Lately I’ve been on a merciless campaign to reduce the paperwork clutter in my lab/office/classroom. Today I dove into the bottom drawer of a filing cabinet (because obviously, bottom drawer = hard to acess = most moldly junk.) and came across an envelope containing the qualifying exam I had to take when starting grad school at Stanford lo those many years ago. The very first piece of paper in the envelope was a cover letter from Dr. Bob Laughlin, who almost single-handedly crafted the qual.
In reading it over, I realized that — consciously or not — it epitomizes a number of common assumptions about testing in physics, or at least, in my teaching of physics. So for insights into the tortured past that made me the teacher I am read on.
I had luckily already taken a class from Bob Laughlin, so these odd directions (and the unconventional problems that followed) were not a total surprise to me. (In Thermo class, Bob had confessed that he wrote the final on the flight back from Japan, having remembered at the last moment that our exam was scheduled for the morning he returned. A sample question, in its entirety: “Derive the melting temperature of iron.”)
As a student, the second-to-least desirable thing to read in a test’s directions is that it is meant to be fun. The absolute least desirable thing to read is that it is meant to be educational. As we know, testing and learning are supposed to be completely orthogonal. But in fact, throughout my time as a physics student, I continually ran into teachers who think that tests should be both. And it’s clearly infected my own thinking on testing. I try to make my test questions relevant but amusing. I have a standard cast of characters who find themselves in improbable situations.
I also favor the open-ended question and disdain multiple-choice or other rote questions. (I am forced, by the format of the exam, to make exceptions in my Advanced Placement Physics course.) My kids often lament that “you problems go to like, part (z)”, because I would rather have fewer problems with many woven parts than a string of disconnected questions. This stems from my own bias that physics is the problem-solving science and thus you don’t really know physics unless you can break a complex problem down into solvable steps. Once I decided that the problems were going to be complex, providing some structure seemed dictated by fairness.
Almost all of my physics profs subscribed to Laughlin’s “harder than you can finish” philosophy. There were many times when I would reach the end of the test at almost exactly the end of the period — and I would be none too sure of the stuff I’d written. I replicate that in my classes, too. My kids routinely and almost uniformly complain that my tests are too hard and too long to finish — that “I would have known what to do if I had had more time”. I deflect that, a little, by having one question out of five as a “take home” question. But that’s the extent of my sympathy. I guess, like my professors, I feel that if you really know the stuff, you’ll be able to do it quickly. I’m not sure that holds up to scrutiny in the full light of day — but I do know it’s common assumption among physicists and physics teachers.
Should a student “learn” something on a test? Yes. Although one purpose of a test is to see whether the student has mastered the recent material, its larger purpose is to assess his/her developing ability to think “like a physicist” — to master the larger skill set, not just the particular material. As such, it’s fair game to throw somewhat-unexpected problems at the students. I have always felt that one of the great strengths of physics — and one of the reasons that justify teaching it to everyone — is its emphasis on generalizability. I had a prof who claimed that if you understood the harmonic oscillator, you understood everything of import in physics. While that is clearly going overboard (sorry, Chick!), there’s a nugget of truth there. The most powerful moment in physics is when you realize that the problem you’re solving is similar to a problem you already understand. Of course the new is exciting — but the familiar is also exciting. As a teacher, my proudest moments are when some student (often not the leader in the class) suddenly exclaims, “Oh, this is just like (that other thing)”.
In the end, I suppose I can only hope that I achieve what Laughlin and the other Stanford profs did for me in the Qual: To write tests that fairly cover the material, that illuminate as well as illustrate, that my students hate while they’re taking them but that they appreciate when it’s done. What better advice can one give than Bob’s:
Just relax, think physically, and have fun!