Why do profs give exams like this?

gravenewworld

All multiple choice exams with only 30 questions. Obviously each question is worth a good amount of points. But why then do they ask questions that say "select all the answers below that apply" and then have a choice of anywhere from 5-6 answers? If you select too many answers you get the whole question wrong. If you just miss one answer you still get the whole question wrong. Then on the whole exam you have 6-7 questions like this. I really have a hard time understanding how it is fair to give out an exam like that. How can you not give partial credit for getting 80% of a question correct for a question that has multiple answers required? The more questions you give that have multiple right answers required, but the questions are all or nothing in terms of points given, significantly increases the chances that a student is going to fail. Why not just break up the questions with multiple answers into multiple questions or give partial credit?

jtbell

I've never given questions like that, in fact I don't give multiple-choice exams, period. But if I did, I'd do something like credit one point for each correct answer, and deduct one point for each wrong one.

dacruick

But then its possible to get -100%, which is faulty in nature. Unless you're going to use a different marking scheme, all possible marks should be between 0% and 100%. Even if you say that no students can get below 0%, it still skews the distribution.

Taking marks off for getting answers wrong is stupid, the marks don't reflect the student's performance. I guess that's why you don't give multiple choice questions

gravenewworld

My point exactly!

I totally bombed the last exam cause either I missed one answer out of a question that multiple answers or I gave too many answers for a question with multiple answers. I really don't get the all or none grading. It is just inviting people to fail.

mathwonk

no matter what scheme, you still get 100 if you know the answers.

jtbell

Unless you redefine the scale.

One thing I don't like about multiple choice is that people get a certain number of correct answers simply by random guessing. For example, if each question has four choices and one of them is correct, random guessing would give an average score of 25%. So that should really be the "floor" of any grading scheme. Either you subtract 25 and then multiply by 4/3 to bring the range back to 0-100, or else you subtract 1/3 point for each incorrect answer (which would be better than my original guess of subtracting 1 point).

The second choice would lend itself better to partial credit on questions with multiple correct answers. Just assign appropriate weights for correct (+) and incorrect (-) answers so that they add up to zero if you choose them all.

Number Nine

Only if the test is written well. I've taken some absolutely bizarre MC tests where simply knowing the material isn't enough (these usually involve unclear or strangely worded choices).

gravenewworld

Of course. But why would anyone group a set of answers such that if you get one answer wrong out of the entire group you lose all credit for answers you provided that were right? Then to top it off you miss a huge portion of an exam like that because you didn't provide 35 out of 35 answers with 100 percent accuracy but only got 31 out of 35 correct. It makes no sense.

Number Nine

This is particularly infuriating in multiple-choice mathematics exams (a stupid invention), where a small arithmetic error in a multi-step problem results in you losing all marks for that question despite getting all of the (say) calculus right.

vela

On multiple-choice exams, this scheme discourages random guessing and minimizes getting points for being lucky. If anything, it makes the grade reflect the student's performance more accurately.

I'll admit when grading free-response questions, I've often been tempted to take points away when a student has written something particularly wrong.

Number Nine

I've had professors dock marks on a particular question for wrong or irrelevant information. You could never get "negative marks", but a correctly answered question worth 3 marks may still only get 2/3 if the student included wrong information along with the answer.

dacruick

I understand the point of the scheme but it shifts averages in an unfair direction. Discouraging guessing is one thing, but taking marks away from previous correct answers goes a step too far in my opinion.

However, maybe it's not the scheme that's so bad, maybe its the weighting. What if you lost 0.33 marks for a wrong answer? This it completely balances out the odds because 1 in 4 has +1 and 3 in 4 have -0.33. That way the expected value of a guess is 0.

Number Nine

The way it was justified by my professors is that understanding something means not only knowing things that are correct, but knowing which information is relevant and which is not, and being able to distinguish between correct and incorrect. I'm tempted to agree with this.

dacruick

It makes sense from a teaching perspective, but having tests with skewed distributions and a wonky statistical mean doesn't make sense. If there were a normalization scheme to go along with it, I don't think it'd be a terrible idea.

vela

Yes, I was thinking of the situation where the weightings are adjusted so the expected value is 0 for random guessing.
A raw test score doesn't really mean anything. So even if a particular test results in a "strange" distribution of scores, who cares? What's important is the scale used to interpret the score.

It helps to look at tests as measuring devices. As with all measurements, there's going to be some error associated with it. Student makes a dumb mistake, fills in the wrong bubble, etc. A well-written test attempts to minimize that error. Most of the complaints in this thread are about how to write a test that doesn't do a good job of that. The blame for that lies solely with the test writer.

Hurkyl

It's not taking marks away from a previous correct answer. It's penalizing a wrong answer. If you get +5 points on problem #1 and -2 points on problem #2, that doesn't change the fact you scored +5 points on problem #1.

Yet another equivalent way of looking at it is you start with -4 points. You got +7 points for your right answer on #1. You got 0 points for your wrong answer on #2. But you could have gotten +2 points for admitting you didn't know how to do #2.

That's not bad enough. If you want to penalize guessing, the expected value of a guess must be less than that of leaving the question blank.

And yes, you really do want to penalize guessing. Admitting you don't know how to do a problem is a much, much better response than making a blind guess.

vela

Spoken like a true mathematician.

One time, I was terribly unprepared for an exam and as a result left it almost entirely blank. The others in the class apparently weren't in a much better situation either, but they wrote tons of stuff on their exams, hoping for partial credit. When the professor discussed the exam with me later, he noted that I didn't write much, but what I had written down was correct. He told me, "You obviously know what you do know and what you don't know. That's a sign of a good mathematician. The other people in the class..." He sighed and rolled his eyes.