On Tue, Oct 30, 2012 at 3:17 AM, Robert Hansen <email@example.com> wrote:
> > On Oct 30, 2012, at 12:58 AM, Louis Talman <firstname.lastname@example.org> wrote: > > Traditional algebra requires letters. But words are symbols, too. Use of > words is no reason to say a kid isn't doing algebra---after all, the > beginning of algebra is the replacement of numbers with symbols for > arbitrary numbers. > > > 1. It was a joke. Letters, words or blanks, all good, as long as point (2) > is met. > 2. Algebra is a form of reasoning. > > Also, children don't understand "replacement of numbers with symbols for > arbitrary numbers". > > If my several clues of the form "Children don't understand X" don't make > sense then add a couple words as in... > > Children don't understand THE SIGNIFICANCE of X. > > Bob Hansen >
Clyde is right. And it's completely irrelevant that children don't understand the significance of replacing numbers with symbols for arbitrary numbers. (Nor did I claim that they do.) What matters is that they do it. And, perhaps even more important, they do it naturally.
Or, as Clyde suggests, they use abstract *things*, which he calls "vectors". That's as good a word as any, I suppose, even though they aren't vectors in the sense that mathematicians use the word.
I'd suggest that very few kids---even among Bob's "mathy" kids---understand that they are abstracting, let alone the significance of abstracting. They just do it.
--Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver