Discovery of Student Strategies using Hidden Markov Model Clustering

Students interacting with educational software generate data on their use of software assistance and on the correctness of their answers. This data comes in the form of a time series, with each interaction as a separate data point. This data poses a number of unique issues. In educational research, results should be interpretable by domain experts, which strongly biases learning towards simpler models. Educational data also has a temporal dimension that is generally not fully utilized. Finally, when educational data is analyzed using machine learning techniques, the algorithm is generally off-the-shelf with little consideration for the unique properties of educational data. We focus on the problem of analyzing student interactions with software tutors. Our objective is to discover different strategies that students employ and to use those strategies to predict learning outcomes. For this, we utilize hidden Markov model (HMM) clustering. Unlike some other approaches, HMMs incorporate the time dimension into the model. By learning many HMMs rather than just one, the result will include smaller, more interpretable models. Finally, as part of this process, we can examine different model selection criteria with respect to the models predictions of student learning outcomes. This allows further insight into the properties of model selection criteria on educational data sets, beyond the usual cross-validation or test analysis. We discover that the algorithm is effective across multiple measures and that the adjusted-R is an effective model selection metric.