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There is a course at my university that has not had a correctly posed exam as far as any student remembers.

The exam consists of five problems of the type "Prove that if A, then B". At least one of the statements to be proved later turns out to be false.

This happens every year. No one from the teaching staff ever acknowledges this in writing, neither before nor after the exam. They usually make the grade cutoffs more lenient as compensation.

Has anyone encountered such a situation? What to do here, as a student?

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    Disprove it for bonus points? – Roland Feb 8 at 18:09
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    Have you checked what the solutions to the exam say? How sure are you that the problem is not designed to be that way? – GrayLiterature Feb 8 at 18:09
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    Country? Is the university system nice to students, arw students generally heard? Any student union? – user111388 Feb 8 at 18:40
  • This should be closed because it is a complaint, not a question. Students cannot do much of anything except switch to a different university. – Anonymous Physicist Feb 9 at 4:12
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You don't say what field this is, but in a logic or math course this might be a perfectly fine sort of question if the objective is to recognize errors, incorrect statements, and poor reasoning.

Recognizing that something isn't true and saying why can be just as valuable as providing a proof of something that is true. After all, in the political sphere there is a lot of such flawed reasoning that you can see every day in common media.

So, before you object, or claim that the professors are incompetent, explore why this is happening. Just the fact that it recurs implies to me that it may well be intentional.

However, I would hope that instructors using such a technique give some sort of warning beforehand.

I used to warn my students that the final would have one question that would be extremely difficult (nearly impossible) for any of them to answer. It was a thought provoker. But I expected students to say "something intelligent" for such questions even though I didn't expect solutions. The grading has to reflect this, of course.

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    A warning to expect a false assertion is absolutely necessary. It might be "one of these requests for a proof is for a false statement" or (better, I think) marking each request "prove or disprove". Warning about and then asking a really hard question with no answer given what's covered in the course is in a different (also acceptable) category. – Ethan Bolker Feb 9 at 0:24
  • "Just the fact that it recurs implies to me that it may well be intentional." This is not plausible. – Anonymous Physicist Feb 9 at 4:11
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    @AnonymousPhysicist how is it not plausible? If the same (perceived) error keeps happening despite it being pointed out to the teachers, you have to at some point conclude that it's probably not an error ... – xLeitix Feb 9 at 14:31
  • @EthanBolker. actually, whether an explicit warning is needed or not would depend on how the course was taught. If finding invalid arguments were already a clear part of the learning process (teaching/exercises) then it probably wouldn't need to be stated that it would be tested. Of course "gotcha" questions of any form are questionable (or worse). But we don't have full context here. – Buffy Feb 9 at 14:34
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    "If all apples are blue, then and blue things taste nice, then all apples taste nice" is a correct statement, if if the assertion that apples are blue is false. I don't think this needs a warning, nor would it be a particularly hard question. – Ian Sudbery Feb 9 at 19:31
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[Answer will surely depend on location; the following is US/Canada specific]

If the grade cutoffs are adjusted as compensation for mistakes on the exam-setters' part (and not for some other reason: perhaps there is actually an intention to grade on a curve?), then that suggests that these really are mistakes rather than intentionally false statements.

Carefully collect as much documentation as you can. Then find the lowest person in the chain of command who will listen to you and politely present your case. (The tradeoff is that the lower-ranking people have less power, but they are also more likely to take the time to listen to you. If you can convince them they will have a better chance at convincing someone with more power to do something. Also, going too high initially [e.g. sending a letter to the head of the university] might get you dismissed as a troublemaker, if your contact isn't just ignored). Starting from the bottom:

  • A current graduate student teaching assistant
  • an instructor (you say "No one from the teaching staff ever acknowledges this in writing", but it's not clear to me what kind of approaches have been made to them in the past)
  • (out of the chain, but worth trying if the instructors won't listen): an ombuds office/person, if one exists at your institution (example)
  • the chair of the responsible department

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