Is there some way we could participate in a discourse that doesn't focus on attacking details? Taking a useful document, one that appeals to many people but not all, and reducing it to this level of debate doesn't help me think about the rest of the questions. There are all sorts of problems that arise when we reify the Standards. The conversations based on this kind of reification seem to devolve -- my experience has been that using the Standards as a place to begin conversation (not as a prescription or a credo) have been helpful to me in my thinking about my teaching and what my preservice students need in order to teach mathematics well (or even adequately).
We want students who have strong foundations in mathematics. We all agree on that. We will never agree precisely on how, and we must acknowledge that there are personal and professional we have about teaching. We are now different, and will continue to be. We'll do some things in the Standards, we won't do others, we may have already been doing some. But it's not a prescriptive document. It's flawed--so who among us isn't? It has some egregious boo boos in it--so we don't? It overstates and understates some points--and we never do???
If we could look at what we teach and how we teach and think about it without having to correct each others' terminology or constantly focus on distracting details, we could really begin to engage in thinking about how students *do* build their own understanding. Or even focus on the ones that *don't* build understanding, because they are legion.
Perhaps that's what's difficult. Once we realize students aren't monoliths, that we aren't always using the One Right Method for each student, that school mathematics is profoundly fun to explore and consider--then we don't Know with a capital K how to Teach with a capital T Mathematics with a capital M, and we have to rethink what we're doing.
It's engaging in that reflection, based on the knowledge that teaching and learning are complex acts, and that mathematics is perhaps not always what we think it is, that makes this such an interesting thing to think about.
Rebecca Corwin Lesley College Cambridge MA ......a college with a snack bar........