MATHEMATICS


    MATHEMATICA Activities Group

The purpose of this group is to make contacts using MATHEMATICA in teaching (including high schools). The interest is not in the use of software specifically designed for educational use (e.g. Geometer's Sketchpad, to note an impressive example) but in "general purpose software for doing mathematics" such as MAPLE, MATHEMATICA, or MATLAB, where effort is required in adapting the software to educational purposes. And, while these three softwares have similar capabilities, the purpose of this group is to concentrate on one software for simplicity. (Other softwares, other groups.)

MATHEMATICA is extremely powerful software originally intended to support computation for research in mathematics and applied mathematics and for industrial mathematics. It has capabilities far beyond the level needed in high school or undergraduate courses. All the better: experience students gain with the software has substantial potential for use in higher classes, including graduate school, and outside the classroom.

There are three typical levels of use:

  1. For transparencies or demonstrations. Here the software is used by the instructor alone to support lecture activities.
  2. For "canned" exercises available to the students. These might be already available or prepared by the instructor. The students might set parameters or other controls and experiment with the results but would not actually "learn the software".
  3. For student use in homework and lab exercises and in projects. Here the students must actually learn commands, syntax, and so forth and use that knowledge in an active manner to solve problems.

Comments:

  • An instructor can devise his/her own examples and exercises, allowing more focused attention on concepts and more tie-in with course material than might be feasible with mass-market material.
  • Multi-step problems can be assigned without the worry that half the class will get the algebra wrong on the first step. Indeed, having students check their work in various ways at various steps can be used to practice and reinforce concepts.
  • Projects can be assigned involving actual applications or similar levels of complexity. In particular, projects could be set up to overlap between math courses and science/engineering courses and involve real data. (I find this interdisciplinary aspect extremely intriguing.)
  • Students get experience with "real-world" software.
  • Although students do not get direct reinforcement of the mechanics of hand calculations, they can get significant practice in manipulating mathematical expressions. Symbolic calculations can involve considerable juggling to get an expression in an informative or useful form, and the use of software forces them to think about this process in a focused, rather than haphazard, manner.
 
For more information on the Mathematica Activities Group, contact Dr. Davis Cope.