My first event was only semi-local, or even semi-demi-local, but I'll describe it anyway. On Veterans Day I gave a seminar on Didactique at the University of British Columbia and Rutgers University in New Jersey. Simultaneously. I'm sure there are many for whom the relevant chunk of technology is now humdrum, but I definitely do not number among them, and the idea that half of the class was living inside of a television monitor but could nonetheless talk to me did very interesting things to my nervous system. What saved the day was that the students both in and out of the box registered a nice interest in Didactique, and asked good questions. I just hope they learned anything like as much as I did from the experience!
To top up the unreality of the situation, one of the little figures in the Rutgers box waved and said "Bye, Ginger, see you tomorrow!" -- and did. Which leads us neatly into the next event, a very local one indeed. The figure in question, who emerged at full scale from an airplane the following day, was Carolyn Maher, and she proceeded to provide us with a very lively couple of days. Rather than divide things up into what she said when, I will give a general description of her work and why it is so exciting to hear about, and follow up with a bit of how and when we gathered to hear about it. Carolyn has led, for the past twelve years, a longitudinal study in which she and her colleagues worked with a bunch of kids -- regular, everyday, mixed-background kids -- from the first grade up until they graduated from high school. The work they did with them consisted initially of going sporadically into their classroom and turning the whole class loose on some challenging but accessible mathematical problem. What turned this into a research project was that while they were working in the classroom several video cameras were recording as much as they possibly could of the ongoing action. Also that at regular intervals they would have a more intensive interview with four of the kids, also videotaped. Then the research group spent hours -- many, many hours -- analyzing the videotapes. One of my favorite tales about that comes from a talk I heard Carolyn give years ago: sometime one July they were looking at a tape from the spring and watching a group of kids arriving with increasing solidity and conviction at an entirely correct solution to a problem that had been set them. Then suddenly on the screen the classroom teacher materialized. After one look, she kindly but firmly explained to the kids why they were wrong and what the "correct" answer should be. With manifest sincerity the kids all thanked her and expressed relief at having been straightened out. Clearly, to the intense distress of the viewers, they really believed her. When school began again, the research group nabbed the first opportunity to go back in with the same problem. Under their hawk-like gaze the group took up exactly where they themselves had gotten to, clearly absolutely oblivious to what the teacher had so kindly explained. There's a moral there.
Actually, there are a number of morals there and in the rest of the study. One is that children love to think and to solve problems -- and we're not talking just children of professionals. These were children in a blue-collar neighborhood school that was in serious academic difficulties. Another is that a relatively sparse (once every few weeks, as I understood it) set of opportunities to get their teeth into some good problems and really deal with them on their own can set students up for life as autonomous learners -- after graduation every one of the kids in the intensive study group headed off to college, including a couple to ivy leagues. And yet another -- and the illustration of this one came from a session at another school -- is that it is not necessarily easy for a regular teacher in a normal classroom situation to understand, much less foster, this kind of learning. We watched a tape of little fourth grader Brandon inventing the binary number system and recognizing a lot of its properties, and all reacted with horror to the fact that he was in the slow learners group in the class. But stop a moment and think about what it takes for someone who teaches mathematics, reading, writing, geography and not to bop the kid next to you over the head to recognize that the bizarre approaches one student takes are mathematically valid. (That's a loaded comment -- our DMI seminars are designed to help elementary teachers do exactly that!)
As is clear, I find Carolyn's work very exciting. So I am happy to report that she spoke on Wednesday afternoon to a packed house. This was one of our PFF socio-mathematical occasions, so the attending population was not only large but highly geographically varied. Not everyone managed to stay for the dinner that followed, but those that did included graduate students from at least three departments (notably, of course, mathematics) and faculty members from five or six UW departments and a whole batch of community colleges and universities in the area. Conversations at every table looked intense and lively -- I was frustrated not to be able to join a whole bunch of them.
Thursday's Brown Bag gave a chance for us to see how some of the same kids invented and dealt with a problem as high school juniors. Neat problem and nice discussion of it, but I think what impressed me most was the way one could see the foundations and even some of the vocabulary supplied by the problems we had seen them working on as fourth graders. Who was it that said that every problem we solve leaves a trail for other solutions to follow?
This is getting too long, so I shall gleep over all else to get to one last item: the Brown Bag on November 29. This was a locally grown one at which Judith Arms, Jack Lee and I talked about sundry non-standard modes of communication with students. The one that knocked my socks off was Jack's. By way of background I should say that I have been intrigued for years by reports on class formats that involve having students do their information absorbing outside of the classroom so that they can use the interactive possibilities of the time with the faculty member for more challenging elements of the learning process. Periodically I have tentatively dangled this on the edges of a conversation, and invariably it has received short shrift: "Students can't read mathematics." Full stop. Well, it seems that a reference Judith had come up with inspired Jack to give it a try. He was teaching a graduate course from a book he himself has just written, and he incorporated the assignment that once a week they were to read the next sections of the book and by N hours before class to send him two questions about the reading. And they did. The questions they asked were frequently very helpful to him in deciding what to emphasize and the students were definitely more with it in class. He's still adjusting to how to run the class time having, as he put it, given away the punch line on all his best proofs, but he is unambiguously and emphatically pleased with how the experiment worked out.
And on that cheery note I shall close and wish you all a very happy and relaxing holiday! --