An intelligent tutoring system approach to teaching primary mathematics

This paper is concerned with recent developments in the construction of intelligent tutoring systems. The authors have developed an adaptive computer tutor for arithmetic, called Shopping on Mars; this activity is unique in that it supports informal methods of calculation. It involves carrying out shopping transactions within the context of an adventure game. The program runs on an Archimedes 310 microcomputer and is aimed at 8-to12-year-olds. Its main purpose is to help children develop an extensive repertoire of informal techniques for performing arithmetic in various everyday situations, and in particular, to learn to formulate shortcuts to problem solving. The tutor keeps a chronological record of how far individuals have progressed and of their observed difficulties, and it provides immediate feedback. Finally, the activity provides a rich, cooperative learning experience; the computer tutor acts as an intelligent participant in activities involving pairs of children. We describe the rationale behind Shopping on Mars, the design of its interface and instructional architecture, our strategies for intervention, and the special description language-based on direct manipulation-that we have evolved for child-computer communication. The results of some preliminary field trials are presented. We conclude by discussing the role of our activity in the classroom and the contribution which intelligent computer-based activities in general might make to the teaching of primary mathematics.