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Re: meaningful standards (fwd)
Posted:
May 31, 1995 8:18 PM
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Judy R writes......
>*Discover* theory, Harvey, *discover* it. And while I'm a college math
>prof and have no first-hand experience with kid discovery inside regular
>curricular constraints, I've seen a lot of elementary teachers doing it
>with all kinds of classes, and have done more and more of it within my own
>time constraints in college classes.
>Addition of fractions (from a previous message of yours) is a perfect
>example. We don't save any time *telling* kids because they instantly
>forget it and have to be taught it over and over again from grade n to
>grade n+3 (where n is either 4 or 5, depending on the school district).
I'm not sure what you meant in the first line above. When I say that I teach
the kids the theory of a mathematical concept.....I don't just "show" the
kids how to, for example, add two fractions together. Many things go into it
including pictures, visual aids, etc. But... quite often a concept is simply
too involved to have kids discover the outcome. I mean...how long would it
take for your average high school student in advanced math to figure out that
if you divide P(x) by x-c and the quotient together with remainder have no
sign changes, then c is an upper bound for the zeros of P(x). I feel in
these cases (and there are many), it serves a kid just as well to see a
logical proof of the assertion or at least a demonstration of its validity.
We cannot just cast time constraints to the wind.....they DO exist. We
cannot shy away from rigorously demonstrating the proof of a theorem just
because some new standards are being introduced which stress investigations
and discovery learning. Much of the reason I feel the jury is still out on
the new standards is because I see too many young teachers neglecting the
need to get rigorous when it is called for in mathematics. Investigations
and discovery, as I said before, certainly have their place.....but let's not
throw out all the mathematical beauty that exists in pure mathematical
theory.
BTW....If telling a kid how to do something necessarily means he/she will
instantly forget it as you imply above.....isn't society in deep trouble?
Gotta go catch the chickens out back....Harv Becker
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