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Re: Benchmarks
Posted:
Mar 27, 1995 11:51 AM


Cindy, this is a very interesting issue, and not at all dull. Actually, two interesting issues. Maybe three.
The first issue is a question: if something works and is important to understanding but appears to be learned only by rote, should we judge children by it (i.e. use it as a benchmark)?
My answer is an unqualified yes. If it's important to the understanding of number, then who cares where it comes from?
But this raises another question: is skip counting really learned by rote? I think some kind of internal representation has to occur, the kind of thing we can't verbalize and isn't amenable to geometric models, but the kind of thing that has to happen for numbers to be *real*. I say this because my quite intelligent LD son in fact never did become comfortable with all but the most rudimentary skip counting, and this clearly lies behind a lot of his problems with understanding and using number  to get from 24 to 27 he has to name every number in between, the *system* of multiples of 3 isn't an object to him.
There's another important issue here, and that's what kind of document the Standards is. My understanding is that it was supposed to point in a direction and not be taken totally literally. Questions beginning with "Do the Standards say that..." are interesting for informational purposes, and can give a sort of guidance, but shouldn't be used to squelch honest and thoughtful opinion, especially of talented, imaginative teachers whose instinct has been honed by years of attention to the experience of their students. Folks like you, Cindy.
Cheers.
==================================== Judy Roitman, Mathematics Department Univ. of Kansas, Lawrence, KS 66049 roitman@math.ukans.edu =====================================



