### Or maybe they just studied really hard.

My early afternoon precaclulus class has always been a shade weaker than my late afternoon precalculus class; class averages tend to differ by around 5% from one class to the next.

Until this week. Class average on the early afternoon test: 58%. I found this bewildering, as I thought that this test was considerably easier than the previous two. My late afternoon class agreed with me: their class average was 78%.

I don’t like to assume the worst of my students, but no mathematician can look at the data I’m looking at, without incorporatinng their knowledge of standard deviations and variance and accuracy within such and such percent so many times out of twenty and concluding that in all likelihood, something is awry. Since my two classes are one right after the other, with only the ten minute break to get between buildings, I’d naively assumed that it would be okay to give the same test to both sections. Curiously, my early afternoon class - the ones who bombed the test - tended to leave the classroom early. Most were gone an hour into the ~~sixty~~ *eighty* (thanks, rohan!) minute test, which left them with half an hour to talk to the late afternoon students. By contrast, I had to pry the test out of half of my late afternoon students’ fingers.

Next week, I’ll write two tests. This shouldn’t be much extra work, as many of my students are so weak that “find the maximum possible product of two numbers that sum to 50″ is a completely different question from “find the maximum possible product of two numbers that sum to 60″. But this still leaves the question of what to do this time. I hope that at the very least, the early afternoon informants were being paid well for their sacrifice.