Many people have told me that videotapes can be put to excellent use in a classroom to generate discussion. Myself, I have never managed to pull it off, but Thursday's Brown Bag certainly illustrated the point nicely. We watched a videotape on Interactive Learning in Large Classrooms, which had some interesting points (of which more later) but what really sticks in my mind is the discussion that followed. For one thing, I found out that a variant of one of the techniques mentioned went on right before my very nose without my being aware of it: last autumn Don Marshall had his Math 120 class do their homework in groups of four, with rotating responsibility for writing up the solutions and for being the one to go ask questions when the whole group bogged down. Ken Plochinski said the results were very clear in the Study Center--lots of very lively study groups. Don reported one clear up-side: feed-back from the grader on four times as many problems, and one unresolved down-ish side: while most groups seemed to function well, there were, of course, some that didn't, and individuals registered a wish that they could get out of their group. Since the groups were self-selected, and scheduling as well as social issues were involved, that was hard to get a handle on.
Another place where local knowledge came into play was in a discussion of how to raise student's perceptions of the underlying concepts, so that they don't lose them in the process of working things out. Chris, from the Physics Education Group, filled us in on how they address a number of such issues. Some were out of our range--functions of their really impressive educational research structure--but others were more imitable. In particular, they frequently launch their lessons with a pre-test designed to be understandable but largely unanswerable before the lesson, and answerable thereafter. That carries a message, all right.
Another point that went by without comment, but I think largely because it was more something to think about than to debate, came from Anita Lenges, who is launching an education doctorate while on leave for a year from teaching seventh graders. While we were registering some doubts about our students' capacities to work productively together, she pointed out that if they can't, perhaps part of our teaching job is to improve their abilities to do so. Obviously, that aspect of the teaching role doesn't carry the dominant aspect for us that it does in a roomful of (heaven help us) early adolescents, but its relevance can hardly be questioned.
OK, back to the film itself for a brief review. We saw five different professors at the University of Cincinatti using a bunch of different techniques to engage students interactively. The first was an incredibly high-tech arrangement involving individual mini-computers at each desk and a read-out of their results on the professor's desk, with a bar graph projected onto a screen so they could see their result. A bit overwhelming. This made me appreciate the fact that the first thing we saw of the next professor was his "question box" which looked to me like a kleenex box covered with construction paper with ??s on it. Students put in their questions and he covered them in the next lecture. All of the tactics included in one way or another generating group discussions among class members, whether in the large classroom (I was impressed that one class of 240 was in a room whose desks appeared not to be nailed down) or outside of class or, in one case, in small groups instead of class. There were many references to the current research indicating that real learning can't go on without active engagement--in effect, there is no such thing as a passive learner. One professor's take on the matter was that lecturing is an active learning situation--for the lecturer. I got a little anxious in spots, because one could draw the conclusion that we should all be going around with our mouths taped shut, which is not what they or anyone else intended us to deduce. But that remark, suitably interpreted, provided very nice support for the idea which, of all of them, I would be most interested in seeing us pursue: one of the professors had arranged to have a small flock of advanced undergraduates who had previously taken his courses assist him in the big introductory one. They joined the small groups in the classroom and helped guide their discussions and lead them into asking themselves the right questions. Payment for the advanced students was in credits (Chris says Physics does that, too) and they have a manifest educational benefit from it. I have certainly met a number of our undergraduates who could do a crackerjack job with that.
I shall now pull a total change of subject, to follow up on a
previous report. A couple of months ago, I reported on a Brown
Bag in which Loyce Adams described Applied Math's
Clinic seminar, which takes on a huge variety of problems. The
problem they had most recently taken on was to do a report for
the North Shore School District to help them in the process of
choosing between two new curricula. That report has now been delivered--many
pages, beautifully done and enormously appreciated by the teachers.
That, of course, pleases me a lot--particularly since the initial
contact which led to this came through our CCML.
But what pleases me almost more is that one of my pet theories
has just been shown to hold true. I think we all know that the
K-12 system needs our help, and many of us, shown a certifiably
useful way to get involved, would be willing to do so. What I
have known for a while but been unable to convey is that this
involvement, besides being good for the conscience, can be just
plain fun. No one who listened to the conversations in the halls
of Guggenheim over the past couple of months would question that
statement any more.
I shall finish with a brief quotation. This quarter my students are sending me e-mail follow-up reports after each class, and one of my students in Geometry for Elementary School Teachers came up with a comment I thought was magnificent:
"It is always good to know how to solve a problem but it is fantastic to know why that solution works!!!"