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Suppose I am taking a mathematics course on something I have studied partially by myself. Say the professor assigns a problem whose proof I have already seen before, whether through owning a textbook that contains it, a lecture or assignment in a different course, or elsewhere during the natural course of pursuing a curiosity.

What is the best course of action in this case? Does it matter how I originally learned it, eg. if I have previously solved the problem myself versus having previously seen a solution?

  • Comments are not for extended discussion; this conversation has been moved to chat. – eykanal Feb 7 '18 at 15:13
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This is not a difficult situation, you worked on a problem and understood the solution, then having it set as an assignment - your grade is based on the effort you have put in - either during the course or before.

Benefit from it - other topics you may not be so lucky...

Whether it is an assignment or a final exam - this is NOT cheating - you put the work in and that's fine.

If the professor was meant to write "new" questions and did not, instead re-using old ones then that is their problem, and they may not see it as a problem ie back to "it's the work you put in".

Some students will do every problem they can find on a topic, others will only do two and say "that's enough" - apart from the students with "genius" level or a photographic memory then the grades tend to follow effort...

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    I totally agree and would add Feynman's distinction between knowing and understanding. – rul30 Feb 4 '18 at 9:37
  • Grades should not be given based on effort but on result, based on the effort that created the result if you like. Otherwise I agree fully. (+1) – Bent Feb 4 '18 at 13:17
  • As in “practise with knowledge of results makes perfect” - it’s no good practising badly... – Solar Mike Feb 4 '18 at 13:31
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    @Bent: FTM, why should "effort" matter? Not to brag or anything, but there were some courses in which I got excellent grades with little effort; others - music sticks in the mind - in which I worked my butt off yet came in near the bottom. – jamesqf Feb 5 '18 at 8:12
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Do not dig out your notes from back then and copy them.

That's really all there is that could be an ethical issue. Solve the problem again, using your understanding of the material and memories of past studies - just like everyone else. You just got lucky that your past studies happened to include very detailed examination of this specific problem, and that you therefore know it thoroughly. Everyone sometimes gets lucky on an exam question that's about a topic that comes easily to them.

Edit to clarify: This is especially for the case where you have merely seen the answer in question in a textbook/lecture. We all agree that googling a problem and copying the solution from the textbook you found that way is wrong. Just because you happen to remember the name of the textbook doesn't make it right.

The goal of a graded exercise is to demonstrate that you can solve certain problems. If you still remember how to solve it, you don't need to look at your notes. If you have forgotten, you don't know how to solve it any more - so it would be cheating to pretend you do.

  • Comments are not for extended discussion; this conversation has been moved to chat. – eykanal Feb 7 '18 at 15:16
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The other answers seem to suggest that you got lucky, which is something I disagree with entirely. Math classes are not a bunch of disparate courses or linearly organized. Last semester, I routinely gave exercises in a number theory class which duplicated material in an abstract algebra course, which some but not all of the students have had. The point was I wanted students to understand certain things from algebra for my course, but I can't assume everyone knows it as it is not a prerequiste.

At least in the US, students come into math classes (from lower-level to upper-level) with very different backgrounds and my goal for all of the students is to reach a certain level of proficiency and understanding of the topic, not to have each student learn at least X much material that is new to them. (Though if a student already knows almost everything in the class, they are probably in the wrong class.)

I am totally okay with exercise/exam problems being easier for people who have stronger backgrounds (or at least stronger in relevant areas). The only thing I am sometimes not happy with is if someone solves the exercises using results we haven't covered/assumed already in the course. If you're worried you might be doing this, or you want more challenging exercises, chat with the instructor.

  • Heh, your "not happy" situation happened to a bunch of us in highschool - our physics teacher taught us derivatives before our math teacher got to them. After seeing some of us using them, she explained that while we could use them to confirm our work, we had to show it using limits on homework/tests because she wanted us to actually understand derivatives, not just use the rules by rote. – Izkata Feb 5 '18 at 4:48
  • I was a victim of approach similar to your "not happy". Getting low score for using more efficient method can be really discouraging. Then, not getting bonus points for using both methods can be even more discouraging. – Mołot Feb 5 '18 at 14:12
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On a homework assignment, it normally doesn't really matter. You might leave a note telling the grader that you've seen the problem before, but it's kind of a point of minor interest.

Even on exams, it's often not a big deal. We might say that you got lucky, but if it just happens to be a question that you've studied independently or remember from a prior assignment (if the instructor's reused them), then awesome. Sure it may not be ideal for an exam, but that sorta thing happens.

One case in which it does kinda get ugly is on a major exam with, say, 3 questions on it. Then, an instructor might give a question from a previous year that a student may've seen the solution approach to through no dishonesty of their own (e.g., an older student may've tutored them and used it as an example from their memory, or the instructor may've forgotten that they did the same in a class one day).

In that more extreme sort of case, it may be worthwhile to bring it to the proctor's attention and ask them what to do. Then, the proctor'll generally make an announcement about the issue, instructing students on how to handle it, e.g. skip the question, do it anyway, or replace it with some modified version or new question.

  • If you write a test using old questions, it's your own fault if some students have already seen the answer, not theirs, regardless of how many questions there are. – Jessica B Feb 5 '18 at 18:24
  • @JessicaB It's not typically an issue of whether the instructor's at fault, but rather an issue of fairness to students as they're often ranked/curved relative to other students' performance. For example, if an exam has 2 versions, and 1 version has a question that was given as an example in class, then it's pretty unfair to the students who got the other version. The typical response in situations like that is to inform the proctor, then they go on damage control. – Nat Feb 5 '18 at 18:29
  • Writing two different versions for a major exam is unfair in the first place, unless they only differ by number changes with minimal effect on the outcome. I'm also not a fan of relative grading. Grades should be awarded for achievement, not for lack of achievement on the part of someone else. – Jessica B Feb 6 '18 at 7:18
  • @JessicaB Yeah, there're a lot of inconsistencies in modern practice. By the time we get to issues like the one referenced above, it's often too late to do much more than damage control. – