A computer simulation of mathematics learning process using Harmony Theory

In the design of Intelligent Tutoring Systems, it is often necessary to understand students' errors so that suitable measures can be taken to help the students. Errors are traditionally described as mal-rules which are thought to be caused by incorrect reasoning; In contrast to these systematic errors, the term "slips" is used to refer to careless work. However, some psychologists argue that it is difficult, if not impossible, to distinguish mal-rules from slips. This article posits a parallel distributed processing model which incorporates both types of errors. The computer system based on this model successfully simulates the process in making either type of error. Furthermore, by suitable manipulation of the parameters, the model can simulate the mathematical learning process as the subject changes from a novice to an expert problem solver. The implication of this model to teaching, and the design of Intelligent Tutoring Systems is then discussed.