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 email@example.com