This paper presents several student models that are applicable for designing web-based CMI. Among them, four representative models are described and compared in terms of model fitting techniques: overlay model, bug-library model, ASPM and Bayesian network model. Considering uncertain factors associated with cognitive diagnosis and learning management, Bayesian network technique is adopted for designing a web-based program that manages prescriptive instruction with mathematical test items. In the prototype, students responses are tracked down and managed in such a way that Bayesian network model can provide adaptive instruction during learning sessions. The design framework illustrates how the necessary model construction and update is done with Netica software in a web environment.