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Re: meaningful standards (fwd)
Posted:
May 31, 1995 8:18 PM


Judy R writes......
>*Discover* theory, Harvey, *discover* it. And while I'm a college math >prof and have no firsthand 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 xc 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



