On Nov 9, 2012, at 2:26 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> That's why I like "meta" better than "symbolic". There are meta levels upon meta levels, not just two levels. The distinctions are always relevant no matter how far one gets. "Meta" also captures better the idea of studying "expressions with variables" as objects in their own right, rather than simply viewing them as ways of expressing things *about* integers or rationals or what-have-you.
I certainly agree there. That's my big deal, development.
There is also an aging aspect involved, which I cannot state better than does this quote from the book "The Calculus of Friendship"...
"When we were learning about the rigorous definition of continuity - a very fundamental, difficult concept in calculus - Mr. Johnson told us something I'd never heard a teacher say before. It was ominous. He said he was going to present some ideas we wouldn't understand, but we had to go through them anyway. He was referring to the epsilon-delta definition of continuity: A function f is continuous at a point x if, for every epsilon > 0, there exists a delta > 0 such that if [x - y] < delta, then | f(x) - f(y) | < epsilon. He said we'd need to see this four or five times in our education and that we'd understand it a little better each time, but there has to be a first time, so let's start."
Strogatz, Steven (2011-03-07). The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math (Kindle Locations 136-141). Princeton University Press. Kindle Edition.