The is a brief note motivated chiefly by a lovely discovery I made last week-end: outside of the pressure-cooker that currently houses everything to do with K-12 mathematics in the state of Washington there still exists a world where people gather and have really interesting conversations about teaching mathematics. In this case, the conversations were specifically about the teaching of mathematics to future elementary school teachers. The occasion was a conference put on by the Institute of Mathematics and Education at the University of Arizona. A couple of dozen of us from university and grade school faculties and related walks of life dug into all sorts of issues about what we think elementary teachers need to know and how they can come to know them. We watched a videotape of a student teacher teaching a lesson from Everyday Math and discussed what parts the students in the class benefitted most from and how other parts could be deepened -- and what one would say to the (very good) student teacher if one were her mentor. We looked at some particular problems or activities that different folks have done in their classes for future teachers and discussed their values and hazards. One bunch that left me absolutely drooling were the "habits of mind" problems that Jim Lewis gives his students at the University of Nebraska. They have one a week, and must turn in articulate, mathematically sound solutions. Characteristically, the last lines are "Can you generalize the problem? If so, can you solve the generalized problem?" Most students work in groups, with Jim's encouragement. They also bombard him with e-mail questions, to which he gives hints with varying degrees of thickness. He's pretty tough with his marking, which is part of what accounts for the difference between the slightly painful collection of responses he showed us from his first set and some really elegant late-semester ones. Unfortunately, even though many of us sat there with eyes sparkling at the prospect I fear there won't be many imitators. Something about Jim's report that the e-mails that come in after 10:30 at night get answered at 5:30 the next morning was a little scary!

There were other lovely sessions as well, not to mention the excellent conversations between the sessions. I'm having a little trouble reconstructing them at the moment, having returned to the cooker, but I may follow this up with details after I find my way to what Bill McCallam, founder of the sponsoring Institute, referred to with a fanatical gleam in his eye as our Wiki. It seems to be a website where you can post things like for instance reports on our sessions and where anybody on the site list can edit things as they see fit. He told us how to get there, but I forgot to leave a trail of bread crumbs.

This isn't a good moment to report on the Washington front -- too much hanging in too many balances. I will say that the revised Mathematics Standards -- pretty much the final revision thereof -- are now on-line at http://www.utdanacenter.org/wamathrevision/standards.php Have a look if you get a chance. Flawless they're not, but me, I think they are pretty doggoned good!

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