Regression to the Mean

At this time of the semester I'm reminded of a passage from Mathematical Fallacies, Flaws, and Flimflam about the silliness of those word problems about calculating what score a student needs on the final in order to earn a certain grade in the course. The passage notes, "Scores on a test are a random variable that regresses to the mean... If she really wanted a B, she should have worked harder earlier on."

1. A student with a strong B has calculated that if she misses fewer than 12 of the 312 points remaining this semester, then she will earn an A. She sent me an email about her calculation, telling me that she plans to work very hard for the remaining three weeks.


2. An athlete who needs to pass my class will need to get a B+ or better on all of the remaining assignments in order to do so. The athletic department assures me that they will tell the student to work harder (unlikely -- as lack of effort is NOT this student's problem) and will provide tutoring. I am very skeptical.


3. A student with a D average has emailed me asking about extra credit: "Hi this is Alexis again. My average is pretty bad right now. Ive never done this bad in a class and I was wondering if you can give me any kind of extra credit. Thanks...." Unfortunately for Alexis, she has only handed in half of the homework assignments (many of them late) and has been absent eight times so far (and late almost every time she has come to class). She would have been better off with regular credit.


4. One of the pre-service teachers has FINALLY turned in an assignment on time. Unfortunately, it was copied from the back of the book. I wrote her a note explaining that the homework is for her benefit and that if she doesn't take the assignments seriously, then she should not be surprised when she scores poorly on the tests. She was not amused.