I tend to have conniptions over events which bill themselves as "First annual", and to cock a mildly skeptical eyebrow over "Second annual", but by golly, I think we have earned our stripes, and I will thus firmly announce that this is a description of the third annual WaToToM gathering. WaToToM, lest that send you fishing wildly in past newsletters, stands for Washington Teachers of Teachers of Mathematics. It is not a conference, congress, seminar or even meeting, but a gathering whose basic objective is conversation--little ones between two people, big ones among the whole group, short ones, long ones, sometimes even controversial ones. So obviously the first thing you need to know is who's conversing. For a start, to justify our clever title, it is a batch of people who teach teachers (especially future teachers) at a whole collection of institutions--two-, four- and more-year colleges and universities--from all over the state. Then there are some people possibly not actively currently teaching but with a highly active interest in the issue (for instance Dana Riley Black of UW's K-12 Institute.) Usually someone from the Office of the Superintendant of Public Instruction (missed this time--I blew it!) And centrally and essentially, some classroom teachers, to ground us and orient us and keep us in touch with the point of the whole enterprise.

Conversation is central, yes, but even conversation needs some launching and occasionally even directing, so we do have a program and an agenda yet, even. And if I follow along on those I can at least give you a miniscule sampling which might convey a little of the flavor of the Conversation.

Events officially began after dinner on Friday, though that's a slight misnomer because dinner--or any other meal--at the Sleeping Lady is an event in itself. I cannot imagine becoming blase about those meals. The other thing that felt eventful on this occasion was celebrating the arrival of each and every carload, because there was heavy white stuff coming out of the sky and each successive load reported seeing more wrecks at the pass. We all made it, though, both those coming over the passes and those coming across the state. Whew!

After dinner was introduction time. Each person had to grab a partner who was not a previous acquaintance and find out a) enough of the basics to make up a respectable description and b) something unexpected that the two partners have in common. Hands-down winner in the latter category was the pair who found they had both been dinosaurs in science exhibitions.

Saturday, fueled by a five course breakfast, we launched the day with a couple of dice games. This produced lots of lively interaction, especially the one with an ambiguity in the rules ("I say you can't have two middle people, and that means you both lose and I WIN!") and some beginnings of strategizing. I had intended to take the discussion on into ways of using the games in the classroom and how to go about insuring that their mathematical content didn't submerge under the glitter of winning and losing, but the siren song of the upcoming DMI session lured me onward and I let that drop.

DMI is another of key acronym on the current scene, so I will take time out to describe it. It stands for Developing Mathematical Ideas, which is a series of seminars put out by the Educational Development Center based on case studies (you know, those things that lawyers and doctors and psychologists have used for years to deepen their professional knowledge. The educational profession is just catching on.) The case studies come out of real classrooms and are written up by real teachers, and are then selected with great care to provoke thought and generate discussion and occasionally controversy among the seminar participants. Seminar materials include mathematical activities and questions to help focus the thinking and the discussion. They are extremely well done. They are also particularly key around here at this point because our elementary NSF project, Expanding the Community of Mathematics Learners, is centered around use of these seminars with a wider and wider circle of teachers.

So with all that in mind, and because this WaToToM was aimed especially at the elementary scene, we decided simply to run a DMI session. We chose one from the second series, "Making Meaning for Operations" and tackled (uh-oh!) fractions. People had risen to the occasion and done their homework (a WaToToM first) by reading the cases handed out on Friday evening, so were ready to delve straight into comparing the fraction understanding of two children faced with task of dividing three brownies followed by two more brownies among eight children. Maribel divided each and every brownie in eighths and distributed one piece of each brownie to each child, reporting a result of 5/8 brownie per child. Alejandro observed that a pair of brownies can be quartered and dealt out, and wound up reporting that each child got 2/4 and 1/8. So what does each of them fully understand? Partially understand? Not understand? And don't you wish you could hear the subsequent conversation between them?

The rest of the morning we spent on the fraction activity of the lesson, designed as a lead-in to the following section, which is on division. The problems involved drawing diagrams to demonstrate the solution to various problems of multiplication and division. For instance, if one batch of cookies requires 1/2 of a cup of flour, how many batches can you make with 5/6 of a cup? Yeah, right, of course you started by using the algorithm and getting 10/6. So now forget that and try to make a diagram that shows the whole schmier--problem and solution--in such a way that you could hand it to someone shaky on fractions and walk away and hear them exclaim behind your back "I GET it!"

That took us up to lunch without a lull. After lunch was official Frivol Time. One bunch went to Leavenworth, a.k.a. plastic Bavaria, which seems to have gotten even more so, though they had a great time finding that out. Another bunch went cross-country skiing almost on site and came back very well exercised. Others quietly disappeared--library? hot tub? zzzz??

In any case, we all reassembled at 3:30 for what constituted for most of us the central portion of the entire week-end. Our three elementary school teacher guests simply sat there and drew us into their lives as teachers. What are their schools like? What are their backgrounds? What are their students like? What are their days like? It was far too richly textured for me to come close to reproducing. A few snapshots linger in my mind: Diane Kane saying "At the end of my first year I hated the way I was teaching math and my students hated math and I knew I had to go find a way to make a drastic change." Ruth Balf using a single well-chosen example to get a parent to understand that his daughter didn't need the long division algorithm he was so eagerly awaiting because she had a really firm grasp on the division itself. Leslee Shepler explaining the degree to which she had thrown herself into adoption of a new curriculum because she felt that without one the children were being cheated by the whole system. What a set of professionals. And what neat people, too--lots of fun to listen to.

Saturday evening we sat around and compared notes about what is going on in teacher education at our sundry institutions. Definite high-scorer in that non-contest were the trio from Green River Community College who described their work of the past couple of years. It seems checked things out a while ago and discovered that some 50% of the graduates of the state's elementary teacher programs start their careers in a community college. Conclusion? Community colleges should design a set of courses which constitute a good lead-in to an education program. So, with the aid of an NSF grant, they formed Project TEACH, which has been doing just that. They have worked particularly with Central Washington University, but are very much game for spreading the word to other community colleges and universities. It's well worth the spreading.

Sunday morning started with another project description: Loyce Adams from the Applied Mathematics Department and Briel (oy! I have forgotten Briel's last name) from University Child Development School described a many-phase process through which a three-pronged community consisting of Northshore teachers, graduate students and UCDS faculty have worked together as Northshore has gone about choosing and adopting a new curriculum, with the primary goal of helping support the Northshore teachers, but with secondary result of vastly better understanding of the K-12 world on the part of the graduate students. Exciting.

The next chunk of the morning was to have been spent asking questions of an OSPI representative, but some communications got missed, so instead we compiled a massive list which I am due to transcribe and fire off. Duck, OSPI!

We finished with a discussion that lends validity to my claim of "third annual", to wit, exploring ways to solidify WaToToM without straightjacketing it, and to break out of the Warfield-production mold into more general ownership. We made a list of whobody else ought to be invited AND WHO WILL INVITE THEM, and of what might be done about the finances AND WHO WILL DO IT. The entire set so far has been possible because the Mathematics Department has supplied advance payments to Sleeping Lady and had faith that we would repay them. I say blessings upon the department, but I would rather not keep leaning that heavily.

And on that heartening note we closed our notebooks, stuffed in one more superb lunch and headed off with what was firmly an "au revoir" and not an "adieu".

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