Thinking Outside the Box

July 17, 2000

From the SIAM President
Gilbert Strang

I am writing this in a quiet time before SIAM's Annual Meeting in Puerto Rico. Normally quiet is good, but now I see why columnists hope for a war of some kind---we get desperate for something to write about. Forgive me if a big part of this column comes from my personal teaching experience (I have got myself into a box and don't know what to do in the linear algebra lectures this fall). This is a chance to think about education on the Internet.

First I can include a brief report on the Mathematical Theory of Networks and Systems conference, which just ended. These MTNS conferences are held every two years, this time in France (Perpignan). In between there is no office and no MTNS society, only a new organizer and a steering committee. The conference was extremely pleasant (SIAM News will mention the next ones, planned for Notre Dame, Belgium, and Kyoto). I was generously given a chance to speak about SIAM, and I mention here two points.

First point: SIAM's mission is to support applied mathematics unselfishly, in all ways we can, including MTNS and so much else. The second is important too: Individuals win by joining a society like SIAM. Journals may be freely accessible and meetings can be planned without the backup of a society, but we all benefit from what SIAM does and it needs our support. It works hard internationally, and every member who joins becomes a part of this wide and constant effort. You contribute to something larger than a lab or a department; it is a cooperation that is crucial to the future.

Now to my teaching dilemma. This isn't about pedagogy (I never have time to think properly about education . . .). Still, some kind of "philosophy" underlies the way I teach. Most students are interested first of all in the applications. I get a lot of pleasure from showing them examples, connecting with their own interests, and convincing them that mathematics is directly useful. It is true that I use the words "beautiful" and "wonderful" to call their attention to ideas that are especially neat. But the beauty is alive, not frozen, and the only theorem mentioned by name is the "fundamental theorem of linear algebra." I would not want the rest of the faculty to know how seldom I complete a proof in class.

Here is the recent event that presents new problems. My linear algebra lectures and review sessions last fall were videotaped live. They can be found on the Web at and viewed with Real Player software. The compression makes my motion a little jumpy, but the blackboard is surprisingly clear. So students now have lectures available whenever they want them, and you will realize the implications. They can safely skip more classes (me too). Let me come back to this new freedom, which is partly desirable and partly alarming.

I can explain about the videotapes. The year before, when Gian-Carlo Rota died so suddenly, I expressed to the class my regret that we had no permanent record of his lectures. They were exceptional in every way. The discussion moved toward more ordinary things, but several students e-mailed me after class. They suggested that I contact the Center for Advanced Engineering Studies, which was embarking on a large video project in physics. Eventually we realized that for a small additional cost, the cameramen could stay in the lecture room and tape the 18.06 lectures. This was all a part of MIT that I had never seen.

I insisted on only one point: The lectures must be freely available to everyone. Modulo congestion on the Web (which depends partly on the viewer's modem), this is now the case. I had no idea what use might be made of the tapes---it just seemed a good thing to try. I still have no idea! Readers of this column are very welcome to make suggestions. I can mention two developments within MIT:

  1. In the semester of videotaping, there were classes that I had to miss. Those tapes were made in advance without an audience. The class could have had a substitute lecturer but chose the tapes. Apparently they did come and watch quietly.
  2. The MIT Lincoln Laboratory learned about the tapes, and decided to offer a linear algebra course this summer. The volunteer students are mature scientists and engineers, who watch two tapes each Thursday afternoon. Peter Clifford, my best teaching assistant, is there to answer questions---and I went twice. I frankly thought it would be a horrible experience to watch the tapes with the class, but it wasn't. They are seeing the uncompressed form---not so different from a live lecture. The group at Lincoln Lab continues to attend, with positive comments (and no grades).

I now realize more clearly and urgently that students will have an alternative to attending lectures this fall. What to do in class, when they can watch the videos at their convenience? Certainly I will vary the examples. I can't vary the mathematics, but perhaps we should experiment with the format. The lecture hour could become more interactive (subject to the limitations of a large class). I am very much in favor of "active learning," with questions mixed in as I go (not always waiting for the answers . . .). Students hesitate to stand out in a large anonymous group, but I have read about the successful use of flash cards and class votes.

It will not be possible to assume that students have watched the lectures in advance. Do I want to assign specific tapes as part of their homework (and risk that they will get in the habit of skipping class)? Of course I hope the tapes will be a complement to lectures and not an alternative.

The new situation offers more freedom, but with it come change and uncertainty. Every innovation implies an altered set of rules. Most definitely, students have learned to deal with the old rules. After long acquaintance, they more or less accept those rules as fair. Any alteration implies that somehow or somewhere, an extra effort is required. This is not so welcome. I have no means of compelling students to attend class, and don't want any. I do try to make the hour more productive than an hour spent reading the textbook (which unfortunately I wrote). I was already competing with myself, and now even more so! I had offered a focus on the important points, with the medium of speech to emphasize them, but now the videos offer speech too. Will a live lecture three mornings a week be preferred to tapes that can be seen at any time night or day? I really don't know. Perhaps in the short run, the lack of anything better to do will bring most students to the classroom.

And there is another question. Could the tapes affect linear algebra classes around the country? I am hopeful that instructors might use them as a supplement to their own courses. I took this videotaping step in the belief that it could only help---not knowing exactly how, but certainly knowing that lectures on the Web are sure to come. They will come in different forms, from many sources. If summaries and additional examples would be valuable, they could be added. First I hope to learn how these videos can be used. I will be grateful for any thoughts and suggestions from readers.

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