Why do profs give exams like this?

  • #1
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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?
 
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  • #2
jtbell
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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.
 
  • #3
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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.

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 :smile:
 
  • #4
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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.

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.
 
  • #5
mathwonk
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no matter what scheme, you still get 100 if you know the answers.
 
  • #6
jtbell
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But then its possible to get -100%, which is faulty in nature.

Unless you redefine the scale. :smile:

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.
 
  • #7
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no matter what scheme, you still get 100 if you know the answers.

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).
 
  • #8
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no matter what scheme, you still get 100 if you know the answers.
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.
 
  • #9
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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.

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.
 
  • #10
vela
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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 :smile:
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.
 
  • #11
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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.

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.
 
  • #12
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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 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.
 
  • #13
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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.

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.
 
  • #14
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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.

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.
 
  • #15
vela
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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.
Yes, I was thinking of the situation where the weightings are adjusted so the expected value is 0 for random guessing.
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.
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.
 
  • #16
Hurkyl
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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.
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 way the expected value of a guess is 0.
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.
 
  • #17
vela
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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.
Spoken like a true mathematician. :wink:

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.
 
  • #18
Andy Resnick
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Like jtbell, I don't give multiple choice exams.

However, as per the thread title, did you simply ask the professor why they chose this particular format? You didn't specify what class this exam was in; I can imagine many classes, for example classes that require rote memorization, that this format would be good for.
 
  • #19
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I've had those on online assignments, but never exams. Personally I've always thought T/F were the toughest (at least with my professors). Most of what I've had are "If True, explain why. If False, give a counterexample. DO NOT CORRECT THE STATEMENT"

And Physics M/C are funniest because you can just use dimensional analysis lol
 
  • #20
Vanadium 50
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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.

I had a professor once who took 15 points off a 10 point problem. "If you kept your moth shut, I wouldn't know if you knew anything or not. But once you started writing...."
 
  • #21
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This was for a med school genetics exam.



Too many people failed it and they already sent out an email explaining that they have to now regrade the exams with partial credit for the questions that required multiple answers. I don't understand why professors make it so difficult on themselves and stress out their students so much. It should have been clear before the exam was given that grading a test in a all or none fashion for many questions was set up for failure for many students.
 
  • #22
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I'm also frustrated with multiple choice exams. I'm taking physics 2 (E&M) currently and it's 100% multiple choice questions for the tests. Most of the time I can get away with analyzing the answers like flyingpig said with dimensional analysis. The tests are 20 questions. The last test tripped me up with some negative signs; in my last physics class I would have gotten docked some points but not the entire question.
 
  • #23
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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.

Maybe it depends on the subject. I am currently pursuing a bachelors degree in physics, and a multiple choice question in physics is cruel enough already. With all the work involved, to either get perfect or a negative score seems foolish.

Aside: Do you think long answer questions should penalize guessing too?

And many on this thread keep mentioning that knowing that you don't know how to do a problem is better than guessing, which I agree with. But you fail to mention when students make a mistake. If a student knows how to do a problem, gets a sign switched up, their 5/5 just turned to -2/5? Thats pretty ridiculous, and IMO, an inappropriate way to test physics material.
 
  • #24
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I had a professor once who took 15 points off a 10 point problem. "If you kept your moth shut, I wouldn't know if you knew anything or not. But once you started writing...."

Lol so people like Newton who made mistake and didn't know something should be penalized more for there mistakes rather then praised for there accomplishment.
 
  • #25
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Lol so people like Newton who made mistake and didn't know something should be penalized more for there mistakes rather then praised for there accomplishment.

...what?
 
  • #26
vela
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Maybe it depends on the subject. I am currently pursuing a bachelors degree in physics, and a multiple choice question in physics is cruel enough already. With all the work involved, to either get perfect or a negative score seems foolish.
It depends on the course, not only the subject. If you're teaching two 300-student sections of lower-division intro physics, the appeal of using multiple choice questions is obvious.
And many on this thread keep mentioning that knowing that you don't know how to do a problem is better than guessing, which I agree with. But you fail to mention when students make a mistake. If a student knows how to do a problem, gets a sign switched up, their 5/5 just turned to -2/5? Thats pretty ridiculous, and IMO, an inappropriate way to test physics material.
Students will, obviously, make mistakes, but that alone is not reason enough to write off the use of MC exams altogether. A good MC test consists of a large number of independent questions, so that the effect of a single mistake is limited. A few mistakes here or there, you can chalk up to random chance. Errors on a significant fraction of the questions, however, likely indicate a student doesn't know the material well.

The main reason I haven't liked using MC exams is because, frankly, they're more difficult to write. It's a lot easier to come up with a small collection of free-response questions rather than a large number of good MC questions with plausible wrong answers.
 
