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revitalizing geometry
Posted:
Dec 6, 1992 10:52 AM
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There have been a variety of posts recently concerning the value of Euclidean
constructions and software such as the Geometric Supposer and Geometer's
Sketchpad to assist spatial intuition. Unhappily this debate in my opinion
misses an important point - how to revitalize the teaching of geometry to put
geometry education on the same exciting footing that events in research in
geometry are undergoing. Althought the software above appear to me to be
technical tours-de-force, they seem to me to breadth life into dead horses.
Geometry is exploding in a variety of directions all at once, and in compariso
n in high school classrooms and college survey classes little recognition of
these exciting events is going on. Instead, the old "tired" geometry of
circles and triangles and constructions are being beaten to death. Not
that this material is not exciting from a certain very narrow point of view
but it is no longer the center of interest for geometers, and for non-math
types in hs, it has none of the excitement of the recent applications being
found in robotics, computer vision, medical imaging etc. etc. There is a
widespread feeling that if we give up circle triangle geometry and the
usual college survey that no one will become interested in geometry in the
future. Nothing seems likely to be further from the truth. By setting up
links between the hs curriculum and college curriculum and what geometer
researchers are doing would be very symbiotic. Take a look at the journal
Discrete and Computational Geometry (Ed. Goodman and Pollack) and published
by springer-verlag to get an idea of the wide range of exciting ideas are
currently being pursued, with the at least in many cases an accessible
component more exciting than the 9 point circle (as spectacular as that
result is, in a narrow sense. Geometers, let us do something to energize
the teaching of our subject.
Joe Malkevitch (math. york college) joeyc@cunym or joeyc@cunyvm.cuny.edu
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