Abstract
Computer-assisted instruction (CAI) offers many opportunities for the application of artificial intelligence (AI) techniques. One advantage of doing AI research within the CAI paradigm is that the curriculum provides a ready framework for the evaluation of any AI model that we might propose. In this paper we describe the models of informal mathematical reasoning that we have employed in developing a CAI system, called EXCHECK, for teaching set theory and other mathematically based courses at Stanford University. Specificially, we discuss how the maturing of mathematical reasoning is accommodated in the EXCHECK model. Methodologically, we wish to conclude that there is a good deal to be learned by implementing entire college curricula within a CAI system, and solving whatever information processing problems are present within those curricula.
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