Why won’t anyone teach her math?

Lots of discussion in my feeds about this Daily Princetonian piece, “Why won’t anyone teach me math?” by first-year student Abigail Rabieh. She just took Math 202, an intro to linear algebra, and the experience was so lousy she’s done with Princeton math for good. That’s bad!

So what was wrong with Rabieh’s class?

“Though I passed MAT 202 class just fine, my experience in it was miserable. The way the course was run did not at all set up students to succeed — or even learn math. For example, though we were provided with practice problems to prepare for our exams, we were never given solutions. My class consistently begged my professor for these, yet all he could say was that not providing them was departmental policy, and it was out of his control.

This begs the question: what interest does a department have in making it impossible to study? Study materials are given so that students can learn the course material and prepare adequately for the exam. Solution sets are part of this: to properly learn, one needs to be able to identify their mistakes and understand why they are wrong. This struggle was reflected in our exam averages, which were, respectively, in the 50s, the 60s, and the 30s.

I am far from the only person who felt this way about my class. MAT 202 has an abysmal rating of 2.71 on princetoncourses.com during the spring 2020-2021 semester. The evaluations on the Office of the Registrar’s website are no better. Students described the course as “disheartening” and said they “lost a lot of respect for the Math department after taking this course.” The advice that came up again and again in many reviews was: “Don’t take this class unless you have to.”

A lot of math teachers instinctively reacted to this with defensiveness, and I was one of them. After all, what’s so bad here? You hand out practice problems for an exam because you want students to do the problems, not because you want them to read the solutions; the mechanism is that the student works all the problems they can and then asks in office hours or review session about the problems they couldn’t do. I don’t think it’s bad to include solutions, but I would never say that not doing so makes it “impossible to study.” Student evals, well — the literature on their unreliability is so vast and I’m so lazy that I’ll only just vaguely gesture at it. And of course, most people taking Math 202 are not taking it for intellectual broadening, as Rabieh admirably was; they are taking it because somebody told them they had to. That makes the evaluations impossible to compare with those for a course people take on purpose. And as for those exam scores, well — a median in the 30s is too low, that would mean I’d made the exam much too hard. A median in the 60s, on the other hand, seems fine to me, an indication that I’d written a test with real challenges but which people could mostly do.

But you know what? Our students, especially our first year students, don’t know that unless we tell them! A student who got into Princeton, or for that matter a student who got into UW-Madison, has probably never gotten a 60/100 on a test in their entire life. No wonder it’s demoralizing!

What we have here, as they say, is a failure to communicate. Rabieh came away feeling like her teacher didn’t care whether she learned linear algebra. I’m sure that’s not the case. But I think we often don’t explicitly demonstrate that care in our classrooms. It makes a difference! We are asking the students to care about our stuff and if we want them to respond, we have to show them that we care about their stuff. What do I mean by that, explicitly? I mean that if we think the median score on an exam is going to be in the 60s, we should tell students in advance that we expect that and talk about our reasons for writing the exam that way! I mean that we should ask for student input on how the course is going before the semester is over — three weeks in, send out a survey asking for suggestions, and then talk to the class about the feedback you got, showing them you want their input while you can still make use of it. It means that if you teach a crappy lecture one day — it happens! — be open about that the next time and talk about how you intend to present a better one next time. And I feel like these are mostly “things I already do,” which could just be self-flattery on my part, so let me add this: it might be that showing students we care could mean making nice prepared slides like the professors in all their non-math classes do, instead of just showing up and writing on the blackboard. (Doing this would be a huge change for me and it exhausts me to think about it — but would it be the right thing to do?)

We don’t really talk about this stuff when we talk about teaching. We mostly talk about content and logistics; in what order should we present the material, how much should we cover, how many quizzes should we give, what should our grading policy be, should we hand out solution sets for practice problems? That’s how we think about what good teaching is, and that’s how our students think about what good teaching is, and that’s why that’s the language Rabieh reached for in her article when she wanted to explain why she had such a bad time. But I don’t think it’s actually the problem.

I’ll bet her teacher did care. Most of us do. But it often doesn’t show; let’s say it out loud! And strive for a classroom where we’re working as partners towards a goal, not just trying to get to the end without feeling like we’ve failed.

Tukey before he was Tukey

There’s no end to the interesting tidbits to be found in The Princeton Mathematics Community in the 1930s, an oral history project hosted by the Mudd Library.  I liked this, about the great statistician John Tukey, from an interview with Joseph F. Daly and Churchill Eisenhart:

Daly: … Tukey was about as pure a mathematician as you can imagine.

Eisenhart: When he first came.

Daly: All he was interested in was axioms and set theory and stuff like that. But eventually he found out there was life after ultrafilters and things, and he had fun in statistics.

 

 

 

Best Writing on Mathematics 2011, and Nathanson on massive collaboration

In my mail:  The Best Writing On Mathematics 2011 (Mircea Pitici, ed.) from Princeton University Press.  Just to get this out of the way:  I’m in here!  They reprinted my compressed sensing article from Wired.

