They’re sitting the final exam for my graduate electromagnetism class right now, having started at the ungodly hour of 8:00am. I’m sitting outside in the bright, lukewarm Winter sun with a cup of coffee, two cheesy biscuits I baked at 6:30am for no reason other than feeling in a baking mood (see right), my phone in case there’s a reason for the TA on duty to contact me, and my iPod, which I am of course using to write to you.
It has been an odd few days. Not so much because of the pair of them that had me wandering around a huge studio lot, being wardrobe-checked and make-up checked, shot from all angles with a live cheering studio audience in attendance (for your viewing pleasure on a new prime-time series on Fox to begin airing next month – more on this later, perhaps), but because early on Saturday I woke up with a severe vertigo attack. 
Very odd indeed and although I managed to get it under control and it had worn off over the days, every now and again it gets close to being triggered again. I don’t know the source for sure – I think it was correlated with a reaction to some of the food I had on set, maybe combined somehow with the severe ear blockage I had about a month ago after catching a (short-lived) cold on a long transatlantic flight? – but I have to say (and this is the point of my digression here) that it is a remarkably odd experience for me to feel slightly off balance for such an extended period. I’m used to being on the tips of my toes ready to skitter along the line at the edge of a low wall if the mood takes me while walking along. But I can’t imagine doing that now. I feel like I’ve lost my powers… it’s often amazing to me how little it takes to make a person feel very mortal, even fragile, again. It will no doubt pass.
I’ve been gentle on this final exam. I still find it disturbing that kids today (yes, I said “kids today” – perhaps my lack of equilibrium has put me in crotchety-old-man mode), even the very smart ones, typically do badly on any advanced exam that is remotely interesting. Somehow they get used to being spoon-fed at lower levels, along with not practicing speed and efficiency in their computation practice so that when thy come to do anything that involves a moderate amount of calculation in the exam, they spectacularly run out of time. the usual reaction to this observation is to declare that doing well in exams is not important, and being able to compute fast and efficiently is not a test of knowledge of the material. This sounds lime a clever advanced. thing to say but it is largely wrong. Or, put differently, for the right kind of question it can be an excellent test of the key abilities one needs. I’m training thinkers here and in physics a lot of the thinking that matters is not just being able to list some of the clever things some long dead professor discovered but to see how to apply those things in a physical situation and to unpack a problem down to it’s essentials and compute aspects of it’s properties. This involves picking good coordinates systems to refer your mathematics to, efficiently isolating which pieces of the computation might be smarter to do first, using your intuition about the principles (the grand ones and the everyday ones like symmetry) to anticipate what some of the structure of the computation might look like, etc., etc. Those skills speed up a computation, illuminate the physics, and separate the leaders from the also-rans. A fixed time exam is an excellent setting to test this, especially in an age when nearly every. standard textbook question has its solution available online to any student with a few minutes google time, so homework only tests so much these days…
That said, I cut down the length of the exam by 25% this time, with three long questions to do over the two hours instead of four. To add to my generous-streak I recycled a waveguide question from the midterm they sat earlier in the semester (a universal timing disaster we all seem to have tacitly agreed to not talk about) and one from a homework on diffraction they did not more than a month ago. The remaining one is a new question that is simple but neat, testing their understanding of the intersection of electromagnetism and Special Relativity. What is it?, some of you ask. Thanks for asking – they start with a plane wave of light in one frame and transform it, using the Lorentz transformations, to another frame, extracting (I dearly hope) that its speed remains the same and that its colour is Doppler shifted by a specific amount. Let’s hope they enjoy the two hours!
Perhaps I’ll go back in now and see how they are doing…
-cvj
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“But the other side of the coin is that if you look at the English maths education system, you might find that it is nothing but drills ie learning how to solve a certain problem using certain techniques.”
Having been through both the US and English education systems, I actually found that this was much less of an issue in the UK than the US. My maths education in the UK was much more about solving multi-step problems that I might not have seen before, using the tools I knew…whereas in the US it was much more about solving the same kinds of single-stpe problems over and over again with different numbers plugged in. But to be fair, I got unusually good maths education (compared to other English schools) in the UK. It is indeed all about balance.
–IP
“It’s about striking a balance wouldn’t you say”
As always.
Cheers,
-cvj
But the other side of the coin is that if you look at the English maths education system, you might find that it is nothing but drills ie learning how to solve a certain problem using certain techniques.
So once these kids get to research level mathematics, they wont know what they’re playing at and will only be trained in problem solving and unable to enageg in research. It’s about striking a balance wouldn’t you say?
It is more subtle than just not being able to tackle advanced and interesting material… I genuinely believe that students are very keen to learn that material, and love to hear about it… I just think that we’re in danger of entirely forgetting what it means to really _know_ the material. Besides reading a text like a novel, one has to roll up the sleeves and dig in and spend hours and hours doing problems. I worry that this latter practice has fallen by the wayside. It is more and more left up to the student, rather than being scheduled in (say) classroom problem-solving sessions. But even the most keen students will largely not be able to appreciate the future value of doing those drills, and so if it is left optional they’ll (especially since students seem to have increasingly busy schedules these days) skimp on that sort of thing…. So I think the solution is simple. More compulsory in-class problem-solving sessions -drills, if you like- supervised by people who can be called on to offer individual advice, suggestions, etc. I don’t know how many places still do a lot of that sort of session, but I think we should be doing more of them, not less, as online solutions become more and more available, making it easier for one and all to find the easy way of solving (by googling) instead of figuring it out.
Cheers,
-cvj
Ear blockages and sinus infections can certainly cause temporary balance disorders — it’s actually fairly common. Beta-histines can be prescribed for the dizziness/vertigo. Caffeine, alcohol, and high-salt diets are thought to make it worse. Drop me a line if you want. Hope you feel better soon.
Cheesy biscuits sounds delicious. My dad and I were making banana bread yesterday, but it is all gone now… 🙂
–IP
What do you think can be done about this problem of students not being able to tackle advanced and interesting problems in this sort of setting? Is there anything that can be done at the graduate level? The undergraduate level?
I am a second-year physics grad student, and I’ve wondered myself if my classmates and I could or should be better at physics. This has also been stated or implied by several professors, particularly those who went to school outside the US, although that may just be a coincidence.
I eagerly await the day when I am on the cheesy-biscuit side of a final exam.
(I type this as I prepare for an exam in Avestan tomorrow. You know, part of it will be a translation, with no reference materials, of a passage from a text. We have worked through the entire text together in class. I think it’s perfectly fair game to ask for such a thing on an exam, but some others in my class seemed a bit offed. Your point about being spoon-fed (in all subjects) at lower levels, and not practicing in the right way (i.e. having homework answers available), can apply to all sorts of subjects, I’d say.)
Speed and sure-footedness in computation are as important in the hard sciences as sure-footedness is in skating. I’ve been going to a local high-school in Pasadena, doing a kind of tutoring in one particular teacher’s classes. She’s a superb teacher, with skill that I am much in envy of, but to my mind she doesn’t stress speed enough. When these kids get to a college-level mathematics class, they’re going to be blown away by the speed of the exposition.