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In this paper we consider two questions related to student modeling in an intelligent tutoring system: 1) What kind of student model should we build when we design a new system; 2) Should we divide the student model into different components depending on the information involved. We consider these two questions in the context of a conversational intelligent tutoring system, CIRCSIM-Tutor. We first analyze the range of decisions that the system needs to make and define the information needed to support these decisions. We then describe four distinct models that provide different aspects of this information, taking into consideration the nature of the domain and the constraints provided by the tutoring system. At the end of the paper we briefly discuss our experiments with enhancing the student model in CIRCSIM-Tutor and some general problems regarding building and evaluating different student models.