Numeric versus symbolic computation

Twentyfive years ago when I studied Physics, only one of the students who participated in a laboratory course that I took was possessing one of the first calculators to process the data we were obtaining. Believe it or not, everybody else, including me, had to use a slide-rule for this purpose. Nowadays, the calculator is used by everybody, by far not only for academic purposes. Hence it is the responsibility of the school education, and here in particular of the Mathematics education, to take this situation into account, and to teach our children the (intelligent) use of a calculator. In my opinion, there is no doubt that sooner or later computer algebra systems like DERIVE or Mathematica will be used by everybody in the same way as calculators are used today. Obviously this gives us a new responsibility to integrate computer algebra systems in the Math curriculum and to teach the students the use of them. When I realized this, I began to use DERIVE in my calculus courses at the Free University Berlin in particular for the Math teacher education [5]-[6]. Whereas calculators brought more numeric computation into the classroom, computer algebra systems enable the use of more symbolic computation. In this presentation, I would like to give examples how numeric and symbolic computations need each other. These examples show in particular with which type of mathematical problems the Math education can and should be enhanced by the use of DERIVE. Same of my examples might be considered to be too advanced or too far away from the current curriculum which on the other hand differs quite a lot in all the different countries which the participants of this meeting come from. Rather than being static material, my examples are considered to supply ideas to Math teachers about interesting and important concepts that might be incorporated in future Math education in connection with the use of computer algebra systems.