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Topic: List of 'good' geometry textbooks
Replies: 9   Last Post: Aug 11, 2007 1:27 PM

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Walter Whiteley

Posts: 418
Registered: 12/3/04
Re: List of 'good' geometry textbooks
Posted: Aug 10, 2007 6:09 PM
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I agree with much of this as a approach to learning geometry!

A very old source (1840's0 which started with some 3-D explorations,
well before anything that was primarily 2D, was Froebel - the man who
developed a revolutionary education program he called kindergarten
(the children all had small gardens). He was trained as a
crystallographer, so he was quite familiar with 3-D, and developed a
series of 'gifts' for the children to use for a variety of
explorations, story telling, etc. While there are a few Froebel
schools still around, the main residual which survives from his work
is the classic wooden blocks for children's play. (Milton Bradley
originally produced all of his gifts for sale, but cut this back at a
time when North American educators were trying to reduce the amount
of intellectual activities which occurred pre-school.)
Foebel's work played with symmetry, with shapes creating by spinning,
etc. as well as the way carefully designed decompositions came apart
and reassembled into patterns. There is some evidence that his
program had an impact on the development of people like Frank Loyd
Wright, and some of the turn of the 20th century art movements. (See
the book the Man who

There is a lot of evidence that all of us learn first to 'see' in 3-
dimensions, and find that cognitively easier in many circumstances.
This even appears to be true among blind people - so the 'seeing'
here is our cognition, with input from the eyes, and the hands. See
for example the book: Brosterman, Norman. "Inventing Kindergarten"
New York: Harry N. Abrams, Inc., 1997.

Walter Whiteley

On 10-Aug-07, at 2:09 PM, Kirby Urner wrote:

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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