My differential geometry course has been an interesting experiment so far. I decided that my aim for the course would be to put the students in a position to practice the skills to handle this situation:
You have a subject with a lot of literature. How do you learn it? How do you structure your own approach to the material? How can you be sure you have learned something?
This involves handing over the reins to the students completely. “Here is differential geometry of curves and surfaces. Go learn it.” To be fair, I knew it wouldn’t really work that way. So here is what I planned before the term began:
UNIT ONE: Differential Geometry of Curves in Space
- Assignment One: spend a week trying to get a big picture view. Make an outline of what seems to be essential, core material. Maybe note a few advanced topics for later study. At the deadline, we negotiated a common class syllabus.
- Assignment Two: Spend a month learning the basics. To enforce some standards, I asked them to produce the following things:
- a “Book Chapter” write up of the mathematics on our basic syllabus,
- a selection of “standard exercises” and their solutions to complement this chapter,
- a “demonstration piece”–this is something visually oriented that highlights some concept from the basic syllabus, and
- a proposal for an advanced topic to be worked out in the next three weeks.
- Assignment Three: complete the agreed upon advanced topic and share work with the class.
UNIT TWO: Differential Geometry of Surfaces in Space
…repeat all of the above for surfaces.
I knew this was a challenging thing to ask of my students, but I still wanted to do it. To help them a little, there was a time line for rough drafts of the pieces of this big project. no student met any of those. So it wasn’t too big a surprise when the final due date came along on Friday that things were in a sorry state. No amount of cajoling could convince them.
Attendance was terrible. When they had questions, we had wonderful discussions. But I don’t get the sense that they were making a reasonable schedule for themselves to keep pace.
So, things have to change. We will muddle through the first unit. I have given comments on the half completed projects, and they are due (again) on Friday. I hope this makes a difference.
In the second unit, I will structure things even more tightly. I hope that this helps them see how to pull this all off. If anyone has advice for what to tweak, I am all ears.