experiments on a
real-world programming education dataset, we show that InfoOIRT can both
accurately generate student code and lead to interpretable student knowledge
representations.
