Abstract: Creating an accurate model of a user's skills is necessary for intelligent tutoring systems. Without an accurate model, sample problems or tasks must be selected haphazardly by the tutor. Once an accurate model has been trained, the tutor can selectively focus on training essential or deficient skills. Prior work offers mechanisms for optimizing the training of a single skill or for multiple skills when individual tasks involve testing only a single skill at a time, but not for multiple skills when individual tasks can contain evidence for multiple skills. In this paper, we present a system that estimates user skill models for multiple skills by selecting tasks which maximize the information gain across the entire skill model. We compare our system's policy against several baselines and an optimal policy in both simulated and real tasks. Our system outperforms baselines and performs almost on par with the optimal policy.