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I am a mathematics student in the US. For a recent exam, I achieved one of the highest scores. The problem is that the final question was intended to be a challenge, rather than one "average" students are expected to solve completely. Most students got only partial credit for their attempt.

I got full marks on this problem not because I solved it during the exam, but because I happened to see both the problem and solution while I was studying. I'm guessing that I would not have been able to solve it on my own had I not seen the solution. Therefore, my performance on this problem was largely a function of my ability to regurgitate the solution I had seen. This problem was worth a significant portion of the exam.

Is this cheating? Should I tell my professor?

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Bryan Krause
    Nov 29 '21 at 19:16
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    You answered the question using knowledge that you acquired honestly and in good faith. This is serendipity, not cheating.
    – Z4-tier
    Nov 29 '21 at 22:21
  • What you did is called "learning" and it is not forbidden. Jan 5 at 16:00
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No, if you saw the problem and its solution through random reading (rather than getting an advance copy of the exam, etc., obviously), then you have not only NOT cheated, but have in fact been a better-than-average scholar.

I realize that some instructors (and students) have some idea that reading ahead, or consulting other sources, is "against the rules"... (I'm not talking about during an exam, but about an approach to studying for a course) ... but this is bad/dumb/anti-intellectual.

So, no, what you did is not "cheating", it is your reward for taking a broader view of the subject, and reading more broadly. Also known as "scholarship/learning" :)

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Bryan Krause
    Nov 29 '21 at 19:17
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No, you have not cheated. When lecturers create an examination they have the option of writing new questions from scratch. If they choose instead to copy questions from another source (e.g., past exam, textbook, etc.) then they are choosing to give a question that a student may have seen before. Some lecturers do this on purpose, since they want to further incentivise the student to practice through a wide array of practice problems.

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    Indeed. To put it another way, did the professor cheat on the exam by copying a known problem instead of making a fresh one?
    – user21820
    Nov 28 '21 at 20:44
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NO, you have not cheated. It's good that you put in extra effort to practice some problems/learn few stuffs on your own, rather than just depending on the assignments and lectures. It was your hard work that paid off.

A very similar thing happened with me in the last year of my undergrad. The professor had given an exercise in the class as an homework. The question wasn't too hard, but still it was on the harder side. None of us were able to solve it properly; all of us just had some intuitive idea. After few days everybody just forgot about that problem. But before the final exam, as I was doing my revision, I again decided to give it a try, but, again, no luck.

Few hours before the exam I went to the professor's office to ask him about this problem and he told me the solution. To my surprise, that exact same question appeared as a bonus (or "challenging") question in the exam.

Obviously I was able to solve it and my other classmates couldn't. Then, after the exam, I talked to the professor about this and he said,"well, lucky you".

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    Your professor's view is exactly what my father (a physics professor) told me early in my career: If you've already composed an exam and then a student asks you a question that's on the exam, you answer the question and you leave it in the exam. Nov 27 '21 at 3:49
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    Nice ...........
    – Ben Bolker
    Nov 27 '21 at 18:36
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    That is an amazing story!
    – Nearoo
    Nov 28 '21 at 14:59
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I graded a lot of written math exams, and I can tell you I'd be perfectly fine with students knowing some answers beforehand. In fact, we often had exam tasks copied more ore less 1:1 from homework tasks that the student had beforehand, inlcuding sample solution, and you would be amazed at how bad the students did at some of those. So good work, reap the benefits of studying well and being prepared.

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    " you would be amazed at how bad the students did at some of those" I totally relate on that. The worst is that, even when it is explicitly told that some of the homework exercises will be 1:1 in the exam, the results are not much better.
    – YYY
    Nov 27 '21 at 19:57
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    @YYY I did enjoy the students who memorized those sample solutions word by word and wrote them dwon exactly like that, even if we changed a variable name or something minor :). Nov 28 '21 at 7:49
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    @JosephDoob: I'll confess those aggravate the heck out of me. I get some students who bizarrely memorize a proof or problem textually with no understanding. E.g.: globally replace ∈ with ⊂, identify the same set for a - b = ℤ as a - b = ℚ, etc. Nov 28 '21 at 14:10
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The fact that you studied and learned to solve a variety of problems is just good scholarship, not cheating.

When I taught, my tests were intended to explore a students knowledge of the material. I would sometimes include material we barely discussed in class to separate the best students from those who were "merely" good. Whether a student had read the solution somewhere, or derived it by themselves, was less important than their knowledge of how to address the problem. If your professor had actually wanted to test your ability to resolve an unknown problem, then he would have invented an original question. However, few questions, or problems, are truly original which is why we study hard to recognize a broad range previously answered questions. Good work, sir!

Oh! Tell your professor if you wish, but he will look at you rather oddly and wonder why you are wasting his time.

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No. This is what exams are for.

However, those papers that offer a choice of two or three problems of equal and considerable weight are problematic. It may be that a good student must know at least one of the problems by rote, otherwise it is a lottery.

