Some techniques for building mathematical intelligent tutoring systems

Abstract Some techniques that are useful in building intelligent tutoring systems for mathematics are described. These techniques have been implemented in Integration-Kid, an intelligent tutoring system for integral calculus. Its production system is a language which helps the problem-solver to interact with students. For the mathematical problem-solver, we have adopted term-rewriting rules which represent basic mathematical knowledge. The situation map is a representation which lays out all possible situations in the process of solving a complex problem. We shall also describe an algorithm which transforms a linear mathematical expression to a readable, two-dimensional expression.