> According to DanH150093@aol.com: > > > > 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. > I think what we're forgetting is that practice only engages the student on a "lower-level" thinking platform. Unless we include opportunities for students to stretch their thinking though tasks like the "24 game", then students will never move beyond rote memory and practice. To define more challenging mathematics tasks as the role of supplementary material or activities scares me. Why? Because, many will say they don't have time for the supplemental materials. Their students will be relegated to the math that machines can do all their life.
> > > 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. > > I think Battleship is an excellent way to introduce the coordinate system. It's highly motivating and meaningful. We are graphing for a purpose. Most American kids do remember what they do from day-to-day if it is interesting. Having been a middle school mathematics teacher for 33 years, I can assure you that the more activities in mathematics that I can associate with a game, the more the skills stay and are remembered. > > > > > 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. > Until the curriculum and pedagogy change so that the CLAS test measures what is being presented in the classroom, the test will have "pretty abysmal scores." No one believes that kids in high school at the moment reflect any of the Standards education. They are too old. Most school systems are barely implementing the Standards right now. We are also just learning now how to serve the needs of a diverse population which is reflected in our cities. I suggest we look at the next six years and see.
> > 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. > > And every good teacher I know does not stay with one curriculum. She is eclectic and picks what is known to work. I believe this is what the Standards suggest.
> > 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. > > > In my 33 years of teaching I have not met "mediocre" teachers. Our mathematics educators are dedicated and anxious to help their students. It is self-defeating to look at ones self as mediocre. And, I teach mathematics and don't use it as an excuse for poor grammar. You can't. Students must see the math teacher as competent in all areas. In fact, students must see that writing is important to mathematics, whether it may be technical writing or expository writing.
> > 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. > > > The Standards do not proscribe curricula. They "guide" educators to what is felt to be the appropriate emphasis on content; and, they suggest pedagogy.
Believe it or not, Dewey suggested many of the same types of pedagogy over a half century ago. The l960's "New Math" had many of the same ideas. Unfortunately, the teacher education strand was left out. But, as a testimonial, much of what I have been doing for 33 years is due to graduate work in the l960's, and having contact with the Madison Project ideas and materials.
Presidential Awardee, Math Karen Dee Michalowicz VQUEST Math Lead Teacher/Trainer Upper School Mathematics Chair Virginia Quality Education The Langley School in Sciences and Technology 1411 Balls Hill Rd, McLean, VA 22012 USA 703-356-1920(w) E-Mail: firstname.lastname@example.org Fax: (703) 790-9712 --or-- KarenDM@aol.com