What have I learned?

When I planned this trip  I suspected that all the college visits would be different. Simply because the people I got in touch with would interpret differently what I was interested in and what questions I tried to find answers to. And the visits have indeed been very different.

Let me say that it all have turned out to be way over my expectations. Very much because the kindness and friendliness I’ve been met with.

This is a short run through of the trip and what has characterized it. First I went to Beloit College and stayed there a week. In a way it was a leisurely week, but it was a perfect start. I went to classes, had conversations and in an unhurried way got used to the college milieu. The nervousness I had felt (and I’m very seldom nervous) evaporated. So I was well prepared for the second week at Carleton and Macalester. This was entirely different. I was scheduled from 8 am to 10 pm for four days with classes, conversations, meetings, lunches and dinners.

The third week included Oberlin College, which apart from conversations and classes also included a lunch with maths majors. So I got a student perspective, although a special one. The third week also included my short visit to Bryn Mawr where I gave a talk. The subsequent discussion, where I just listened, was highly interesting as I’ve reported in another post.

The fourth week, I went to Bennington College (which I wrote a post about just the other day). This was different, both as regards the teaching and the contents. A hint of humanistic mathematics in a liberal arts setting? Furthermore at Skidmore College, I began to see other hints of humanistic approaches to mathematics although it is not labeled explicitly as such.

Then I went to Maine for the fifth week. At Colby College I talked to nine professor in the course of one day. Very intensive and impossible to remember it all, but I remember at least three complementary (and partly new) answers to my key question (see another post about this that I will write shortly). Then at Bates College I discussed humanistic mathematics with Bonnie Shulman (reported in another post).

At this stage, as you may very well imagine, I was a little tired. With one week left the trip was drawing towards its end. And had I found what I set out to find? Had I found examples of humanistic mathematics at Liberal Arts colleges? Not really. Had I found dramatic differences as compared to mathematics taught at other schools? Not really, to the extent that I could judge. I became awkwardly aware of the fact that now, knowing a little about mathematics teaching at Liberal Arts schools, I knew nothing about teaching at other schools, not even in Swedish schools. So how should I be able to compare? It seemed that my vaguely formulated hypotheses were proved wrong. The project looked like a failure.

With these dismal thoughts in mind I went for the two last visits. I met with Rob Benedetto at Amherst on Monday. After a brief chat I sat in on his Calculus class. Then something dawned on me that had been implicit for some weeks. I had sat in on many classes, quite a few of them Calculus.

I now realized that what I had been observing was mathematicians teaching mathematics! Not theoretical physicists, or physicists, or engineers, or whatever, but real mathematicians.

That makes a difference, so subtle that I have to devote a separate post to it. But the thought that appeared in my mind was: It flows so easily from the pen.

I went to lunch with some of the faculty at Amherst and then I had a conversation with David Cox. More pieces of the puzzle fell into place.

Today I’ve been to  Wellesley College and met Stanley Chang. I also had conversations with Alex Diesl, Andy Schultz, Ismar Volic, Oscar Fernandez, Jonathan Tannenhauser and Karen Lange. I now understand what we see at Liberal Arts Colleges.

We see mathematics taught humanistically. Notice the distinction: Teaching mathematics humanistically and/or teaching humanistic mathematics. The first focus on the way the subject is taught, the second on the contents of the subject. These things naturally overlap to some extent, but there is shift in focus. This so important that it will be the topic of a separate post.

So the project has not been a failure after all. Gradually I have gained an understanding of what I have seen and heard. And I have seen and heard a lot. I’ve been to 11 colleges. On average I went to 3 or 4 classes at each college and talked to an average of 5 professors at each (I will add up the exact statistics). As I’ve had pointed out to me, that’s probably far more than anyone else have done. I’ve been immersed in Liberal Arts mathematics for six weeks.

Thus it has ended on a happy note. I will use the coming few days to begin summarize it all and try to draw conclusions.

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