This is mainly an AWM column preview, but before I get to it I need to burble a little while the burbling is good. A little background is required:
Somewhere out there is a person whose anonymity has been so well maintained that I know nothing of his identity except that he is a man. What I do know about him is that sometime in his youth he attended a summer math camp and it proved to be a highly beneficial experience for him. Also that he now has enough money so that he can afford to be extremely generous -- and he is. The form of his generosity that I am aware of is that he has funded the department to run a summer math camp for bright high school students for at least two years, with the only requirement being that we make it a really good experience for them. So we spent the year designing what came to be named SIMUW (Summer Institute in Mathematics at the University of Washington), and it is now in full swing. Twenty-four students, chosen by competition and recommendation, are residing in McCarthy Hall and living the mathematical high life. We have divided their six weeks up into three two week chunks, during each of which they spend four of the days with two professors (one morning, one afternoon) and Wednesday with two special speakers, some local, some imported. They are now finishing their fourth week, and I have had the good fortune to teach them in the mornings for the past two of them. It has been a phenomenal experience. I approached it with some trepidation, but it was definitely uncalled for. To be sure, they do want a challenge, and some of them think alarmingly fast, but when they polish off a problem they dive straight into a discussion of it, or set themselves to generalize it, or stand by to bail out a comrade who is hung up on it. They're bright beyond the need to put anyone else down, and beyond the need to cover up when they are a little muddled. In all, the kind of teaching that leaves one higher than a kite. And I think they really are having a good time -- not just judging by class reaction, but also by incidentals like the comment of one of the undergraduate TAs : "I've never been with a bunch that got such joy out of just hanging out in a mathematics library!"
And now on to the AWM column, about a different, and also excellent, teaching experience:
Sometimes the explanation for an event is that one thing led to another. This column is about a case where two things led to another - and a very good nother it was!
The origins of the situation go back to 1994, when four departments at the University of Washington were awarded a grant from the Pew Charitable Foundation entitled Preparing Future Faculty (PFF). The general idea was to broaden the horizons of graduate students in terms both of the importance of teaching and service and of the existence of good, solid academic mathematical careers at places other than Research I universities. With characteristic generosity, the Pew Foundation, having approved or our goals and general plans, left us a pretty free hand in carrying out those plans. We established a partnership with Seattle Central Community College and Seattle University, a four-year private university, and in consultation with their faculty spent the two years of the grant trying out a number of ideas. The really central one was to have a collection of graduate students visit our partner campuses for a full quarter, each observing one particular faculty member and spending time talking with her or him. Faculty members at our partner institutions were extremely generous with their time, and our graduate students benefited greatly.
Once the two years were over, we were never able to send students in the numbers in which we had done, but thanks to support first from the Graduate School and later from a second version of the PFF grant, funded by the NSF and administered by the MAA, we continued to be able to send a few each year for a considerable period. That period ended in spring of '02, when we were left with nary a trickle of funding from any source.
Meanwhile, in another part of the woods, a different development was occurring. Of the original bunch of graduate students who enthusiastically took part in the initial PFF project, a couple were certified movers and shakers. They came back to campus sufficiently inspired to want to delve further into the issues of teaching and learning that their experiences has raised. For several quarters, they organized a reading course. They asked a couple of us on the faculty to join them, which we did with pleasure, but it was unambiguously their course. Equally unambiguously, it was a success, which provided my colleague, Judith Arms, with exactly the ammunition she needed. She had been studying the issue of graduate needs unmet by our course offerings, and had arrived at the conclusion that a major gap was a course on the teaching and learning of mathematics. With that much evidence, she was able to persuade the department to vote such a course into existence, and it has been around (slightly sporadically!) ever since. And that was the combination that led to this spring's Math 503, in which in lieu of offering graduate students financial support for visiting and observing at other campuses, we offered them credit. Student response was very positive, and Judith and I had a great time co-teaching it, so I shall offer a sketch of a template and (below) a list of the readings and video that seemed to have the most impact, so that anyone whose circumstances are remotely similar can consider trying it. The key ingredient is connections with mathematics departments on other campuses in the area. In our case, we had begun making connections through the PFF activities, but over time we have established contact with quite a number of other institutions as well. We restricted ourselves to ones in very easy reach (it was a luxury to be able to do that!) and at each one asked if there were faculty members who were willing to be observed and then talk with our students. At every single one at least one, and generally several, faculty members instantly offered to take part. This pleased us so much that we immediately extended the observations planned. The resulting requirement was as follows: Students observed in pairs (or in one case as a trio). Each pair chose one class for their "major observation", which meant that they observed that particular class once at the beginning of the quarter, once in the middle and once at the end, and had a chat with its instructor each time. In addition (and not necessarily with the same partners) they did a "minor observation" of a single class on some other campus, again with a conversation to go with it.
