>I think, however, that Richard (and Dan & many others) have misinterpreted the > Standards and other materials of the reform movement when they say such >documents "overlook focus and practice". The practice is there, but it is >not in the form we are used to seeing it. Practice and focus do not have >to be routine, dull, or >meaningless (without context) to be effective. A fairly good example of >this is the "24 game" where students are given four numbers and must >use the operations and each of the four numbers to get a total of 24.
Problem is I'm very aware of how the standards would like practice included. I've done lots of exercises like the "24 game". "Four 4's" out of the Lane County books is an example. These are fine assignments, I wouldn't argue, but I think they should mostly be used as supplementary material, not a replacement for a core curriculum of practice.
As an example, I'd point out the new Glencoe book, "Investigating Mathematics", one little "gem" of the PC math movement (see page 7 and the list of historical events to plot on a timeline if you doubt my assertion), but I'm digressing. This book is intended as a replacement for basic math in the ninth grade. In order to learn how to plot points the kids are asked to play "Battleship". Now that might be a very fine strategy for introducing the concept or for reinforcing it down the road. But that's it!! There's no well developed system of practice that cements the knowledge in the students' heads. And this is very important given that most American kids can't remember what they did from day-to-day no less year-to-year.
So please. I do know how the standards incorporates practice, most often to solve irresistibly interesting problems and I simply don't think it works very well. High schools in LA which are thought to have the most "progressive" math departments also seem to have some pretty abysmal scores on the CLAS test, a test written by and for the reformers.
And as far as research is concerned, I don't have much faith in it, given the nature of our universities (particularly education departments) and the fact good teachers can make most any curriculum sing.
Give me field testing of different schools and mediocre teachers like most of us with classes of forty kids on standardized tests that can be studied for. (Sorry for ending my sentence with a preposition. I am a math teacher) Then we'll see what's working and what isn't.
It seems to me the standards folks would be thrilled to finally demonstrate the efficacy of their curricula. Again, I'd recommend you read "Class Action", a new book on what I'm discussing.