[Pre-post post-note: an amazing alignment of the stars! Just hours after writing this, I came across the much stronger Lockhart’s Lament. A must read, I daresay.]
Professors, teaching assistants, professional exam-writers, lend me your ears; I come to fix the exam, not to praise it. The exams that students solve, live after them; the results are oft interred with their bones.
This week I had my final examination in quantum mechanics 1. It had three open questions, two of which can basically be reduced to something as follows:
1) Apply the second order correction according to the scheme you learned in class to the following perturbation: …
2) Diagonalize a 3×3 matrix. Using the basis transform, express some vectors as a linear combination of other ones. Use these to obtain a wavefunction and integrate it.
In essence, the questions were just (very) technical mathematics exercises, not-so-cleverly disguised with an excuse for a physical background. This type of question is exactly what keeps me off my ass when studying for these exams. Is this a test in integration? A test in algebra? I already had those last year. I want to do some physics! In this case, converting the physical premise to the mathematical relations, or identifying the right equation in the formula sheet definitely didn’t count as “physics”.
As an analog, imagine a computer science class; over the semester, you went over the whole deal – sorting, graph flow, DFS/BFS, pattern matching. Now comes the final exam, and as you open up the questionnaire, your eyes grow wide with despair.
Question 1: Apply the quicksort algorithm to sort the following array. Make sure to write the complete derivation; a final answer only will not be accepted:
318, 330, 44, 304, 181, 472, 80, 245, 185, 45, 250, 285, 404, 370, 430, 194, 273, 180, 233, 146, 132, 473, 331, 291, 265, 444… [74 more items omitted]
What, isn’t that a legitimate question? After all, you learned about the quicksort method in class; here is your chance to show that indeed you know it, earning your exam points in earnest.
Oh, what’s that? It would be a dull and error-prone thing to do, that doesn’t really show the student’s proficiency in algorithms? It would be much better to have the student invent a similar but distinct algorithm to show that they grasp the concepts? In fact, inventing new algorithms and proving correctness and bounds is what actually happens in algorithms tests?!
It’s certainly possible to ask interesting questions, that actually require invoking the student’s physics-neurons instead of just the high-speed-integration ones. In fact, we had plenty of those in our classical mechanics lessons. And they might involve some difficult mathematics in order to get the right answer.
But when I compare my classical mechanics 1 exam with my quantum mechanics 1, I notice that the former’s (great) difficulty was in understanding what the hell I needed to do, while the latter’s was in diagonalizing quickly and keeping track of the trillions of minus signs, ‘s and ‘s. Admittedly, I am no expert, but for some reason I am quite certain that it is not quantum mechanics that is at fault here – certainly there is no dearth of physical reasoning which can also be backed up by mathematics (see Feynman vol. III, for example).
Professors, teaching assistants, professional exam-writers, lend me your ears! Cease the technical absurdity, and return physical insights to your exams! They shall make your students all the wiser, in addition to sparing them the sprained wrists and CTS. And if you claim that the exam should portray only what has been taught in class; well, what exactly have you been teaching then?