The Social Construction of SportsCenter
I was watching the morning loop of SportsCenter (a show which has its fanatical fans, but which, unsurprisingly, others think has jumped the shark) while trying to pump enough caffeine into my system to get through this morning's lab/ lecture, and they ran highlights of Maryland's 108-58 shellacking of Hampton. One of the highlight clips (Steve Blake passing behind his back to Drew Nicholas) was described by the anchor as "Blake dishes some tasty love to Drew Nicholas." To which I had two reactions: 1) Can they show that on tv? and 2) I bet that would've sounded cool had Stuart Scott been the one to say it. In reference to Nicholas, he also stated that "Long Island homies are the craziest," which really sounded about as dorky as it looks in print.
I can't help thinking that there ought to be some lesson here about the social construction of race, especially given that the anchor in question was, like Scott, African-American (I can't recall his name, and ESPN no longer seems to have a list of its anchors on their site in any sensible location, so I can't find it...). Scott's unending stream of hip-hop style catchphrases is pretty entertaining (though not everyone thinks so), but he's about the only one on the network who can carry that stuff off (though, sadly, he's not the only one to try...).
I'm not sure what that lesson is, but it seems like there ought to be something...
Ask Dr. Principles
In comments following my posting of my final exam from last term, John Novak asks:
How do you teach your students to go about solving those SR problems? The way I was taught (in an undergrad class which admittedly became very adversarial, very quickly) emphasised a quick diagram, almost for form's sake, and then rote manipulation of equations.
The way I can actually do them (I think) is to conentrate on a more elaborate diagram and transform the exercise into a geometry problem.
This actually brings up one of the more challenging issues in teaching this sort of stuff. There are usually at least two ways to approach a problem, and what works well for one person won't necessarily be any help at all to another. As a professor, I'm expected to teach the material to everyone, though, which sometimes means that I have to present a method of problem solving that I find needlessly complicated, in the hopes that some of the students might find it helpful. In a similar vein, I'm also sometimes forced to teach problem-solving methods that aren't really necessary for the specific problems being studied, but which become essential for more complicated problems.
The latter problem is particularly annoying, because it goes down very badly with the students (which I know, because it went down very badly with me, back in the day). To pick a fairly general example, in introductory classes, it's a constant battle to get the students to actually do algebra-- what they want to do is to immediately plug every number given into the problem, and then solve everything using a calculator. This isn't too bad at the intro mechanics level, where you're solving simple equations with one or two terms in them, but as the equations get more and more complicated, it becomes a real problem-- the more steps of calculator math you have involved (and these students have only the sketchiest grasp of significant figures, and so tend to use eight or nine digits for every single number), the greater the chances of errors creeping in from simple mistyping. I've had completely nonsensical results handed in-- one pair of students came up with something being 10-83 joules-- with no way to see where they went wrong, because it was all done on a calculator. It's better by far to work the equations algebraically as long as possible, and only plug in numbers at the very end-- if nothing else, there are often terms which cancel each other out, making even the data entry simpler, but it's a huge hassle to get students to do it on problems which will eventually have a numerical answer. I can force them to do algebra by assigning problems with no numerical values (which draw bitter complaints from the engineers), but even there, I've been thwarted by students who solve the whole problem assuming that the unknown mass is five kilograms, and then divide the final answer by five and stick in an "m".
(This mental block regarding algebra was one of the most surprising things I've found in teaching the intro classes. I expected the students to be befuddled by calculus, but they're fine with derivatives and simple integrals. They just won't do algebra unless absolutely forced into it, though, and I can't recall ever having this problem, so I don't know how to get them out of that mode...)
As to the more general issue of teaching unhelpful methods, I generally try to present even the methods that I don't find helpful, but I can't swear I do a good job of it. I never really know what some future professor will expect them to know, though, so I have to give it a shot, even if I never use those methods in solving problems myself.
Of course, sometimes I use the leeway given me in setting up the syllabus to just skip things I find unhelpful. Which gets us back to the specific question John asked...
