>And now Harvey Becker here again: > >Judy....I agree with you! I absolutely don't believe that mathematic must be >justified in terms of practical immediate problems. My point above was in >response to Dan Hart's mentioning that he felt we should teach general >information before we ask kids to solve big complicated problems. I agree >with that notion. I think discovery learning has its place, but considering >the educational time constraints under which we find ourselves, I feel it is >fine to teach theory FIRST and then let kids use that theory to solve real >life problems SECOND............. OR just use the theory to use the theory. > Math has a beauty all to itself and need not be used to solve real life >problems. > >Harvey Becker >Woodside High School >Woodside California
*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 suspect that lack of using discovery is why we keep repeating the same idea in different guises instead of acknowledging the unifying idea. For an example, consider the distributive law, which in UCMP's Transition Math (which, by the way, I generally like provided you have to use a textbook) is presented in two forms: a(b+c), and a(b-c). This is ridiculous! If kids were already comfortable with moving blocks around and back and forth, i.e. with inverse operations, you wouldn't need two separate days to do this.
==================================== Judy Roitman, Mathematics Department Univ. of Kansas, Lawrence, KS 66049 firstname.lastname@example.org =====================================