The class met twice a week for an hour and a half. To offset the time commitment involved in going to another campus and observing and visiting, we cancelled several of the class sessions. Most of the remaining days we spent discussing a series of readings which Judith and I had selected with the aim of having them be provocative but not infuriating. Discussions varied in intensity and in depth, but we did note with pleasure that different readings engaged different students, and for most there was at least one reading that was really intriguing.
As a final project, each was supposed to write up a report on their primary observation. The projects made interesting reading. Perhaps the most interesting were produced by students who cut loose almost entirely from the expected (though expressly not required) format and discussed some aspect of their philosophy of learning or teaching. One, for instance, discussed the importance of trust, and another issues of involvement, interest and relationship in the classroom. On the other hand, others that stayed within the basic expectations produced some very clear-headed and very much to the point observations. One, for instance, wrote: "...enthusiasm is vital to the teaching of mathematics because it becomes a basis for creating an environment conducive to learning, as well as a starting point for engaging the students. The enthusiasm engenders respect, and as I observed ..., the respect for the mathematics was a platform for the ideas considered in the course, while the respect for the students was a foundation for the student-instructor relationships." Another reported, with some awe, observing a class where upon being told that they had "bombed" their test the day before, the students responded with questions like "Why do you think that happened?" and "What suggestions do you have for next time?" And another observed "She has a very gentle touch at getting the students to realize they made an error without embarrassing them, and to get them to figure out what went wrong."
The students came into the class with different needs and expectations. One who is nearing her doctorate, for instance, wanted to see what life would be like if she were to find a position at a small four year college. Others who are stopping with a masters and were on the brink of looking for work in local community colleges had a far more specific agenda. What they took away was correspondingly also varied, but each seemed to be able to find what he or she needed. And the lone undergraduate, whom we had admitted with some concern that his lack of teaching experience might limit the impact of the class for him, did a beautiful job of applying what he had learned from the readings and discussions as well as the observations to analyze the instructor's teaching and his own learning in the other courses he was concurrently taking.
In all, it wound up being an engaging and enlightening experience for students and faculty members alike. Although some aspects of the course were unique to our own situation, it seems to me that the underlying structure must be possible to reproduce at many other institutions. If I am correct, then my strong message to anyone considering trying it is: "Go for it!"
Readings: The second edition of How to Teach Mathematics by Stephen Krantz. They read the appendices, generally in contrasting pairs.
They're not Dumb, They're Different: Stalking the Second Tier, by Sheila Tobias
Punished By Rewards : The Trouble with Gold Stars, Incentive Plans, A's, Praise, and Other Bribes, by Alfie Kohn
Teaching and Learning Groups: Dissolution of the Atlas Complex, by Donald Finkel and Stephen Monk
Videotape: "Let us teach guessing", featuring George Plya. It was filmed in 1966 and is still available through the MAA.
Final comment: if you have any questions, or would like any details, by all means get in touch with me (warfield@math.washington.edu) or Judith (arms@math.washington.edu).