Intelligent tutoring systems adapt the curriculum to the needs of the individual student. Therefore, an accurate representation and prediction of student knowledge is essential. Bayesian Knowledge Tracing (BKT) is a popular approach for student modeling. The structure of BKT models, however, makes it impossible to represent the hierarchy and relationships between the different skills of a learning domain. Dynamic Bayesian networks (DBN) on the other hand are able to represent multiple skills jointly within one model. In this work, we suggest the use of DBNs for student modeling. We introduce a constrained optimization algorithm for parameter learning of such models. We extensively evaluate and interpret the prediction accuracy of our approach on five large-scale data sets of different learning domains such as mathematics, spelling learning, and physics. We furthermore provide comparisons to previous student modeling approaches and analyze the influence of the different student modeling techniques on instructional policies. We demonstrate that our approach outperforms previous techniques in prediction accuracy on unseen data across all learning domains and yields meaningful instructional policies.