I have often spoken and written about computers in schools. E.g., see this paper for a conference in Rio. It is clear that software in schools is inevitable and necessary. It is also clear that it has its problems. Most of them are related to available hardware and also to the existing software. These problems might be resolved in a very near future by technological advances. But other problems concern the curricula and and the school system itself. Tests are a central part of it. Cynically, we can say that the only competence our kids learn is to answer well prepared test questions under time pressure. A self guided, research driven team learning with the computer as the main tool has no place in this system.
While I am interested in these questions and consequently in teacher education my research interests remained in approximation theory. Nevertheless, In 1988 I started a project in dynamic geometry on my old Atari ST just to see what could be done with an object oriented approach. This project was ported to OS/2 and to Windows, and finally rewritten in Java. At that time, it was novel and many people got interested in it. That was the beginning of C.a.R (Compass and Ruler), aka Z.u.L. in German. The primary idea, however, was not very deep and similar software existed, starting with Cabri or Geometer’s Sketchpad. Later came the star of today’s programs in Europe Geogebra.
C.a.R. followed the main ideas of dynamic geometry software. But what I tried to do is to implement advanced ideas in C.a.R. The following, e.g., are examples of main features of the program. Some were innovative.
- automatic generation of points and intersections by user click,
- automatic tracks, generated by a point moving along an object,
- automatic polar curves belonging to a set of lines,
- computed points depending on formulas,
- graphics export with preview depending on resolution and image size,
- transparency and other object features depending on computed formulas,
- generation and presentation of geometric construction problems,
- advanced macro generation with formulas and dependency checks,
- elliptic geometry with the Poincare model implemented with macros,
- automatic export of construction on web pages.
Most of these are now present in other programs. The graphics export, however, is still neglected in most systems.
Over the years, it became apparent that the program is not perfect, or rather, the times they are changing. So C.a.R. lagged behind more and more. What were the drawbacks and problems of C.a.R.?
- Teachers are more interested in Algebra than in Geometry now. While curves or graphs can be drawn in C.a.R. by formula, and a coordinate system is present, Geogebra e.g. puts this into the center of its interface. In contrast, the first versions of C.a.R. were centered around pure geometry without coordinates. Together with all the efforts of Geogebra in teacher assistance this puts the program into an advantage compared to C.a.R.
- C.a.R. has only rudimentary support for 3D using its advanced macro features. A true 3D program like Archimedes Geo3D is much easier to use and more capable.
- The user interface of C.a.R was based on modal dialogs. This was remedied with CarMetal. Its development was based on C.a.R. going its own ways now. The interface is very nicely done. The files are not completely compatible, however.
In recent times, I am more interested in Euler Math Toolbox (EMT). While hybrid programs with numerical and algebraic features like this are still not used in schools I have the feeling that they are more useful than geometry programs of any kind. Moreover, EMT can do geometry too, albeit not interactively. It is nice to have C.a.R. for the teaching of geometry or for an easy way to create geometrical figures. But EMT is much more useful in schools and universities.