>*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