Algebra Subsystem for an Intelligent Tutoring System
Joel A. Shapiro · 2002
To help a student in an introductory physics course do quantitative homework problems, an intelligent tutoring system must determine information of an algebraic nature. This paper describes a subsystem which resolves such questions for Andes2. The capabilities of the subsystem would be useful for any ITS which deals with problems involving complex systems of equations. This subsystem is capable of 1) solving the systems of equations at the level of introductory physics problems, 2) checking the validity of equations the students enter, 3) investigating whether an equation is independent from a set of other equations, and if not, determining on which equations it does depend, and nally 4) providing tools to help the student with algebraic manipulations, including a \solve-tool that solves her equations. The ability to determine dependence of equations is rst used by Andes during problem generation, by providing information to that component of the ITS which generates correct solutions to the problem. Later, during tutoring, it enables the help module to model which equations the student appears to know. One new feature of our algebra system is that it deals with the dimensional units of physical quantities throughout. An important change from a previous approach is in the meaning of \correctness of an equation and in the method of determining which equations it can be derived from. An evaluation of the theoretical dierences between the two methods, and the pros and cons of each, is given here.