There are complicated graphical methods of working problems in Special Relativity, and one of the books I used for reference purposes relies heavily on them. In general, though, I find those techniques profoundly un-illuminating-- you end up calculating times and positions by projecting points onto tilted and non-orthogonal axes, and I just don't get much from that. So I didn't teach any of the graphical stuff. (I also had only two weeks, total, to spend on relativity, so I couldn't cover too many alternate methods...)
For solving Special Relativity problems, I relied on a combination of equation manipulation and common sense (or tried to...). If you work from the Lorentz transformation equations, and check your work against the important results that 1) Moving Clocks Run Slow, and 2) Moving Objects Shrink, you can solve all the problems I put on the exams fairly easily. I find that method easier to deal with than the graphical techniques I've seen. If I had more time to spend on it, I'd probably give the graphical stuff a shot, as Relativity was the stuff that confused the students the most, but with the compressed schedule we had, I couldn't see taking the time to do it.
The Library of Nonexistent Posts
I really ought to write something about the epic collapse of the Giants yesterday, but, well, I don't have the energy. About the most I can manage is to note that it was at least an exciting game, which can't be said for other teams.
In a similar vein, I've been wanting to post something more about Tolkien, particularly given the large number of interesting posts in blogdom on the subject: Jim Henley has some slightly flippant material (scroll up for more), Seablogger has an interesting essay (found via Unqualified Offerings), Charles Murtaugh weighs in on some of the same issues, and the always-entertaining Making Light has spawned a comment thread with some good stuff (you have to go by a fair bit of other stuff (and one messy disemvowelling) to get to the actual discussion, but it's worth it for the classically inscrutable post from Graydon Saunders). Unfortunately, my thoughts on the matter stubbornly refuse to evolve into anything coherent, and I don't have a whole lot of spare time to bang out drafts and refine them, nor do I have the energy to deal with the shitstorm that would undoubtedly be kicked up by posting something semi-coherent on this subject. I may come back to this, I may not, but in a shameless bit of self-promotion, I'll note that I have reviews of the original books up on my other web site, which can be found from the review index (along with lots of other stuff).
Life in a Greeting Card
According the the weatherman on the radio this morning, average annual snowfall for this region is 63" (that's one Kate worth of snow...). This winter, we're already at 68". That's right, we've already had an above-average winter's worth of snow, and it's January 6th.
On the bright side, everything looks really pretty right now-- we had a bit of ice on New Year's Day, so the snow that followed stuck nicely to trees and houses and fences, giving everything a festive winter gloss. That is, until you note the way the trees are sagging under the weight of the snow, and the power lines stretched like guitar strings where branches are leaning on them... It's not expected to warm up for a good while yet (and, indeed, light snow is predicted for much of the rest of this week), so it'll be a tense week here in the Capital District.
In other news, the snow played hell with my return to work-- we've lost a couple dozen parking spaces to snow, and another large swath of lot space to the fact that people take a little snow as license to park any damn fool way they like, meaning that we've got ten widely-space cars in space that ought to hold fifteen, including a couple of whopping huge SUV's parked diagonally across two spots. The temptation to break a couple of windows on the Ford Army of Conquest taking up the last two spots in the nearby lot was really hard to resist, and I better get some Karma Points for this...
Compounding the problem, the geniuses in Facilities Services had closed off one whole lot so they could bring in big earth-movers to shift the snow out of the lot entirely (as opposed to piling it up on the edges). An admirable goal, and the right thing to do with this quantity of snow, but perhaps the morning of the first day of classes is not the best time to shut down the biggest parking lot on campus...
Anyway, it's back to work here in Schenectady, a change from stripping paint off walls to cramming knowledge into the minds of impressionable youth... Though given that I'm teaching classical mechanics this term, there'll be a little breaking down of previous misconceptions before we can get to anything constructive. Happily, this doesn't require anything as noxious as the chemical paint stripper we've been using in the house, which contains ingredients so deadly that their names have been known to cause cancer in rats, but maybe this is one of those analogies that shouldn't be stretched too far...