My numerical class finished up the second (and final) week of student projects tonight, and I am still very pleased. So are the students. They told me they enjoyed it. I enjoyed it. I learned about a number of things that I hadn't before, including some tantalizing glimpses into topics such as the use of quaternions in computer graphics and how GPS works.
I had good students, and I think I structured the assignment well. Early in the semester, I asked everyone to pick (separately or in groups) a tentative topic one week as part of their homework. The next week, I asked everyone to find three sources about their topic. Next came a brief outline, and I started meeting with the students in their groups. We met about once a week, and I think it made a real difference. I got to find out what was going on and direct each group of students a little more each week, refining and refocusing their work. Most of the projects needed to be significantly reduced, but sometimes they needed redirected, too.
Over the past two weeks I also watched each group show me a practice run of their presentation and made some final suggestions for improvement. You know what the number one suggestion I had to give almost every group (including my very best students)? "Make sure you start by telling people what problem you are trying to solve." It was an odd sense of deja vu when I watched each new group during the practice presentations dive in and start explaining how to carry out, say, the Wronski-Schwarzchild Decomposition Algorithm,* without ever mentioning what the algorithm was supposed to accomplish. But this is why asking to see the presentations first is such a wise idea (for anyone who plans to do this); I got to let the students know that they ought to discuss such things. And to my delight, I found that the students by and large took my suggestions when they actually presented to the class.
It's been a good few weeks for this class, and we'll be off next week for Thanksgiving break, so it will be a while before I see them again. It was a good place to take a pause.
*Yes, I just thoroughly made this algorithm up. And it was fun. Although I had a friend who came up with the idea that, should he ever develop some new mathematical operation which he got to name, he was going to call it the "Poopyface matrix," which I also like a lot. I think that also shows that he's funnier than I am.