The design of a user interface to a computer algebra system for introductory calculus

Document Type

Conference Proceeding

Date of Original Version



We are developing a unique computational environment for use in conjunction with the two-semester introductory calculus sequence. Our system, called Newton (formerly The Calculus Companion), runs on Macintosh computers and consists of a user-friendly interface to the symbolic mathematics package Maple, supplemented by an extensive library of our own Maple code. Formulas are easily constructed and modified, appearing exactly as they do in textbooks; multiple windows allow users to see and work with several formulas at once. Formulas, graphs, and text can be intermixed on worksheets. Users do not interact with Maple directly and need know nothing of Maple's syntax and command structure. Mathematical operations are selected from menus, with the added bonus that this makes it possible to document solutions. In addition, dialogs have been constructed to illustrate computational methods such as the chain rule for differentiation and integration by parts. As part of the project, we have also developed an interactive package for two-dimensional plotting that allows users to manipulate graphs of functions rather than merely view them as static objects. The system additionally contains an intelligent tutor that can assist users in solving problems on techniques of integration. The software enables students to concentrate on learning the important concepts of calculus, guiding them through complex problem solving requiring multiple steps, and freeing them from boring and error-prone calculations. The computer thereby encourages creativity through rapid feedback and experimentation, making the exploration of mathematics more exciting and enjoyable.

Publication Title

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC


Part F129620