December 8, 2008

A-level science courses are fun because my students have progressed to a relatively advanced level, and I can talk about subjects in ways that interest me. A-level is also challenging for the same reason; the students are bright (at least some of them), the exams are difficult and the syllabus is incredibly broad. Often I teach myself topics the night before I teach my class, and sometimes my lack of experience is painfully obvious. Going off on tangents can provoke interest, but often they end up in places I don’t expect, places I’m not prepared for, and in the end I look moderately stupid in front of my class.
My Physics class has been learning about waves for the greater part of this term; we’re starting a chapter on thermodynamics after Christmas. At the beginning of the year I told my students I would try to derive every equation I wrote on the board, and I had been successful until the end of last week. The equation is for the Doppler Effect, which explains why the sirens on an approaching ambulance are higher-pitched than the sirens on a departing ambulance. The equation for the Doppler effect looks like this:

Light is different:

The two equations look similar, but they’re really not. The question was whether I could pull this past my students without any awkward questions; but as soon as the equation went on the board a couple hands went up. Ramadhani Nkucha is one of the students who seems to breeze through class without working at all, although he has turned in every assignment I’ve handed out. He rarely speaks in class. “Why?” he asks.
So could I avoid a pointless foray into relativity, a subject which I don’t really understand? Even in this class of Tanzania’s best and brightest, at most five students would walk away with some inkling of what I was talking about, but the class wasn’t buying the “light is different” line. I had no choice. Mentally cursing the syllabus which forced me into this situation, I ran towards Ramadhani and threw my eraser at him. “Say I throw this thing at 5 m/s. If I’m running away from you instead at 2 m/s, what is the velocity of the eraser?” The class got it, 5-2 = 3 m/s.
“But now, instead of throwing a ball I shine a flashlight on you. How fast is the light moving now?” The answer was written on the board, c = 2.99 x 108 m/s. “Now I run away from you at 5 m/s; what is the speed of the flashlight now?” A chorus of voices shouted out 2.99 x 108 m/s – 2 m/s and were dismayed when I told them they were wrong. The speed of light in a vacuum is constant; it is marginally slower while travelling through air or water. Why is light slower in air or water, anyway, given that it doesn’t need any medium? I was confused myself; but I had them on the run. “Light is different. We think in terms of fixed space and time, and define velocity as the ratio of the two. For light the ratio is fixed, but the space and time parameters can change.” I talked about time dilation and length contraction and the twins paradox. I talked about black holes and the beginning of the universe; most students had a healthy skepticism of the big bang. I tried to get my students to figure out how we could find a black hole, which emits no light whatsoever.
And that was that, the next day we were back to talking about diffraction patterns. I realized most Tanzanian students have never internalized their advanced science courses before. All of my chemistry students can define the “wave-particle duality of matter,” using terms they don’t understand; but they haven’t grasped the implications, for example that their books are made up of energy waves. They can recite the theory of evolution but they don’t see any conflict with a fundamentalist brand of religion. Perhaps a few of them got something out of my lecture on relativity; I was not particularly coherent.