As the term gets underway, I’m working on a number of projects trying to address some of the issues that I discussed in the Looking Backwards post… I was chatting with Thomas Mawora yesterday, listed off all the ongoing projects I could think of, and came up with five. (Or up to seven, depending on how you count it…) It’s a lot, but luckily there’s a good deal of overlap, so work in one place often helps another project move forward. If you’re going to spread yourself thin, you might as well be maximally efficient about it.
Seminar
Looking Backwards
The term has come to a close, finishing the first half of my Fulbright year, which provides a bit of time to look back over what I’ve done, what’s worked well, and what’s worked less well. A big part of the plan for the first time was to try out the existing structures, get to know what’s going on in the university, and figure out interesting ways forward that might work in the local context. There were a lot of failures this term, places where things didn’t work as expected, where it’s clear that things need to happen differently next time around. So if this post sounds bleak in some ways, rest assured that I’m already working hard on projects for next term that will try to get around these difficulties in one way or another.

Teaching FacetoFace
Despite my mandate to work on electronic education, I felt it was very important to teach a facetoface course in order to better understand the undergraduate students and their context. To that end, I cotaught Foundations of Mathematics with David Stern.
The course went reasonably well, but has definitely made me consider the degree of work necessary to really address the problems in the education system. We were working with firstyear students, which is ideal in many ways. It’s easier to do something revolutionary with firstyears, simply because they haven’t lowered their expectations too far yet. (This was true even when I was teaching at the University of California; the firstyears are a lot more open to nontraditional techniques, simply because they expect University to be different from secondary.) Continue reading
Computational Problem Solving Workshop
One of the things that we believe strongly is that there needs to be better use of computers in math education, in part because computers play such a huge role in how math is actually done these days.
To that end, I ran a oneday workshop on mathematical problem solving using Sage today. The idea is to run this workshop as a kind of seminar series next term, once we get back from South Africa, and today served nicely as a dressrehearsal. The students who came today were all in firstyears in computer science; it should be interesting to see how things play out with math students next term, who haven’t necessarily been exposed to the programming side of things as much.
Here’s how things went down:
Teaching, teaching, teaching….
Yesterday I spent five hours in front of a board! Getting some good honest work in… Two hours of normal class,doing the Foundations of Pure Math course, two hours of seminar, and an hour making a video lecture for the algebraic structures class.
Here are the videos for the algebraic structures class; it seems like a nice deliverable! It’s for the first section of the notes, which gives an introduction to the definition of a group, along with a bunch of examples.
Group Definition
Integers modulo n
Permutation Group
Dihedral Group
General Linear Group
The videos were shot in David’s house; the clipon microphone that I picked up last year all but eliminated the terrible echo in the room. On the other hand, there’s a good bit of noise in the audio, which it would be great to figure out how to eliminate.
Groups, Groups, Groups…
Lots of teaching things going on right now! David and I were tasked (with extremely short notice) with developing an online abstract algebra course (entitled ‘algebraic structures’) for secondyear undergraduates, and have been hashing out a good direction for the course to take.
One of the main things we realized (in a few hours of back and forth) is that the usual first course in abstract algebra probably isn’t really locally appropriate. This is largely because we can’t be assured that the later maths classes — which hook abstract algebra into a wide variety of different contexts — will ever be available to the students. The other big idea we came up with is that it would be great if we got students to the point where they could look at a mathematical problem and find the influence of algebra, and (in a perfect world) craft solutions to the problem appropriately.