I have just had an extremely heartening experience. I ducked out of the continuous barrage of depressing reports and dire predictions about K-12 education and spent Monday through Saturday with a bright, motivated and delightful collection of people, almost every one of them an elementary school teacher. In a week that was doing its best (though unsuccessfully) to break heat records, I watched them tussle with some of the stickier aspects of rational numbers, cogitate changes they have made in their teaching and more that they plan to make, and grapple with how to lead their fellow teachers into tackling the same changes, all with astounding and unflagging energy. And very exciting watching it was.
Before I go into detail, I should give a spot of context. As I have mentioned before on these pages (screens?) the second of our NSF projects, which is designed for elementary teachers, is centered around a series of seminars put out by the Educational Development Center, entitled Developing Mathematical Ideas (DMI, for short). The central philosophy of the seminars is that the ideal mode of teaching is to listen to students well enough to understand their ideas and conceptions and misconceptions, and then use that knowledge to shape questions and lessons and activities so as to guide them towards the chosen mathematical goals. If you think that sounds easy, think again. And if you think it applies only to elementary teaching, think againer.
Our structure for using the DMI seminars is the classic pyramid. Gini Stimpson and Christopher Fraley, who are among the originators of the materials, first taught a small batch of teachers, and then a larger batch with the originals as apprentices. Now the larger batch, who hail from all six of the project's school districts, are preparing to go and run seminars for local leaders within their own districts, whom they will then help to run seminars for more teachers. Many, many more teachers.
Last week's Institute was an intensive siege of preparation for their next level of responsibility. One thing that entails is developing a confident conviction that it is worthwhile to dive in and deal with the mathematics behind the standard algorithms. That's a pretty heavy demand to make of someone with a solid background of "Yours not to reason why--just invert and multiply!" (no, I didn't make that up, but I wish I had!) So I was particularly impressed with the fact that even at 2:00 on a non-air-conditioned afternoon I saw no one whose response to the challenge to produce a diagram making sense of 5/6 divided by 2/3 was "I don't get it. Just leave me alone." Plenty of "I don't get it"s , mind you, but the follow-up was "You don't either? OK, let's see what we can do with it."
Another activity of the Institute was examining some of their own students' work with an eye to tuning in to the students' ideas. One piece of that was a discussion of how each level of student from kindergarten through 5th grade responded to "If five children share one pizza and another six children share an identical sized pizza, who gets more? Show me why." The degree of the participants' enthusiasm for that discussion was a commentary in itself on the fact that their professional existences contain absolutely no mechanism for developing a longitudinal image of the growth of their students' knowledge.
The rest of the time was spent on leadership, both the direct kind involving the DMI seminars and the indirect and far subtler kinds through which the rest of the community--fellow teachers, parents, administrators and interested bystanders--can be induced, enticed, persuaded, cajoled, or otherwise influenced to understand and appreciate the goals and means of this manner of teaching.
It was, as I said, very exciting. There's just one alarming feature to the situation: it's terribly easy, in the excitement of seeing something that good, to telescope the calendar, or pay lip service only to the time element involved. Even the teachers at this Institute are only starting to make changes in their own classrooms. And it's well over a year before this carefully supported exponential growth process will begin to reach anything like an appreciable percentage of the vast number of elementary teachers in the six districts in question, after which they will begin to commence the enriching but highly challenging process of classroom change. If we pull the manoeuver which is horrendously characteristic of America dealing with educational reform, we will say in two years, "I see lots of kids with no appreciable improvement in their mathematical abilities. The reform must be a dud--let's throw it out!" A thought so chilling I can't sustain it for long, so I shall go back to thinking about what has already been solidly accomplished. It may be small as regards numbers, but I think it's huge as regards impact within those numbers.
That's as many screensfull as I normally permit myself, but I have been exceedingly remiss in keeping you posted on the ongoing developments on the departmental teaching/learning front, so I shall go ahead and append an extremely compact summary of what has gone unrecorded.
For a start there were two excellent seminars neither of which I can report on directly because both conflicted with my teaching schedule. One was run by Judith Arms, and was in part a pilot of an NSF sponsored project to develop a series of case histories through which TA's can think together about some of the thornier aspects of teaching. I couldn't attend the meetings, but very much enjoyed being on the e-mail list for the comments, some of them very thoughtful, that the participants made on the readings before they came together to discuss them. Another was Paul Smith's continuation of his series of Calculus Education lectures by visiting speakers. I only got to one of those (it was on an off-day). Erik Mazur of Harvard spoke with the title "Education: Transferring information or engaging the mind? " I suspect he could rivet an audience with a lecture on the life cycle of the glow-worm, but in this case his subject was dear to my heart and I was in nearly complete agreement with his conclusions, so of course I thought it was just great!
I can report more directly on developments on the PFF front (lightning review: that's Preparing Future Faculty, and it's a project funded by a grant to the department from the NSF.) For one thing three graduate students spent chunks of time during spring quarter at Seattle University and/or Seattle Central Community College, observing classes and talking with faculty members. Each got a lot out of the experience, with the nature of the lot varying widely, as is totally appropriate to the project's goals. For another, one student (out of three who planned it, but that's another story) got to the regional MAA meeting in Vancouver. And for a third, a graduate student and I went to the Washington Community College Retreat in Wenatchee. She has since been awarded one of Highline Community College's internships for next year, which might well have happened anyway, but surely the PFF can share a little in the glow. And meanwhile I spent the time shuffling hats (PFF, WaToToM, Math 170,...) so frequently that my brain got a bit shuffled, too. Not too shuffled, though, to register a great deal of pleasure in the lively conversation and interesting people around me. And in fact not even too shuffled to finish by producing a limerick which a) was perfectly clean, b) contained a genuine mathematical pun and c) won me quite a nice prize donated by one of the publishers supporting the conference. Definitely a well spent week-end!