One of the hardest things to do, I’ve found, is figure out someone’s final grade.
Putting “D-” on one lab report is relatively painless… double check to make sure that yeah, it really is that bad, but it’s only one grade out of many.
Entering “C” into the official records takes a little more work. It’s particularly hard for the ones that I know have tried consistently all semester. “C” could mean that the student will have to repeat the class. It could prompt them to change majors or careers. It could affect their scholarship or financial aid. Then again, turning all “D”s into “C”s and all “C”s into “B”s isn’t doing them any favors, either, because it overestimates how prepared/apt they are for the next class. So I have to check my sympathetic wish to nudge them up, just a hair, they’ve worked so hard for that “C” and is there really THAT much difference between their work and that of the lower-end “C” students?
Ignoring the names, though, it’s an interesting problem in classification. I’ve got 119 samples, who’ve been tested in various ways with the intention of sorting them into 5 categories, which just happen to have alphabetic labels. Now all I have to do is work out the best way to classify the samples, starting with some pre-determined borders for the categories. There are two types of measurements available, which can be broadly described as measuring independent understanding (“exam” type measurements) and as measuring consistent work to gain understanding (which includes homework, lab work, and attendance grades). The easiest of these to work with are the averaged exam grades and the work-over-time-except-lab. Plotting the exam average against the other average doesn’t take into account the lab grade, however. Should that go into the exam average (because it includes some lab quizzes) or into the other average (because it’s mostly work over time)? Let’s average the lab into both grades. (Losing some orthogonality, but I don’t feel like shoving the data into Matlab for PCA.)
This actually works out pretty nicely:
There’s a fairly clear line between most of the categories. Which means…. that it’s quite easy to draw straight lines between those categories as grade boundaries. This also agrees well with the grades based on the overall average (collapsing the two dimensions here into one dimension, so no surprise)… but it makes it a little easier to show a student that “yeah, you really do fall right into the middle of the ___ pack, so better luck next semester”.
Now to finish up grading the senior class… this is much harder to do with 7 samples than with 119!
