teachers (and parents and curriculum administrators) must be able to start out feeling that what they do, they do for the sake of geometry. But they must be able to end up feeling that what they have done, they have done for the sake of mathematics, and, even more, for the sake of good thinking.
This chapter is adapted from the paper "Making Connections With Geometry," originally prepared for the keynote address to the Geometry Working Group at the International Congress of Mathematics Education, ICME 7, Université Laval, Québec, August 1992, and first published in 1994 in Czech translation in Pokroky matematiky, fyziky a astronomie [Advances in Mathematics, Physics and Astronomy], Association of Czech Mathematicians and Physicists, 39, 275-304. This work was supported in part by the Science Foundation, grant numbers MDR-8954647, MDR-9054677, and MDR-9252952, with additional support from Apple Computer, Inc. The views represented here are not necessarily shared by any of the funders. We are very grateful for the substantial intellectual and editorial contributions made by Glenn Kleiman at various stages of the preparation of this document and its many ancestors.
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