MATHESIS: An Intelligent Web-Based Algebra Tutoring School
This article describes an intelligent, integrated, web-based school for tutoring expansion and factoring of algebraic expressions. It provides full support for the management of the usual teaching tasks in a traditional school: Student and teacher registration, creation and management of classes and test papers, individualized assignment of exercises, intelligent step by step guidance in solving exercises, student interaction recording, skill mastery statistics and student assessment. The intelligence of the system lies in its Algebra Tutor, a model-tracing tutor developed within the MATHESIS project, that teaches a breadth of 16 top-level math skills (algebraic operations): monomial multiplication, division and power, monomial-polynomial and polynomial-polynomial multiplication, parentheses elimination, collect like terms, identities (square of sum and difference, product of sum by difference, cube of sum and difference), factoring (common factor, term grouping, identities, quadratic form). These skills are further decomposed in simpler ones giving a deep domain expertise model of 104 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 we call 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. Forty teachers who evaluated the system in a 3-hours workshop appreciated the fine-grained step-by-step guidance of the student, the equally fine grained student model created by the tutor and its ability to tutor any exercise that contains the aforementioned math skills. The system was also used in a real junior high school classroom with 20 students for three months. Evaluation of the students’ performance in the domain of factoring gave positive learning results.