Rule-based expert systems to support step-by-step guidance in algebraic problem solving: The case of the tutor PAT2Math

In order for an Intelligent Tutoring System (ITS) to correct students’ exercises, it must know how to solve the same type of problems that students do and the related knowledge components. It can, thereby, compare the desirable solution with the student’s answer. This task can be accomplished by an expert system. However, it has some drawbacks, such as an exponential complexity time, which impairs the desirable real-time response. In this paper we describe the expert system (ES) module of an Algebra ITS, called PAT2Math. The ES is responsible for correcting student steps and modeling student knowledge components during equations problem solving. Another important function of this module is to demonstrate to students how to solve a problem. In this paper, we focus mainly on the implementation of this module as a rule-based expert system. We also describe how we reduced the complexity of this module from O(n^d) to O(d), where n is the number of rules in the knowledge base, by implementing some meta-rules that aim at inferring the operations students applied in order to produce a step. We evaluated our approach through a user study with forty-three seventh grade students. The students who interacted with our tool showed statistically higher scores on equation solving tests, after solving algebra exercises with PAT2Math during an approximately two-hour session, than students who solved the same exercises using only paper and pencil.