You might now be wondering:  are there really enough popular math articles published in a given calendar year to fill up an anthology?  No.  There are not.  But this is part of the charm of what Pitici has done.  His very broad definition of “writing on mathematics” allows him to include useful professional advice for young mathematicians from Andrew Schultz, reflections on a career in math education from John Mason,  and academic-yet-readable philosophy (“What Makes Math Math?”) from Ian Hacking, whose The Emergence of Probability is my favorite book in history of mathematics.

I especially like Mel Nathanson’s pessimistic take on massive collaboration in mathematics — because it is a forcefully written, carefully argued case for a position with which I mostly disagree.  “I would guess that even in the already interactive twentieth century,” he writes, “most of the new ideas in mathematics originated in papers written by a single author.”  I would guess otherwise — at least if you restrict to the second half of the century, when joint papers started to become really common.   Mel calls me out for writing about Tim Gowers’ Polymath Project in the New York Times with “journalistic hyperbole” — and here he is right!  It is very hard, in the genre of 300-word this-year-in-science snippet, to keep the “gee whiz!” knob turned down and the “jury is still out” knob turned up.

Gowers claims the classification of finite simple groups as a pre-Internet example of massively collaborative mathematics.  Nathanson agrees, but characterizes the classification as fundamentally uninteresting, “more engineering than art.”  What would he say, I wonder, about recent progress towards modularity of Galois representations?  It’s very hard to imagine him, or anyone, seeing everything that’s happened in the last 15 years as a mere footnote to Wiles.  (But maybe some of the experts who read this blog would like to weigh in.)

Nathanson concludes:

Recalling Mark Kac’s famous division of mathematical geniuses into two classes, ordinary geniuses and magicians, one can imagine that massive collaboration will produce ordinary work and, possibly, in the future, even work of ordinary genius, but not magic.  Work of ordinary genius is not a minor accomplishment, but magic is better.

Yes, but:  magic can only happen in the already-enchanted environment created by the hard work of many minds, alone and in teams.  Math is like earthball.

 

 

 

Gehry/Serra

Back from a very brief trip to Princeton. The much-maligned new science library, built by Frank Gehry, is now up. I like it — it’s very much like the Stata Center, but more humble. Here’s a small piece of it viewed from inside the Richard Serra sculpture “Fox and Hedgehog,” also much-maligned, and which I also like.

Note: this is my first attempt to blog by iPhone. I’m sitting in my car, in the back of which CJ has dozed off, and I thought I’d let him sleep instead of continuing immediately with the shopping as planned.

Harvard beats Yale 29-29, both beat Princeton

I’m sorry to say that I only made it to one movie at the Wisconsin Film Festival this year.  But I picked a good one.  I went to see Kevin Rafferty’s Harvard Beats Yale 29-29, a documentary about the most thrilling Harvard-Yale game ever played between two of the best teams Harvard and Yale ever fielded, just because I sincerely like Ivy League football.  But in fact it’s an authentically good documentary whether or not you care about Harvard or college football — though it might be hard going if e.g. you don’t know what “pass interference” means.

I won’t say too much, to avoid spoiling it.  But it’s particularly remarkable how Rafferty manages to develop Yale defenseman Mike Bouscaren, over about five minutes of total screen time, from a comic caricature to a sincerely terrifying villain (drawing hisses and gasps from the packed house) to a thoughtful and even remorseful ex-combatant.  There’s a good interview with Rafferty at the New York Times college sports blog.

In less inspiring Ivy news, Princeton’s admission rate bumped up a half a percentage point and disgruntled seniors went nuts on the Princetonian comment page, decrying the current administration and everything associated with it.  One of the enjoyable things about teaching at Princeton was getting the Princeton Alumni Weekly — that’s right, their alumni magazine is a weekly! — and reading the three pages of cranky letters from alumni with something on their chest about how they do things nowadays. The Princetonian comments are a great opportunity to hear from the cranky alumni of tomorrow.

At the moment, the CAoT are upset about “grade deflation” and the “war on Fun.”  Both got started while I was teaching at Princeton.  The former policy was aimed at the fact that grades in science and engineering classes were about a half-point lower, on average, than those in humanities; so that students who were planning grade-sensitive careers in law or medicine had a weird incentive not to major in science.  The “war on Fun,” refers, I think, to the establishment and promotion of a four-year residential college as an alternative to the eating clubs — and more generally a sense that the administration is hostile to the clubs.  When I was teaching at Princeton, about a quarter of the students weren’t in clubs, and life seemed to be sort of logistically annoying for them.  It’s hard for me to get my head around the idea that club members object to a nice cafeteria for the students who didn’t bicker in.

Oh, and I think “the war on Fun” also includes some kind of rule about registering dorm parties in advance with your RA.  Harvard introduced this policy when I was an undergraduate, and people grumbled about it then, too.  And you know what?  People still had parties.  Message to all undergraduates everywhere — your university is not conspiring to keep you from drinking beer in groups. I promise!

Anyway, the comment thread got linked from lots of places and so there’s some question how many of the posts are from authentic Princeton undergrads.  This, for instance, can’t be real — can it?

I am a triple legacy and I feel I have a more outstanding right to be here than a lot of the so-called Academic 1’s. Princeton used to stand for something, not just be a humorless grade factory. What’s next, bed checks? The Street is a shadow of what it was in my parents’ day and the current workload is just ridiculous.