If on day 1 you are given 20 problems and promised that the final exam will be any two of them, master all twenty. This can happen for any number of disciplines. Study.

Now, if this is not a local examination, and papers are not the same across a federated geography, it may be unfair to others that a past question has been re-used verbatim.

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Not cheating, but you are correct -- there's a possible ethical(?) problem. But not in this case.

If you were given, say, a placement exam and specifically told it's about problems you've never seen, clearly you should speak up about ones you've coincidentally studied. Ethically, you're lying by implicitly presenting it as "here's how I solved a problem which I have never, ever seen before". And of course, it's in your best interest to be placed correctly. One could construct examples where it's less and less important and less and less dishonest. A problem on a school test is somewhere below 0 on that scale.

You're probably getting an A either way, and one test isn't that big a thing, and minor changes in grades don't matter than much anyway, and if you did so well your score will be left out of the curve (if there is one). You were only told about "to see how you handle a problem you've never seen" afterwards, and there's no practical way to fix it (the instructor is not going to find a new problem for you), and it's already understood that tests contain a certain element of luck as far as what-they-studied vs. what's-on-the-test.

I've had students come in and tell me they got 2 extra points on an exam (their final score was 2 points higher than if you added the points they got for each problem). That's fun. I generally dead-pan it, telling them it would be too much trouble to change but I'll try to keep it in mind for final grades. If you wanted to bring this up with the instructor, they'd probably be amused, understand where the impulse came from, and not consider for even a fraction of a second that this was anything they needed to fix.

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  • I would add that this "ethical" issue might happen in the case of an oral exam (or an oral job interview); in that case, the ethical thing to do might be to mention the prior knowledge.
    – Stef
    Nov 27 '21 at 21:07
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    @Stef Maybe, but I feel like the OP is already very attuned to possible deception. I'm going for just any "yes, as you've noted, this would be a problem in some situations". Nov 28 '21 at 1:04
  • "it's about problems you've never seen" is a ridiculous claim to make. How in all the tarnations would anyone else know what I've seen? Nov 28 '21 at 20:51
  • @BlokeDownThePub But that's the entire point of the Q, isn't it? The hard test problem was intended to be something the students had never seen -- since it wasn't that way to the OP, they feel they didn't solve it in the spirit of things. That's the key to why they feel they may have cheated, right? Nov 29 '21 at 1:25
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When I was in graduate school, I realized that the professor of the Real Analysis class was taking homework (and later test) questions from the textbook I had used for Real Analysis as an undergrad. My recollection is that I got a C+ as an undergrad. Might have been a B–. I finished third in a class of over 20 as a first-year grad student. Many of my answers came from my undergrad homework, including the solutions provided by others for the problems I didn't get the first time.

I would add a number of my classmates had used the same text as undergrads and had a similar experience second time around. None of us thought twice about any ethical issue here. Nor should you.

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I agree with the other answers that you have not cheated on the exam, or more precisely that you have not violated ethical/academic principles to gain an unfair advantage.

However, depending on the nature of your solution, it is very possible that you should have given some kind of citation or attribution when you reproduced the solution. This applies especially if you saw the solution not in the course text but in some external resource. Even though you did not cheat and deserve full marks on the problem, standard academic principles of not passing the work of others off as your own still apply.

Fortunately, this is not a big deal, and if you're so inclined you can send an email to your Professor letting them know what happened, and including the attribution to the source of your answer in that email. If they are reasonable, the most they will do in their response is thank you for your honesty. Sending such an email may also help to relieve some of your anxiety about whether your conduct constituted cheating.

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    That seems a bit extreme. I would be very puzzled to receive such an email. Also if you study an extensive amount of material, demanding a precise citation is (in my opinion) asking too much. Hmmm, was this in the old exercise sheets of Prof X, the book of DreamConspiracy or the old exam of last year. Furthermore, I have friend that is in his masters now and likes to ask me for some exercises I would put on the exam if I was the prof. How would you want this to be cited (private communication by S.S. Schraven, 2021?)? Nov 27 '21 at 10:41
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    The full citations for a solution to FizzBuzz would be longer than the answer!. Nov 27 '21 at 11:42
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    It's simply not possible to give citations for things you have learned, not knowing you'd ever need again, in an exam, and I really can't imagine anybody expecting it. When you're writing a paper, of course you need to check and cite your sources. When you're writing a closed-book exam, you can't check, so you can't cite.
    – Auspex
    Nov 27 '21 at 15:07
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    DreamConspiracy, I'd say this isn't practical in real life. I have a large set of knowledge at this point.... yet I have no idea where I got each aspect, or even a composed solution, from. Human knowledge doesn't work at this level. It has nothing to do with the formatting and more to do with humans are not computers with indexes tying everything back to some source. Nov 27 '21 at 15:51
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    But then shouldnt also the teacher cite where they got the question from? (Even more so since they have more time to do so?)
    – lalala
    Nov 27 '21 at 17:49

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