DT Tutor uses a decision-theoretic approach to select tutorial actions for coached problem solving that are optimal given the tutor’s beliefs and objectives. It employs a model of learning to predict the possible outcomes of each action, weighs the utility of each outcome by the tutor’s belief that it will occur, and selects the action with highest expected utility. For each tutor and student action, an updated student model is added to a dynamic decision network to reflect the changing student state. The tutor considers multiple objectives, including the student’s problem-related knowledge, focus of attention, independence, and morale, as well as action relevance and dialog coherence. Evaluation in a calculus domain shows that DT Tutor can select rational and interesting tutorial actions for real-world-sized problems in satisfactory response time. The tutor does not yet have a suitable user interface, so it has not been evaluated with human students.