Computer Science Department
School of Computer Science, Carnegie Mellon University


Intelligent Tutoring Systems have Forgotten the Tutor:
Adding a Cognitive Model of Human Tutors

Neil T. Heffernan III

March 2001

Ph.D. Thesis

Keywords: Model-tracing, cognitive model, intelligent tutoring system, artificial intelligence, tutoring, mathematical education

This dissertation makes a contribution to 1) the cognitive science of algebra learning as well as to 2) intelligent tutoring systems architectures. I present a new intelligent tutoring system for the domain of writing expressions for algebra "story" problems. This system is novel, because it is the first intelligent algebra tutor that combines a cognitive model of the domain with a rich pedagogical model of dialog-based tutoring. The algebra model is novel because contrary to prior work that has emphasized the difficulties of using variables, as well as the difficulties of comprehending the text of a word problem, I establish the empirical result that articulating a complete expression (e.g., 800-40*3) is a major determinant of problem difficulty. The tutorial model is also novel because it is based on the observation of an experienced human tutor and captures the rich tutorial strategies specific to the domain of symbolization. The resulting system, called Ms. Lindquist, has been demonstrated to improve student learning. Over 350 students have used the system available at

187 pages

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