## Tuesday, December 11, 2007

### 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.

Courtney said...

I've seen fellow students do this, as well, but it is awful stupid. I don't understand it. But then, I'll study for a final even if I only have to make a 30 on it to make an A. Maybe I'm just a strange person.

This attitude generally comes from a desire to get a piece of paper, and not anything else. If all you want to do is pass some annoying classes so that you are more desirable on the job market, target shooting seems reasonable.

Anonymous said...

I once had a student who was particularly obnoxious and was clearly making an effort to NOT participate in class. He almost never did his homework, which was a component of the final grade. Really, I would've been much happier if he were just not there.

When the end of the semester came, everything was tallied and weighted and he ended up with something like a 69.97 average. The cutoff for a C was 70 and I gave him a D.

He was furious! At first he asked why I didn't just give him the extra few hundredths of a point he needed. I told him it was because he never did any homework and never participated in class in any fashion. (In any other circumstance, I almost certainly would've been done it.)

When that didn't work, he then said I had to roundup to 70%. Why?, I asked. What would compel me to round up? The cutoff - clearly stated in advance - was 70% and he didn't have it.

He then tried to go above my head, to no avail.

I, too, hoped he learned a lesson but I doubt he did.

Interrobang said...

I used to hear a lot of my fellow students making those kinds of calculations, and I always thought that was kind of dumb. I usually went into an exam with the attitude (and often the expectation) that I was going to ace it, and I usually did. (I am the Queen of "Walk In With a 68, Walk Out With an 81" style exam-taking.)

I also don't feel it's often possible to know beforehand how you're going to do on an exam (maybe this is different with math, where you either get it right or not, I don't know), because at least in my exams, you never quite knew what they were going to ask you. In the case of exams I took, that might involve sitting in the exam thinking, "Do I remember how to say 'subway car' in Japanese, or not?" In that kind of situation, your grade is essentially the overlapping part of the Venn diagram between "material on the exam" and "material you recall from the course material."

The Ridger, FCD said...

And then today I had a student spend twice as long as anyone else on her final. She needed a 56 to pass the course (with an 80 cutoff) and she aced it. But she agonized over every half-point question.

People are just plain interesting, aren't they? (Sometimes too much so...)

Anonymous said...

Why do people aim for a C in the first place? Why is mediocrity so acceptable to people? How depressing.

Anonymous said...

I had one this past Spring. He needed 9 out of 15, and left (first or second in the room) having answered just 10.

When he saw the grade he contacted me asking for additional time, or a regrade, or for waiving the minimum passing score, and was furious when I refused. He explained that he was in a rush because an emergency had cropped up, but I reminded him that I had stopped him on the way out, and he had every opportunity to communicate about any problems at that time.

All he needed was 9.

Jonathan

Anonymous said...

That sort of information was very useful to me in college. Typically I had 4 finals to study for and 4 large projects due at the end of the term. When I knew that my grade in say vibrational mechanics was locked in I studied for that final last. That one sticks in my head because I needed a 99% to get from a B to an A and less than 50% to drop from a B to a C. My time was better spent elsewhere.

I still did every problem and took the full 3 hours. There's no reason to tempt fate or risk pissing of the professor by being arrogant.