  • #27
mathwonk
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Although the analyses by instructors here of the value of different types of questions is useful, the intent of this thread seems misguided. instead of griping about how many points your wrong answers are worth, you should be focusing on getting them right. only weak students fume about scoring.

i once took 3 high school physics tests in one day, (to make up work after being absent) that were all multiple choice and I got two 100's and one 97. Yes the tests were stupid, but my response was just to nail them, all but one question. Moreover the only question I am proud of was the 3 point one I missed.

It asked what fraction of the sun's light is received by the earth, a number that had been mentioned in the book without explanation. I calculated the surface area of a sphere whose radius is the known distance from the sun to the earth and divided it into half the surface area of the earth, which was wrong. Do you see why I should have used the area of a plane section through the center of the earth?

Now you are right that this story illustrates the potential weakness of (poorly written) MC tests, but when I explained my answer to the prof and asked why it was wrong, I got his respect since my creative wrong solution was more impressive than a memorized correct one, and his explanation got some from me. That was far more valuable than the 3 points, which I did not complain about losing. Someone who argues points unfortunately tends to come off as a whiner.
 
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  • #28
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To the OP,

There could be good reasons for why you would want this type of exam. For example, it might be crucial to the subject that you know exactly the right answers and can determine what the wrong answers are.

Example:(From a math class exam)

What is (are) the cube root(s) of 1?

a) 1
b) i
c) e^(i*pi*2/3)
d) e^(i*pi*4/3)



A question like that shows that if you just pick a, you don't understand the question, and if you pick a, b, c, and d, you're making a really careless mistake. Chances are if you can get c, you won't miss d (or vice-versa), and if you do, you're missing the very important fact that there are always n nth roots of one.

Another example (From a US history exam):

Who of the following was (were) president(s)?
a) Benjamin Franklin
b) Alexander Hamilton
c) Thomas Jefferson
d) James Madison

In US history, it's important to know the presidents! You should know c and d, and the inclusion of a and b is testing whether you have the common misconception that they were presidents (since they're on dollar bills).
 
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  • #29
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Although the analyses by instructors here of the value of different types of questions is useful, the intent of this thread seems misguided. instead of griping about how many points your wrong answers are worth, you should be focusing on getting them right. only weak students fume about scoring.

i once took 3 high school physics tests in one day, (to make up work after being absent) that were all multiple choice and I got two 100's and one 97. Yes the tests were stupid, but my response was just to nail them, all but one question. Moreover the only question I am proud of was the 3 point one I missed.

It asked what fraction of the sun's light is received by the earth, a number that had been mentioned in the book without explanation. I calculated the surface area of a sphere whose radius is the known distance from the sun to the earth and divided it into half the surface area of the earth, which was wrong. Do you see why I should have used the area of a plane section through the center of the earth?

Now you are right that this story illustrates the potential weakness of (poorly written) MC tests, but when I explained my answer to the prof and asked why it was wrong, I got his respect since my creative wrong solution was more impressive than a memorized correct one, and his explanation got some from me. That was far more valuable than the 3 points, which I did not complain about losing. Someone who argues points unfortunately tends to come off as a whiner.
Mathwonk,
I definitely agree with you that a creative response that may be wrong is much more valuable then a regurgitation of memorized material. The fact that you tried to construct an answer using your knowledge of the subject illustrates your strength as a student (when you were a student). I myself have ran into at least a few situations where I have provided a creative proof, that was original in the sense that I had never seen it before, in order to answer an examination question. Although it did suck when i found out I had missed a small step or gone astray somewhere, loosing the marks never compared to the insight I gained. Of course, I would not recommend any student always try to do such a thing on an exam, but they should not be put back when the effort was put and they did not get the marks. Sometimes I still get upset, especially when I have found out a friend or colleague has received the full marks for providing nothing original (it is hard not to get upset sometimes!). There are many exam's I have written that were trivial in the sense that they required little "original thinking", and although I have performed well on such exams, I never find myself particularly proud of doing so as I have not really demonstrated anything special.
 
  • #30
mathwonk
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Theorem, you are indeed kind to look for the good in my response. To the OP, it dawns on me occasionally also that i am getting a bit grumpy and preachy in my dotage.

You are right that a teacher should consider what it is he/she is actually measuring with his questions/scoring. I agree too that you might ask yours the rationale behind the one you question. Like mine, he may have something to say that you will learn from.

In my case, I had arrogantly thought my teacher was an idiot until he showed me he really did know how to deduce the answer to the one I missed. Then I realized he was just not exhibiting his knowledge to us, perhaps assuming we would not appreciate it.
 
  • #31
Andy Resnick
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<snip>
You are right that a teacher should consider what it is he/she is actually measuring with his questions/scoring. <snip>

I could not agree more; I would only add that the teacher should *clearly* communicate their metric/rubric to the students.

There are lots of things that can be measured with any test: factual knowledge, reasoning ability, creativity, communication skills and the ability to deal with a stressful situation are a few. By selecting a particular format, the instructor also chooses to focus on one or a few of these.
 
  • #32
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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.

I strongly disagree with this. If a student is able to eliminate choices, that demonstrates some knowledge of the subject, and should have a positive expected value.
 

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