An Algebra Subsystem for Diagnosing Students' Input in a Physics Tutoring System
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 finally 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 first 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 this algebra subsystem 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. The theoretical differences between the two methods, and the pros and cons of each, are discussed. Then we evaluate how the capabilities of the subsystem have affected the Andes tutor's effectiveness, with a particular emphasis on the effects of the changed method.