Two weeks after Columbia Splash, I taught at MIT Splash! I taught the same two courses, Mathematical Modeling and Introduction to Hungarian Through Song.
Thoughts on how the classes went are below the fold.
I started the class the same way that I had at Columbia, with the problem about choosing a computer from the GAIMME report. It was still shorter than I expected, but it was about the same as last time. Students came up with looking at just performance or just ease of use, looking at the sum, or looking at the product. I had to prompt a lot to get the idea of a weighted sum, which surprised me. I also mentioned distance from (0,0) or (10,10). (I had tried to prompt those with “what would the worst/best imaginable software be rated?” but didn’t get anywhere.) Unlike at Columbia, the computer problem didn’t generate any questions or conversation, which was disappointing.
I then explained the food truck problem and the newt problem and had the students split into groups. There were two groups of four and one of three initially. Two of them jumped into the food truck problem. One group started on the newt problem but they weren’t really working together; it was mostly one person working. One or two others in the group were maybe thinking, but when I went over to talk to that group it was always one person who answered.
Two people came in late (after groups formed), so we ended up with two groups of four and a group of five. (People have told me that modeling tasks like this don’t work well in pairs, so I wanted to avoid that, and it seemed awkward to split up existing groups.) The group of five was too large and by far the least engaged group, and the person who was the fourth in what had been a group of three was never well-integrated.
I had told the class that I’d interrupt them and have them talk to people in other groups after thirty minutes. I stopped them at twenty minutes instead to try to get ideas moving again, but not many students bought into that. A couple of people had already been cross-talking about newts and that continued, and a couple of others found someone from another group and talked, but that was it. I was able to get everyone together to write a good summary of different approaches to the food truck problem on the board as well as some first observations on the newt problem.
This class tackled newts totally differently than my Columbia class did. They started looking at linear regression and fits immediately. When they got a bit stuck there (the data is pretty sparse and not remotely linear), I told them to look for patterns in the newt population before there were any crawfish. The response was still to plot the data; they found that it looked sine-like and tried to fit in Desmos. A different student called it out as a seasonal cycle during the discussion, but no one was looking at ratios of the populations across months, and the students at Columbia had jumped to that really quickly.
It felt like people were a little stalled, so I proposed a couple of other variations to the food truck problem (multiple trucks, which I hadn’t thought about before but should be interesting) and put up the elevator problem from the GAIMME report, which is more vague and feels like you’re lacking in information. One person and a group of three made some headway in at least thinking about the elevator problem, but I hinted about different elevators being able to go to different sets of floors. (Based on the backgrounds of students, that’s something I expected to have to prompt, though.)
I didn’t feel like I had good control of the classroom for about half of the time. I’d like to learn more about how to support the modeling process better — how to actually teach modeling and not just give modeling problems. On the survey, one student commented that class was a bit chaotic, which was absolutely true. In class, one student had mentioned liking how relaxed it was. Instead of having a lot of information thrown at them (a la “drink from the fire hose”) it was just interesting problems and time to think and talk about them.
One student wrote on the survey that the problems were really open-ended, and they would have liked comparing their solutions to an accepted model. That’s not an encouraging statement for me about how well I communicated the modeling process. It does make a good point, though; there’s no validation built in here (which I’m used to having as part of the modeling process), and I’m not sure what kind of validation you would do for some of these problems. It is a bit unsatisfying. When I was first thinking about this kind of class, I wanted the groups to present at the end (just for a few minutes) for some kind of closure, but with how hard it was to get any communication outside of groups I never tried that.
I’m not sure that the computer problem is really doing what I want as an opener. It’s good for providing the idea of defining the question, and it is accessible, but it doesn’t seem to build up the idea of what the modeling process looks like. Here’s an idea for a new way to open: I pose a problem and present two solutions as “models people came up with.” Both solutions should be strong and interesting but non-trivially different. I then ask the students to vote on which they like better and ask a few students why. I can then ask how we could improve/add complexity to each model. That might provide a better sense of the idea that there are many good solutions and that part of the process is iteration.
Only three students responded to the Splash survey about the class, but of those three, two rated the difficulty as 4 and the other as 2. I’d assigned the class a 2. If I teach the class again (which I’d like to), the difficulty is something I should maybe consider adjusting.
Another aspect of the class I’m wondering about: what would happen if I made this a one hour class instead? It would give people less time to work and doesn’t feel like enough to me, but the tightness might help.
Overall, this felt like it didn’t go as well as it did at Columbia, which was disappointing. I have some ideas for the future, though, and I’d like to try it again. I probably won’t do it at Spark in the spring, though; trying to make the changes I’m considering and adjusting for a middle school audience seems like too much.
This class went really well overall. I had three students again (twelve had been pre-enrolled, but it was a 7pm class and an odd topic, so the low turnout isn’t surprising). They were much more willing to participate than my group at Columbia Splash was. They sang (sometimes listening through to something once then singing after), told me if they wanted to hear something again, and asked questions about pronunciation and words. That buy-in made the class more comfortable and effective.
There was one very key thing I had changed. I tried to weave in more useful vocabulary/grammar with the songs, though this was still far from a traditional class. (I still forgot to include hello and goodbye, which I meant to cover.) We went through numbers 1 through 100, yes and no, the constructs for there is/there are and there isn’t/there aren’t, the verb to be in the present for singular subjects (which we practiced by saying how old we were), and short formal/informal conversations asking and answering “How are you?” These all spun off of words or phrases in songs (some more indirectly than others).
The first two songs (Csipp Csepp and Számoló dal) and the corresponding vocab/grammar took 30-35 minutes. We sang two more songs (Málna, Tigris) and listened to one (Új élet vár) in the last 15-20 min. Ideally I would give Új élet vár a little more time at the end, but we heard most of the song (just not all the refrain repeats at the end). We didn’t sing Hét Najpai Dal, which was on the song sheet, but I was fine with that. It included the same numbers other songs had covered, and days of the week don’t add much. I could probably cut it and use the extra space on the song sheet for some annotations.
On annotations: the students were writing down a lot, and sometimes I went a bit fast. It would be nice to annotate some of the information for them so that they were trying to write everything down.
I had a lot of fun with this, but it’s a really niche class, indicated by my three students both times I’ve run it. I’m probably retiring the class now, but I’m glad I did it this year and that this run of it went so well.