Sorry to be so verbose, but I there were two issues I thought should be addressed in Standards 2000, and below is the second. (My preveious post was the first issue.) Again, I forwarded this to future@NCTM.org, but would like others' comments.
>Subject: research behind standards 2000 Status:
At the research presession, I learned that there will be a "research addendum" to the NCTM standards. I have some thoughts I wish to share:
Specifically, the "research addendum" needs to address THINGS WE DON'T KNOW, as well as things we know. I recently sent a lengthy piece on a recommended "support for teachers" standard. One thing that became clear as I prepared the piece is that we don't know for sure just what kinds of support teachers need in order to implement the Standards. Somewhere, NCTM needs to admit this kind of thing forthrightly, and lay out a research agenda. Perhaps the "research addendum" is the appropriate place.
On a more political issue: we really haven't PROVEN that constructivist instruction (e.g., working FROM engaging problems TO the embedded mathematics) is superior to more direct-instruction. (Probably, it would be more accurate to say "superior for some purposes", and to identify by research specifically what purposes.) We have a learning-based THEORY of how to teach, but the "backlash" folks in California really do have a point in claiming that we need more evidence of success for large-scale constructivist curricula. (The best evidence we have for constructivist teaching seems to be clinical and small-scale studies, mostly done with younger children, and cross-cultural studies, mostly done comparing Japanese and American K-8 classrooms. The "experimental" evidence is only coming out now, and is still often focused in younger grades and on a relatively small scale. Isn't it a "leap of faith" to assume that these ideas will work on a large scale, or that they'll work at all in High School? Isn't it assuming a little bit much that comparison to Japan reveals teaching methods with superior performance, when we have not yet confirmed that other high-scoring countries like Singapore use instructional methods similar to those in Japan, or that better achievement in a different culture can't be attributed to things like peer support for studying mathematics, vs. attributed to instructional differences?) I think forthrightly admitting what we have and haven't proven is important,in order to move the discussion of reforms to one based on evidence instead of ideology.
I currently believe in the constructivist theory upon which the Teaching Standards are based. However, I see a desperate need for testing this theory as rigorously as possible--both because I'm willing to admit that I could be wrong, and because we will never get political acceptance of the theory without better evidence.
In sum, I think it is critical that somewhere the NCTM standards project address "what we know" and "what we don't know" about teaching and learning. I've listed two issues that desparately need more research: 1)what kinds of support do teachers need to successfully implement the Teaching Standards; 2) Do large-scale implementations of the Standards produce the results we hope for--and if so, is this true for all topic areas, all student populations, and all grade levels?
I'm sure others can come up with additional areas that should be addressed.
Steve Kramer doctoral student (mathematics education) University of Maryland, College Park