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Re: Why?
Posted:
Oct 30, 2012 11:59 AM
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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 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
<http://rowdy.mscd.edu/%7Etalmanl>
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