As Elias Toubassi finished off today's Brown Bag with one last development from the University of Arizona, the closest I could come to an adequate comment was "Wow!" That still seems to me to sum up the situation, but I'll see if I can supply a few details to substantiate it.
The origins of the current state of affairs can be traced very neatly and precisely to 1983. That was the year that the administration of the University of Arizona decided that the teaching situation in the mathematics department was really terrible and something needed to be done about it. The reason they decided that, says Elias, was that the teaching situation in the mathematics department was really terrible and something needed to be done about it. The student course needs were so overwhelming that the department had been reduced to teaching their business calculus in sections of 600, and their pre-calculus algebra as a "self-paced" course (the learn a module, pass a test, forget that module and start the next one format.) The only tenet they had managed to maintain in this embattled state was that calculus would NOT be taught in sections of more than forty. Even there, though, the attrition rates were huge (albeit not as spectacular as in the other two) because the placement test had no teeth--it was strictly advisory and students signed on for whichever course they were in a mood for.
Enter the Provost's Outside Examining Committee, consisting of a number of faculty members from around the campus. They duly inspected the situation and made their report: "Yup. It's pretty awful. Furthermore, on the resources you guys allocate to that department, there's no earthly way it's going to get any better." And the Provost, by golly, responded. The next year they were funded to run a couple of sections of actually taught pre-calculus, keeping lots of data in the process, and to propose a convincing long-range plan. The data were highly encouraging, and the plan was duly accepted. It involved teaching everything in small sections, for which they hired some additional regular faculty members, some additional TA's and scads of temporary faculty members--the last a point of discomfort then and now, but one on which they have made a fair amount of progress. Next they re-vamped and tightened up their placement tests and made them mandatory and binding (with an appeals committee to loosen the bind a tiny bit). But this, as it progressed, brought to their attention the fact that high schools around the state who were sending them their students wanted and needed and deserved to be kept informed about their expectations. So they set up various forms of communication, the most notable being a system whereby each year a small bunch of high school teachers spends the entire year at the university, teaching some sections and taking some courses and being part of the departmental community, while the university sends replacements into their classrooms for the year. [This model, by the way, is one which Don Marshall and Dave Collingwood have been laboring mightily to set up here at UW.] A spin-off of this has been a considerable enlivening of the teaching/learning scene, because the teachers selected for the program are exactly the ones who have interesting thoughts to contribute to discussions in that area, with the result that what started as a dutiful response to the obligation to set up courses for the teachers during their stay has developed into some seminars and colloquia which quite a number of faculty members find highly engaging. Most recently, this ferment has produced a new format of doctorate--two people who have completed all of the course work and examinations for a mathematical research degree have then written theses in educational research, and been granted Ph.D.'s through the mathematics department. No, not all of the faculty members are thrilled by this development, but their collegiality has weathered that and the various other inevitable strains of change.
Meanwhile, having discovered the possibilities and benefits of communication with the outside world, the department has gone on to involve itself with middle and even upper elementary schools, and, having established its credibility, has received four (4) NSF Teacher Enhancement grants. Not small potatoes. It is also in the process of establishing a new form of Post-Doc which will offer new Ph.D.'s, especially those whose career goals are directed more towards college teaching than university, a chance to build their teaching skills and experience. It is one more tack in dealing with the "temporary faculty" issue and is being thoroughly supported by the administration.
One interesting development which somehow hasn't fitted into the story so far is that somewhere along the line, after the placement test had begun sifting out the students who really didn't belong in calculus in the first place, they realized that they still had a huge spread. So they made a two-tiered system: students who look as if they have a really solid background can take it three hours a week, and the rest (some 75%) have to have five hours. The ground covered is the same, it's just a question of how much detail-filling and hand-holding they offer. And the three hour one gets just three credits. Interestingly, where one might expect a flow of students into the easier going, higher credit option, the petitions almost all run the opposite direction. It's a status thing.
And all of that, I suspect, is simply the tip of the iceberg. There's just a huge amount going on down there. I said as much to Elias after the Brown Bag, and he concurred, and it was clear that the scene, of which he has been a part since the very beginning, gives him great pleasure. But what he emphasized most strongly was that it has all evolved as it has gone along--it didn't spring fully armed from the brow of the original planning committee. It's a matter of developments leading to opportunities, and opportunities to new developments. And who knows what the next ones will be!
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At the risk of sending you all into culture shock from the change of scale, I want to finish off by reporting on a recent local event. Last week-end I had the privilege of attending a Colloquy on Collaborative Learning sponsored by the Offices of Assessment of Washington's various universities, at the Sleeping Lady Retreat Center in Leavenworth. For a start, let me say that if you get an invitation to attend a conference there, you should definitely accept it. Never mind if the conference is on the wormcases of slimipherous larvopoli--go anyway. It's quite a place. And, more to the point, the Colloquy was terrific. For me, aside from a whole bunch of good conversations, the high point was a session on Physics Education run by Lillian Macdermott and company (lots of company--a really impressive number, including TA's, post-docs and faculty). We actually got to carry out one of their inquiry tutorials, complete with light bulbs in sundry shapes, and holes in different shapes to shine them through. It was a magnificently tailored sequence of questions leading to a far meatier conception of geometric optics than I had ever had--a sequence whose development, refinement and testing constituted an appreciable portion of a doctoral thesis. Needless to say, it came complete with a good, crisp set of assessment data, at least as far as the concept itself goes. Further assessment information of what sounded to be a convincing, if perhaps less formal, nature involved the question of whether turning one of the course's five lectures per week into one of these tutorial sessions diminished the information intake of the students: it appears not to. What they didn't have time to discuss, and I would some day very much like to, is whether they have come up with any means of assessing the non-subject-matter benefits that seem to me highly present in the tutorial format: increased autonomy, improved communication skill, piqued curiosity. If you're going to be thinking about assessment of collaborative learning, it is an issue which produces what Jerry Gilmore referred to as a high level of interocular trauma--it hits you right between the eyes.