I taught two classes at Columbia Splash at the beginning of this month. The first was a Math Modeling course, and the second was Intro to Hungarian Through Song.
Here were the course descriptions:
Mathematical Modeling: Math modeling is how we use mathematics to study open-ended questions about real-world phenomena. What’s the best location for a food truck? How does an invasive species affect an ecosystem? How do we clean up space debris? These are all questions that we can start to answer with math modeling. The goal of this class is to introduce you to the modeling process. By the end, you’ll have developed models to answer questions about a couple of different scenarios, and you’ll know about some of the tools you can use to tackle more significant modeling problems.
This was a two hour course, and I gave it a difficulty rating of two stars out of four. The prereq was listed as “comfort with basic algebra and a willingness to tackle very open-ended problems.”
Introduction to Hungarian Through Song: We’ll cover basic Hungarian by singing (mostly children’s) songs! You’ll learn very important vocabulary words like yellow, raspberry, icicle, and animal. I do not guarantee that you’ll be able to hold any kind of reasonable conversation.
This was a one hour course with a one star difficulty rating. The prerequisite listed was “willingness to sing very silly songs.”
Thoughts on how the classes went are below the fold.
My plan was to start with the computer problem in the GAIMME report and talk about it as a class. The key part of that problem is defining the question and defending your choice of how to use measures of performance and efficiency to choose a best computer from a set of six. After that, I was going to explain the set-up of two problems (the hot dog cart/food truck problem from GAIMME, and one I wrote about newts and invasive crawfish based on presentations I saw at MathFest). The students would work in groups of three or four on one of the problems, I’d float around talking to them and asking questions, and occasionally I would stop them to talk about the different approaches people were taking, having different groups explain their work to each other, etc.
The beginning went mostly as I expected. On the computer problem, I started by asking what ways people could think of to define “best.” The first suggestion was to set some kind of standard, maybe based on an average. Other suggestions were to add performance and ease of use, adding with some kind of weighting, or multiply them. We talked a little bit about possibilities for the setting a standard and looked at which computer would be “best” for each suggestion of how to determine best-ness. (I didn’t have them calculate this themselves in most cases; I just told them.) One of the students asked about the difference in P+E versus P*E, so we talked about the geometry of that (lines vs hyperbolas). With all that, though, it still only took ten or fifteen minutes, which was less than I expected.
There were eleven students, so they split into two groups of four and a group of three. All three groups chose the food truck problem to start. They had a couple of different ways of thinking about it. All approaches used distance along the paths, assuming that students only walked on the paths, but one group looked at average distance of each intersection only from the dorms, and the other looked at average distance from all intersections. A couple of the groups put some work into thinking about putting two of the intersections with dorms on a hill and how that changed their conclusion.
As opposed to really working on that and other variations of the food truck problem, though, they then drifted towards the newt/crawfish problem and found it interesting. (A couple of students later told me it was intimidating at first but that wore off after the food truck problem.) Two out of the three groups immediately started looking for and noticing patterns in the populations. No one really got to a full model, but they did answer the first question (will the newts die?) and had a lot of questions of their own. I stopped everyone at one point and we talked about the patterns they found, the questions they had, and how those questions would lead to assumptions in their model.
One group assumed that the crawfish were mostly eating newts, and so as the newts died the crawfish would too; they thought that would let the population rebound. The other two groups assumed the crawfish had other food sources and said the newts would die in the next couple of years.
2 or 3 students out of 11 were not really engaged for maybe the second half of class (from the time they felt done with the food truck problem). There was another that I was worried about — when I came over and asked what he was thinking about, he said “Not much,” — but then he asked a question about how he could write a function for how probability of going to the food truck decreases with distance. He had a graph of the function in mind, but didn’t know how to get from that picture to an expression for the function. What he wanted ended up being something like a quartic with an exponential envelope, and I helped him work through that at the board. Later, one of the other students asked him what we’d been doing, and he explained it. I was really happy with how this situation (which could have been bad) ended up going, even though I didn’t really do anything. When he told me “Not much,” I was scrambling, and he was the one who fixed it. I just ran with his question.
I don’t think I finished class as well as I could have, and they definitely didn’t come away with the sense of iteration or communication as part of the process in the way that I wanted. (I did pull up a chart of the modeling process and talk to one student about it because she asked.) That was something I wanted to improve on for MIT Splash. (Spoiler alert for that post: it didn’t go better.)
I had three students for Hungarian, one more than had been pre-enrolled. (I only had three song sheets; for the future I should have an extra copy or two of handouts.) The class overall was a bit awkward. The students didn’t really buy into the singing. One asked near the beginning what the point was, and another made a comment later along the lines of “This is very different from how I learned Spanish.” That sort of response convinced me that before MIT Splash I needed to incorporate some more traditional/useful material.
I had seven songs on the song sheets. I didn’t expect to make it through all of them, but I wanted to have extra material if we went faster than I expected. We started off singing “Csipp Csepp,” which is pretty short, contains the numbers one, five, and ten, and also has two of the more difficult sounds for English speakers. I had planned to do an animal alphabet song after that, but we ended up getting a bit derailed in the middle talking about small cultural things, like Hungarian chocolates, desserts, and endearments. That wasn’t the worst use of time, but it ended up being pretty focused on my time in Budapest, which felt odd.
We got back on track and looked at “Hol jártál báránykám,” then finished at the end with a pop song, David Fekete’s “Új élet vár.” I had chosen this because it was one of the easier to translate and more repetitive songs, but one of the students pointed out that it’s also slow enough that they could follow along with the words easily. I had thought about switching to a less sappy song before MIT Splash, but that was a good argument for sticking with this one.