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.
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.