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On an AP exam, are points awarded or not when a student doesn't use exactly the variable notation as stated in the problem (such as, M vs. m, or I vs Io)?
The answer is, it depends on the context. There's no one universal approach, because each part of each problem is testing different skills, and the rubrics are developed independently by different leadership teams who might make slightly different decisions from year to year and problem to problem.
When we develop each problem's rubric, the leadership spends a long time discussing just this question, looking at hundreds of samples to see the range of responses. I'd say the line we try to draw is, we don't want to award a point where a student may have been ambiguous about communicating their physics understanding; but we don't want to be pedantic splitters of hairs.
To give a couple of examples from an AP question about a modified Atwood machine: on the free body diagrams, we didn't care about the specificity of the labels. The objects were of different masses, m[a] and m[b]. But who cares whether they wrote "mg" or "m[a]g" on the free body! They had communicated that each object experiences a downward force of the earth. The fact that these forces were of different magnitudes wasn't relevant to the particular skill that was being tested in this part. We accepted anything reasonable and unambiguous - Fg, mg, Fe (for force of earth), etc. Failing to award points because "you didn't put the subscript on the m!" would have felt pedantic to those of us charged with creating the rubric, especially when each free body dot was even labeled "object a".
But in the derivation in the very next part, it made a significant difference which mass the student was talking about! Here, the problem was indeed checking to see whether the students understood, in "F=ma", which F, which m? So here, we demanded the final answer have correct notation throughout. I did not feel like a pedant when I failed to award points for no subscript on mg in the numerator of the final expression - such a result does not communicate a full understanding of the physics of the problem!
If you're not sure, ask yourself the question - are you splitting hairs, or are you demanding clear communication? And if you're not sure, just pick one way and be consistent. If you do corrections instead of handing back graded tests right away, then students won't notice or care - they'll learn from the correction that they needed, in that case, to use the notation given in the problem. Which isn't an onerous ask. :-)
I think the issue is more, notation on the test question vs. notation the kid's used to using. Say 3 kids have been using "d," "D," and "delta x" to mean "displacement" all year long. Then a problem comes up on the AP Exam wherein a block slides with friction along a certain horizontal distance D before coming to a stop. They derive an equation for the block's initial velocity in terms of some variables, one of which is D (as directed by the prompt of the problem--"derive an answer in terms of the variables given"). If all three students are imperfect not-quite-angels who didn't read the last bit of that sentence, and they use their prefered variable instead, well, the student who used D is automatically fine, of course; what grader's the wiser? It's students 1 and 3 where I could see a grader saying, "Oh, they just used lower case d; they clearly know what they're doing." While a student using "delta x" gets a point off because they clearly didn't do any substitution.
ReplyDeleteOn the one hand, it's such a minor thing. On the other hand, "derive" problems are all over these exams, so it keeps coming up over and over again. I'd bet it's caused more than a few problems on the multiple choice, too, just for even more quirky reasons under the hood of the students' brains.