# Topology, Moore or Less

I get to teach Math 429 this semester.

This is the introductory topology course for undergraduates at Penn State – “point set topology” as the old-fashioned name would be.  I used to teach some of this material at Oxford but I have not had a chance to teach it at PSU before now.  I have about 25 students.

I decided to try a variation of a Moore method approach in this class.

So I started by showing the students the two-minute video above, which shows Steph Davis free-soloing and then BASE jumping from a Utah desert tower. Then I asked them, “Now you have watched the video, could you do that?”

No (duh)

“Suppose you watched the video ten times, or a hundred times, could you do it then?”

Still no

“Suppose you wanted to learn to climb, and Steph was going to teach you.  Would you expect that your learning would mostly consist of watching her do amazing things like you just saw?”

No

“What would you expect?”

Exercises. Practice. Being put on the spot. Having to climb stuff for myself – even if it is really easy by her standards.  Being scared.

“Why should the best way to learn math be different?”

That is the basic question that proponents of the Moore method ask.  Mathematics is a performance art; watching an expert mathematician perform mathematics, like watching an expert climber perform climbing, is not at all the same as doing it yourself.  In a Moore class the students do it themselves; they devise the proofs and present them, with the instructor providing an outline which may be no more than a list of definitions and theorem statements.

To this basic idea I’ve added the use of a collaborative TeX platform, Overleaf.  There is a book for this class, I told the students; the catch is that you are going to write it.  I have put the outline up as a shared file, and after a proof has been shared and agreed in class, the students who presented it have the task of writing it up in the book.

As a little extra motivation, the final exam is an “open book” exam…but the only book that will be open is the one that the students themselves have written.

We’re only a couple of weeks in to the course so far, but it seems to be going well.  It is hard work for the students (and for me!) but we all are enjoying it so far.

If anyone is interested in the detailed arrangements, here is a link to the syllabus.