Even in this age of graphing calculators and supercomputers, pencil-and-paper exercises are a major component of every matrix algebra course. Obviously, students still need to strengthen and evaluate their understanding of the various concepts by solving numerical exercises and examination questions. But computer-based numerical exercises can be much more powerful than the traditional pencil-and-paper approach. Because we can use a random-number generator to create new problems of a given type, students have an almost unlimited number of exercises with which to practice. Also, the computer can check students' answers immediately. Interactive exercises form a kind of training ground where students can improve their skills in a selected area of mathematics.
We have used Mathematica to implement interactive matrix algebra exercises through a specialized front end called Exercise Maker. Exercise Maker (EM) is part of a computer-based hypermedia learning environment for mathematics developed at Tampere University of Technology . Currently it is running on the Macintosh platform. EM displays questions, gets the answers, verifies them, and reports if something went wrong. It can be characterized as a specialized front end to Mathematica because it carries out all the needed computations by passing data, commands, and programs through MathLink. Exercise Maker is not a general purpose front end and therefore it is not intended to compete with the standard Wolfram Research notebook front end in any of its basic functionality. Rather, it is meant to provide new functionality essential for interactive exercises: intuitive buttons, popup windows, better graphical formatting of certain classes of simple expressions, etc. In this article we present the general framework of the exercises, illustrated with several examples, as well as the basic design of the interaction between the kernel and EM and some aspects of its implementation at the C/C++ code level.
Converted by Mathematica October 5, 1999 [Next Page]