Interaction Network Estimation: Predicting Problem-Solving Diversity in Interactive Environments

Intelligent tutoring systems and computer aided learning environments aimed at developing problem solving produce large amounts of transactional data which make it a challenge for both researchers and educators to understand how students work within the environment. Researchers have modeled student-tutor interactions using complex networks in order to automatically derive next step hints. However, there are no clear thresholds for the amount of student data required before the hints can be produced. We introduce a novel method of estimating the size of the unobserved interaction network from a sample by leveraging Good-Turing frequency estimation. We use this estimation to predict size, growth, and overlap of interaction networks using a small sample of student data. Our estimate is accurate in as few as 10–30 students and is a good predictor for the growth of the observed state space for the full network, as well as the subset of the network which is usable for automatic hint generation. These methods provide researchers with metrics to evaluate different state representations, student populations, and general applicability of interaction networks on new datasets.