I have always believed in the power of conversation in personal life, not to mention the pleasure thereof. It took a number of years, though, before I began to see how that belief applied to professional life. When I did, I still ran into some difficulties of articulation. "Ginger, what do you expect will come of this conversation if you do arrange it?" "Well, uh..." Now I can give a much firmer reply: "I wouldn't dare predict what, but I can just about guarantee that something positive will." Recent examples of several sorts have helped confirm this view.
Twice this year our NSF project, "Creating a Community of Mathematics Learners" (CCML), has invited high school teachers from several nearby school districts to the University of Washington campus for a day's visit. The visits are billed as an opportunity for them to observe classes and see what it is their students are heading for, and indeed it does have that function. The most interesting comments and reflections, however, have come from the lunchtime they shared with the faculty members who taught the courses they observed. The high school teachers have come away with a much deeper understanding of the demands both by and on the mathematics department and the faculty members have increased their insights into high school teaching, not to mention their interest in it. Perhaps the best of the outcomes was one I could have hoped for but in no way could have planned--the parting remark of one of our guests: "I had no idea there were university professors who cared that much about their students."
Conversation on a grander scale took place on a recent weekend at the third annual gathering of WaToToM (Washington Teachers of Teachers of Mathematics.) Two dozen people from all across the state converged with the sole and entire purpose of talking with each other. Our common thread was involvement in teacher education, an involvement which took many forms. We had people from mathematics departments and education departments and departments that combine the two, people from two-, four- and more-year institutions, elementary school teachers, graduate students--lots of variety. The programming existed entirely as a mechanism to launch, or occasionally shape, conversation. Perhaps the best measure of success was the level of difficulty getting people from one place to another. Nobody would move, because they were too busy talking. I can't report on most of the individual conversations, but one example from a general discussion serves to illustrate the nature of the discourse: a group from a community college, recognizing how many future elementary school teachers pass through their portals, has gotten NSF support to set up a course sequence designed as preparation for university level teacher preparation programs. Their hope is to involve as many as possible of the state's community colleges and universities in this project, and judging by the "Wow!"s at WaToToM, they are now several steps further along that route.
That was an example of a large-scale conversation which will manifestly give rise to wide-ranging consequences that may or may not be traceable to it. At the other end of the scale is a conversation whose ramifications are completely traceable and to me quite stunning. Like the first of the examples above, it began with a CCML event, in this case the 1997 orientation session that kicked off the whole project. Members of the mathematics and applied mathematics departments at the University of Washington were invited to help create that community by joining us for lunch. One applied mathematician who took up the offer was Loyce Adams. She had a long chat with Aaron Feik, director of mathematics curriculum for one of the local school districts, and thoroughly enjoyed it. More than a year passed before she got a phone call beginning "I don't know who you are, but you are just who I need." It seems Aaron's district was deciding on a curriculum adoption and he wanted the opinion of someone who used mathematics rather than just doing it. He had found in his notebook a record of a conversation with an applied mathematician, and with it her name and phone number. Would she help in the curriculum study? Loyce replied that that was too large a task for one person, but there was some chance that she might interest a few graduate students and turn the exploration into a seminar. Somewhat skeptically she put out an e-mail offer of such a seminar, and within half an hour had positive responses from twelve graduate students. Delighted to find such an unexpected lode of interest and civic-mindedness, Loyce set up the seminar. Over the next months she and the students immersed themselves in the realm of the NCTM Standards, the TIMSS results and NSF curricula. They visited classrooms, talked with teachers and wrote a hefty report strongly recommending one of the choices, while emphasizing throughout that this was just a data point for the use of the teachers, who were the actual decision-makers.
In due course, the decision was made, and the recommended curriculum was selected. But the seminar's study had also netted further information: this particular curriculum has a large mathematical potential, but correspondingly presents a large mathematical challenge to teachers as well as students, and teachers faced with that challenge need support. Loyce's response was to ask the teachers if they would like to have graduate students coming to them on a regular basis, and when their reaction was highly positive she set out to arrange that. She rounded up financial support from the NSF and the University of Washington and professional development support from the University Child Development School, and with that support ten graduate students spent hours each week of the following year in classrooms. The year was highly successful, but improvable, so Loyce set up a preparatory seminar through the university's Physics Education Group and a more elaborate summer workshop with the UCDS, and sent this year's students out appreciably better prepared.
That's where that conversation has led so far, and it would seem exceedingly rash to predict where else it may lead in the future. One quotation, though, brings us neatly back to where we started. A teacher with whom one of this year's graduate students is working remarked that he loved the mathematics enrichment lessons the student was tossing in, and he loved having mathematical emergency aid available, but "you know, I think the thing that may have the most impact of all on the kids is the chance to see two adults talking about math--to realize that mathematics is something you can actually have a conversation about."
Conversation -- yes!