
Re: List of 'good' geometry textbooks
Posted:
Aug 10, 2007 2:02 PM


As a curriculum reviewer myself, I'd go through each of these and see what, if anything, is included of 1900s postEuclidean geometry, in particular the neoclassical arrangement of polyhedra in a signature concentric pattern recognizably in the Keplerian and Pythagorean traditions (yes, Platonic too), but in this case from the pen of American Transcendentalist R. Buckminster Fuller (better known as the architect behind the geodesic sphere, later domes, as memorialized in the recent Coxeter bio).
Starting in like 2nd and 3rd grade, my ethnic group (lots of Islamic heritage) has the polyhedra front and center, and not just (lame, obsolete) "blocks" like the cylinder, rectangular prism (brick), cone and sphere. We believe in early exposure to the greek roots 'tetra', 'hexa', 'octa' and so on. Also, because the child's world is demonstrably volumetric, we go with Piaget in sticking with volumes as more natively experiential. The idea of strictly "two dimensional" shapes is a much higher level abstraction, suitable for 5th graders maybe, but not so much for 2nd & 3rd  which doesn't mean we avoid tiling or polygons, we just don't wax metaphysical about 'em the way the Euclideans do.
I'm confidant that by the above criteria, it will be found that only cybercurricula are doing a worthy job of educating our young these days. We discourage adoption of any physical text books, which tend to be expensive plus make the smaller kids tip over backwards, given their backpacks have more than just math in 'em.
Kirby

