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Re: List of 'good' geometry textbooks
Posted:
Aug 10, 2007 2:02 PM
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As a curriculum reviewer myself, I'd go through each of
these and see what, if anything, is included of 1900s
post-Euclidean geometry, in particular the neo-classical
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 cyber-curricula 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
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