Missing the mark
Target practice
“What score do I need on the final to pass the class?”
'Tis the season to wake up and realize that all is not as it should be. Students who missed the drop deadline are coming to class and anxiously asking me what they can do to salvage their grades. Since they are not amused by answers involving time machines and reconstructions of their past, I usually just give them the straight dope:
“You can pass the class if you get 124% on the final exam.”
“Okay. How do I do that?”
“You can't.”
“Then how do I pass the class?”
“You can't.”
“Well, can I get some extra credit?”
“No.”
It's not always so stark, though. Some of my lagging students have at least a theoretical shot at a passing grade, although it usually means getting a better score on the final exam than they have ever managed on any previous math exam. When I post the final exam target scores for the students' information, I always wonder whether that knowledge is actually useful. How does a student use the information that she needs a final exam score of 84% in order to earn a C in the class? Does she redouble her efforts, or does she get discouraged? What about the student who discovers he needs only 43% on the final exam in order to earn that C? Does he get happy—or dangerously lazy?
That last example is real. I had a student in one of my algebra classes several years ago who examined the most recently posted grade distribution and discovered he could coast to a C with a final exam score of 43%. On the day of the final, “Bob” swaggered in, set pencil to paper, and scribbled rapidly for several minutes. Having filled in solutions for the exercises in the first half of the exam, Bob strolled up to the front of the classroom, dropped it in front of me, and headed for the door. We still had over ninety minutes left in the two-hour exam period.
I followed him out the door.
“Bob, are you sure you're done?”
“Oh, yeah. I only need to do half the exam to get my C.”
“No, Bob, you need to get half the final right to get your C. We still have plenty of time for you to do more.”
“That's okay. I did enough.”
And off he went.
You can anticipate what happened next. I graded his final exam and his score turned out to be 42%. Not the 43% minimum required for him to get C, but only 42%. No, I did not go out of my way to screw the foolish kid over. I graded his final exam in a batch with all of the others, using the same rubric uniformly for everyone.
As is my habit, I regrade the finals of all students who end up teetering on the cusp between two grades, just to double-check. Given that Bob had left half the pages blank, his final was particularly easy to regrade. If anything, I had been a bit generous. I could make a case for giving him 41% instead of 42%, but there was nothing on which to base an argument that 43% was justified (unless I gave him more partial credit on certain mistakes than I had given anyone else). There was, of course, absolutely no rethinking required regarding the blank pages.
In Bob's case, his knowledge of the magic number had prompted him to try his hand at target shooting. He needed 43%? Okay, he'd try for 50%, just to give himself a little margin. But this sort of “precision exam-taking” is more than risky business—it's damned foolishness. He would have been better off not knowing.
His phone calls started within hours of the posting of the semester grades. Please, could he just do another page of the final? Could he retake the final? Did I offer any extra credit? Would I let him take someone else's algebra final and substitute that score for the one he had earned on my exam?
No, no, no, and no.
It was not the happiest of lessons, although I hope it was learned.
