Transforming Maple into an Intelligent Model-Tracing Math Tutor

This article describes an intelligent, model-tracing system for tutoring expansion and factoring of algebraic expressions. The system is implemented as a set of procedures in a Maple document that tutor a breadth of 18 top-level mathematical skills (algebraic operations). Twelve (12) skills for expansion (monomial multiplication, monomial division and power of monomial, monomial-polynomial and polynomial-polynomial multiplication, parentheses elimination, collection of like terms, identities square of sum and difference, product of sum by difference, cube of sum and difference) and six (6) skills for factoring (common factor, identities square of sum and difference, product of sum by difference, quadratic form by sum and product, quadratic form by roots). These skills are further decomposed in simpler ones giving a deep domain expertise model of 68 primitive skills. The tutor has two novel features: (a) it exhibits intelligent task recognition by identifying all skills present in any expression through intelligent parsing, and (b) for each identified skill, the tutor traces all the sub-skills, a feature called deep model tracing. Furthermore, based on these features, the tutor achieves broad knowledge monitoring by recording student performance for all skills present in any expression.