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What is a good strategy when you realize (e.g. while grading the exam) that a question on an exam was incomplete/wrong?

More concretely:

  1. If it is decided that additional points should be given:
    • How many additional points should one give to the students?
    • And to which students?
  2. Are there other good solutions?

The problem here is that you can never tell who really tried this question and maybe who tried but did not write down anything for it (but maybe saw the problem coming). Other students might argue that the tried most of the exam time an that particular question, so they could not do other questions.

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I feel that this will be handled on a case by case basis, but there are some guidelines that can help.

If a question is difficult due to bad wording or poor setup:

  • Throw out the question and grade the exam as if it weren't part of your total.
  • Give bonus points to students who got it right or partially so.

If a question is wrong:

  • Give full credit for the question to every student.
  • or Give a quiz sometime after the exam worth points on the exam. (a mini make-up exam)

If you have students complaining that they did not have enough time on a question, reevaluate the time allotted for the exam and use your best judgement based on class performance to determine if the question should be treated as a poorly setup question. If not, use this as a teaching opportunity about time management during an exam! Many students will spend time staring at a problem they haven't prepared for properly and then "run out of time" on the other questions.

I tend to err on the side of generosity in these situations, but each should definitely be considered separately.

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    $\begingroup$ One thing that makes this situation difficult is that some students may spend so much time on the non-answerable question that they don't have time for the other questions; whereas other students may have (wisely or luckily) done the other problems first. $\endgroup$
    – Mark Meckes
    Mar 15, 2014 at 8:17
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    $\begingroup$ @MarkMeckes, yes, writing exams is * hard*. $\endgroup$
    – vonbrand
    Mar 15, 2014 at 14:54
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    $\begingroup$ @MarkMeckes, it's a test taking strategy that every student should know! If you get stuck on a question, skip it. I've had to deal with running out of time because I haven't skipped around and it's just something that students need to learn to do. $\endgroup$
    – David G
    Mar 16, 2014 at 18:08
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    $\begingroup$ @Skytso: "it's a test taking strategy that every student should know!" Yes, of course. But this whole question is about what to do when certain things don't happen the way that they should! $\endgroup$
    – Mark Meckes
    Mar 16, 2014 at 20:18
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    $\begingroup$ @DavidG There's still an element of luck if you attempt questions in a random order and happen to choose the impossible question last. Then you won't waste time determining that it's too hard. $\endgroup$
    – Rag
    Mar 27, 2014 at 21:07
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Anticipating that such scenarios are inevitable, a certain amount of warning/advice to students _in_advance_ is helpful. But don't go overboard, or you may generate paranoia about flawed questions.

Especially in upper-division or graduate classes, encouraging critical/skeptical thinking as a matter of course is a good thing.

Trying to "correct" an exam part-way through may be the worst reaction, insofar as some students may have already wasted time. Thus, either throwing the question out or giving everyone full credit is not "fair". After seeing some debacles of this sort on PhD qualifying exams, it finally dawned on me that declaring the exam to simply be whatever it is, possibly with some flaws, rather than trying to repair it during the exam itself, is saner than any compensation scheme.

(Some ways of dodging the issue of flawed exams strike me as adversarial-to-students, e.g., the "prove or disprove" gambit, wherein implied context or forgotten minor hypotheses are "gotchas" potentially unrelated to the mathematics itself. Or use/mis-use of English articles "a, an, the" and modifiers "all, any, every"...)

In summary, I refuse to discuss exams during the exam, so would not overtly admit a flaw in any particular problem... because someone may have already wasted time on it, while others haven't. If an exam is so flawed that it grossly fails to serve its design purpose, probably throwing it out entirely and doing a new exam is the only reasonable course. Even then, some students will have been stressed by the thrown-out exam...

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When I teach a first year undergraduate class I try to emphasise exam technique, and mostly this boils down to them having to communicate that they know what they are talking about to the marker. Mostly this is to stop them skipping lines of working (so when they get the wrong answer I know what they have done), but it is relevant here. If they spot the error then I would expect them to write down an explanation about what the issue is, certainly if they are wanting a good grade. If they understand the examinable material then they should spot the error! Therefore, if an unanswerable question slipped into one of my exams then I would re-write my marking scheme accordingly and mark to this scheme. If a student didn't write anything then I would give them zero. However, I would mark generously (and would read all their scored out stuff to see if they had the right idea etc.).

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If you find out during the exam, announce that the question won't be graded, and explain any grading adjustments. Ask for partial work to be handed in regardless, to be handled as @Skytso's answer states.

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