On Nov 3, 2012, at 1:02 AM, Louis Talman <email@example.com> wrote:
> B. The invention of modern mathematics by the ancient Greeks---who were almost completely innumerate by today's standards---renders your "natural progression" untenable. And I'm not the least surprised that you chose to ignore it.
What do your mean by "completely innumerate"? Arithmetic predates their advancements by a thousand years (much longer by some accounts). Are you suggesting that they poorly understood the four operations and their application? Or are you saying that they had a crappy number system. The latter is true, at least from our perspective, but that is all they had and yet they still persevered with arithmetic.
I didn't ignore this. I didn't find it factual as stated. Can you elaborate more on what you mean? Obviously, Euclid knew arithmetic even though his view was that geometry was where it is at. As far as I can tell, Where "it is at" in mathematics has changed many times over history, even very recent history (last 50 years), but I don't see this pertinent to a discussion of elementary pedagogy. The order doesn't change much at all, even though more advanced things await our kids than did Euclid's.