CATO is a new user interface, developed by the author as a response to the significant difficulties faced by scientists, engineers, and students in their usage of computer algebra (CA) systems. Their tendency to use CA systems only occasionally means that they are unfamiliar with requisite grammar and syntax these systems require. The author…

In this article, the authors describe how a Java applet can help to build learners' intuitions about basic ideas of algebra. "Matchbox Algebra" is a Java applet the authors have designed to enable learners to grasp a key idea in learning algebra: that the letter "x" may be thought of as representing an as-yet-unknown number. They describe the…

Describes PRECEPTOR, an intelligent tutoring system that provides multiple explanations for algebraic word problems involving two variables. Modeling the cognitive processes of an effective teacher is discussed, the capacity for individualized tutoring is examined, and differential tutoring based on varying difficulty levels is explained. (17…

We present the design principles for a new kind of computer system that helps students learn algebra. The fundamental idea is to have a system based on the microworld paradigm that allows students to make their own calculations, as they do with paper and pencil, without being obliged to use commands, and to verify the correctness of these…