sborník

Gunter Weiss
5 “e-learning Geometry”
The needs of teaching classical 3D-geometry on one hand and the lack of
teachers on the other could force the development of e-learning material in
Geometry. Such e-courses are generously supported by European Community
programs, as they aim at a unification of educational systems in
Europe. What can be found of e-courses up to now supports the respective
Geometry courses of each author of those e-learning modules, such that
they are not really of general use. By the way, not everything is correct in
these e-learning materials! For example, in an Analysis e-teaching project
supported by the EC the left figure 2 represents the graph of a cubic surface.
This seemingly complicated surface is depicted also by its top view, using
the same rough discretisation based on default values of MATHEMATICA..
Here mathematicians neglect essential mathematical fundamentals: the
influence of discretisation, parameterisation, regularity. (The right figure 2
shows a ‘correct’ image of the left surface, which is the well known
PLÜCKER conoid.)
Cartesian graph
Graph in cylinder coordinates
Figure 2: PLÜCKER conoid plots with MATHEMATICA ®
New media require other methodical approaches than classical ruler and
compass constructions involve. For example, it can no longer be the central
task of Descriptive Geometry to dissolve a 3D-problems into incidence and
measure problems in the drawing plane. The classical set of geometric
objects should be enriched by freeform objects, a listing of the single steps
of the solution of an arbitrary problem should be based on argumentation in
space. A one-to-one translation of former strategies to 3D-Cad-software
surely is the wrong conception! As long as e-learning units have authors,
whose education in Constructive Geometry only is based on engineering
standard knowledge and who have not fathomed the subject scientifically, I
have great reservations about the use of such teaching software.
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