Self-explanatory symbolic computation for math education

In this position paper we will try to state some new ideas concerning the design of software systems for symbolic computation which are to be used in math education. Up to the late seventies computer algebra systems were running only on big mainframe computers. The muMATH-80 system was the first to be used on microcomputers running under the CP/M operating system. Since the first hand-held computers that can run CP/M are on the market, it seems obvious that in a few years we will have computer algebra systems on cheap hand-held or even pocket computers. The use of such computer algebra systems will probably have more influence on high school math than the appearence of electronic pocket calculators did have. If we now take a closer look at muMATH, one can see that most topics of mathematics that are relevant in high school, can de treated by the system. Some parts that had not been covered in the muMATH-80 version are covered by the muMATH-83 version, like for example vector algebra and simple differential equations. This shows the direction where things probably will go. Sooner or later all topics of high school math or even undergraduate math will be covered, at least in principle, by systems running on microcomputers. Further developments in the hardware field will accelerate this process, e.g. if the standard size for RAM storage in micros and hand-held computers increases from now 64 KB to, say, 256 KB.