Another Term Bites the Dust
Reflections on a weird fall
I got a nice plug from Razib Khan yesterday, which has brought a significant bump in the number of free subscribers. Welcome, new folks; also, apologies in advance for what’s going to be a bit of an inside-baseball post, here. But I just turned in my grades for the Fall 2022 term, and need to type out some thoughts on it to clear up mental processing cycles for other things.
This was my first term back teaching after a much-needed sabbatical last year, and also my first term as Chair, stepping in on short notice after the previous guy left for personal reasons. It was also my first time teaching this particular course, and the combination of all those things almost killed me. One star, Do Not Recommend.
The course in question was our intermediate-level quantum mechanics course, (PHY-220 in our numbering scheme), which is basically a second pass through basic QM after a sophomore-level “Modern Physics” course (a term of art meaning “Physics Developed from 1900-1950”). The students taking it are mostly junior physics majors, coming to it after a term of intermediate classical mechanics.
This is by nature a very mathematical set of material, involving a whole lot of derivations, introducing and using a bunch of mathematical techniques that are central to the discipline, but often turn on some fiddly and complicated bits of calculus. As such, it has a tendency to become very lecture-y— it’s a hard to make it participatory when students are seeing this stuff for the first time, as a lot of the tricks are not especially intuitive. This is also a pitfall that I am personally very prone to— I’m not good at waiting out students who aren’t eager to answer questions. I’m afraid the end result was probably a bit more dry than I would’ve liked.
As I said, this was my first time teaching this course, and there are only two other people around who have taught it recently. One of the two used a very detailed set of personal notes, the other used a standard textbook; I got copies of both, but went with the traditional textbook (the latest edition of David Griffiths’s book, as seen in the photo above) for fear that the personal notes would prove too idiosyncratic.
That was, in retrospect, probably unjustified. Not because my colleague’s notes aren’t idiosyncratic, but because the book is odder than I realized. There are a whole bunch of places where, as I was going through the course, I found myself saying “Wait, why in hell would you do that here?” This sorta-kinda worked with the schedule— I gave two midterms as “self-scheduled” tests, allowing students to take them at a time of their choosing within a block of several days, and those happened to line up with book sections that were largely mathematical asides. But there were other places where the ordering of topics just seemed too weird to me, and I had to flip things around on the fly. That’s a real fly-without-a-net moment, and I doubt I entirely pulled it off.
Unfortunately, this is the kind of thing that’s really hard to pick up from just reading through the book, especially when it’s by a very smooth writer like Griffiths. The weirdness only becomes obvious when you’re actually in the process of turning text into class notes, at which point it really slaps you in the face. I’ll probably take another look at my colleague’s notes, having gone through the book version, and consider switching to those when I teach this next year. Which would be a good deal of work— I already have lecture slides and problem set solutions for the book version, after all— but still less than starting from scratch.
The other thing that I’ll likely look at doing more of is incorporating Mathematica into the course. Quantum mechanics famously features only a handful of problems that can be solved analytically with pencil and paper, but there are a lot of interesting systems that are more amenable to numerical solutions, so a computer system opens up some additional probabilities.
I did try to do a bit of Mathematica, but ran into the same two issues that I always do with that program. First and foremost, there’s the problem that I am not personally all that comfortable with using it, so putting together useful class exercises in Mathematica is extremely time-consuming, involving a lot of reading help documentation, etc.. The one significant Mathematica exercise I did with them took ages, because I was making a stupid syntax error that made every operation take ten times as long as it should’ve (which I eventually got a colleague to debug for me). Incorporating a lot of that just wasn’t in the cards this term, given all the other demands on my time.
The second problem is that students tend to struggle with it in ways that aren’t the ways that I struggle with it, and because I don’t teach it all that regularly, I don’t have the pedagogical tools to address those near to hand. There’s a kind of conceptual breakdown around (I think) what it means to define a function in a computer program that I just don’t recall ever having a problem with. Which makes it hard to help students get through, because unlike with many of the non-intuitive math derivations, I don’t remember the thing that made it click into place for me back in the day. At a fairly deep level I don’t understand why they don’t understand, and when I can’t get into their headspace, it’s really hard to get them past that block.
(I have a closely related problem with writing-intensive courses, where a lot of student writing fails on a level that is a couple of steps more basic than I can remember ever struggling with. Which again, makes it hard for me to understand the issue, or offer useful feedback to address it.)
These are, to some degree, issues that can be fixed in the next go-round (and the one benefit of being Chair is that I can ensure that there is a next go-round, because I’m the one who does the teaching assignments…). I’m not going to have fewer demands on my time, exactly, but I’ll have a bit more familiarity with the material, which will make it easier to make adjustments and do new things.
Anyway, those are the main take-aways from the term that was. And now we’re on to the next thing…
That is, as I said, very inside-baseball, but will probably produce a certain amount of “I feel seen” in fellow faculty. If this is something you’d like more of, here’s a button:
And if you have suggestions of great resources for teaching either QM at this level or getting students to be more fluent with Mathematica, please leavethem in the comments:
I was always team MATLAB/Maple rather than Mathematica — I found Mathematica much less intuitive than that combo. Engineering tends to prefer MATLAB usually although I’m also seeing a lot of Python now.
As far as students having trouble with understanding functions, the biggest problem I see is that they don’t understand the concept of scope for variables (the idea that each function has its own separate memory, and variable names inside the function don’t have to match the place they are called from, nor will those variables be visible from the “outside”).
I'm always amazed at how compact Mathematica notation can be, and doubly amazed at how it always takes me about four times as long to come up with the right combination of /@ and # & and all that than it would to write out the same thing in a more conventional programming language.
I know when I first learned about computers, I was almost immediately learning about programming, and learned a number of ways of writing subroutines and functions with arguments and so forth. But I wonder if your students, even if they're science- and math-minded, don't really do any computer programming unless they have to for a class, because learning about computers these days is about browsing the web?
Twenty years ago (!) there was a book, Visual Quantum Mechanics, which made heavy use of Mathematica. The website is still up, but I suspect that all the included software can only run on outdated platforms. https://vqm.uni-graz.at