Logic and Computation in MATHPERT: An Expert System for Learning Mathematics

MATHPERT (as in “Math Expert”) is an expert system in mathematics explicitly designed to support the learning of algebra, trigonometry, and first semester calculus. This paper gives an overview of the design of MATHPERT and goes into detail about some connections it has with automated theorem proving. These connections arise at the borderline between logic and computation, which is to be found when computational “operators” have logical side conditions that must be satisfied before they are applicable. The paper also explains how MATHPERT maintains and uses an internal model of its user to produce individually tailored explanations, and how it dynamically generates individualized and helpful error messages by comparing user errors to its own internal solution of the problem.How MATHPERT is to be used in education, and the implications of learning environments like MATHPERT for curriculum and pedagogy, are discussed in Beeson [1989a, 1989d, 1989e]. The details of the design of MATHPERT are discussed in Beeson [1989b].