
Re: Why?
Posted:
Oct 30, 2012 11:59 AM



On Tue, Oct 30, 2012 at 3:17 AM, Robert Hansen <bob@rsccore.com> wrote:
> > On Oct 30, 2012, at 12:58 AM, Louis Talman <talmanl@gmail.com> wrote: > > Traditional algebra requires letters. But words are symbols, too. Use of > words is no reason to say a kid isn't doing algebraafter 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 kidseven among Bob's "mathy" kidsunderstand 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
<http://rowdy.mscd.edu/%7Etalmanl>

