Affiliations: Learning Research and Development Center, University
of Pittsburgh, Pittsburgh, PA, 15260, USA and Department of Physics and
Astronomy, Rutgers University, Piscataway, NJ 08854-8019, USA. E-mail:
shapiro@physics.rutgers.edu; http://www.physics.rutgers.edu/_shapiro
Abstract: 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.
Keywords: Intelligent tutoring systems, solving algebra problems, physics problem tutoring
