This is the newsletter with which I annually cause great confusion. I wish to deliver it to A) all the folks on my regular mailing list and B) the Math Department so that newcomers can be invited to join the list. The problem is that no matter how I have phrased the introduction, a certain number of people in the intersection of those two sets have felt that they were being threatened with involuntary de-subscription. So this time I am doing two separate mailings. That means that some of you will receive a second copy right after this. Stand by to hit the delete button!
I am once again sending my editorial column for the AWM newsletter. I figure many of you do not get that particular newsletter, and those that do will probably have forgotten this by two months from now when it gets published.
For many years I have been helping graduate students learn to teach with a modified group discovery format. It has been a joy and a challenge and a huge learning experience for me. I have developed tactics for working with the timid and the brash, with speed demons and plodders, with scrawlers and with people who let their concern for a neat board interfere with the mathematical content. One category, however, has completely eluded my efforts - the ones who don't listen. I'm not convinced I ever help them. Well, perhaps I help a little in the most benign cases, where the issue is a cheerful assumption that a half-heard answer is the correct one (splendid reinforcement for mumbling!).
A prime teaching need is the ability to listen for the sense behind a student's somewhat muddled question or answer, which is an art that can really only be developed from within by someone who feels the need and desire to do so. For those who feel neither, a question posed to the class tends to represent a tray being held out for someone to put the right answer on, and incorrect answers are allowed to drop to the floor. It is hard to tell who is the more exasperated in those cases, the instructor at the board, waiting and waiting for the intended response or me at the back, watching the barrage of dropped opportunities to learn what the students understand and what they don't, and to observe the impact of the choice and phrasing of the question itself. On rare occasions I can find a marginally helpful comment to write in the notes I am taking as a mentor. More often I sit and resist the urge to write "LISTEN!" which is about as productive as shouting at somebody to RELAX!
It is probably as a result of working with these decades of graduate students that I have become conscious of the degree of influence of the presence or absence of genuine listening. On a conversational level, I have heard someone accused of having two modes of conversation: talking and waiting. My amusement was accompanied by a wince, because I am sure that description sometimes applies to me. At a larger level, it seems to me that a lot of the quality of functioning of a university department or any other community is determined by how well the people within it listen to each other. And at yet another level, reverting to the topic of a previous column, a lot of the acrimony in the "Math Wars" results from a tendency of too many of us on both sides of the issue: instead of listening to each other, we listen for statements we can refute, or even ridicule. This is not helpful.
I make no claim to originality with this thought. In fact, with very slightly different labeling, it is the central idea of a whole new trend in professional development for teachers. The earliest representative of this trend, and the one with which I am best acquainted, is the "Developing Mathematical Ideas" project. It originated with Deborah Schifter and Virginia Bastable as the Summer Math staff at Mount Holyoke College, and is being enlarged and produced with support from the Educational Development Center and published by Dale Seymour. It consists of several planned seminars for elementary school teachers. At the heart of each seminar is a collection of case study video clips or transcripts and a structure for leading teachers deeper and deeper into a discussion of just what a particular student understands and what kinds of partial understanding might lead to the confusions and errors observed. From there the next step is to consider what more there is for this student to learn and what further questions or problems might challenge and extend the student's current understanding. With the support of an NSF grant, we have been running these seminars in the Seattle area for the past three years. I have thus had the opportunity to listen in on a great multitude of groups working their way through the seminars. To me, one of the most exciting things is watching the teachers as they begin to take the listening skills developed through the case studies back into their classrooms and use them with their own students. The impact is both profound and inspiring.
All this was recently returned to the forefront of my consciousness and brought into focus by yet another graduate student. I had the good fortune to be on the Masters Committee of a young woman in the Mathematics Department who chose an unusual direction for her thesis. She was taking part in one of the NSF's GK-12 projects, which meant that part of her support for the year came from spending time working with teachers at a nearby elementary school, and in particular regularly being in a sixth grade classroom. She took on the challenge of trying to get the class to do some "genuine mathematical thinking."
The classroom teacher kindly allocated her four days, and she chose her topic, produced (with due agony) a set of lessons, and launched the class into them. Very little worked the way she expected it to, but a number of the surprises were good ones, and the class clearly did some good learning. What impressed me most, though, was the amount of learning the graduate student did -- and she did it by listening. First she listened to their immediate responses and adjusted upcoming lessons accordingly (a basic, but alas not universal, occupation.) Then she listened to their tones of voice and recognized when bravado was covering a refusal to think, and when a particularly muddled explanation represented a break-through happening. Then she listened to the overall tone of the class and recognized the place where an outburst of giggles and pre-adolescent humor resulted from an incomprehensibly written question.
As I said, her listening resulted in huge amounts of learning. Now I have to admit that some of that learning happened on the fifth or tenth time of playing back the tapes she had recorded during the classes. This is clearly not an option as an everyday procedure. On the other hand, she wasn't using anything as high tech as a video camera - just a plain old audio recorder. I wonder how many of us might profit from taping an occasional class and then listening to it afterwards. Really listening!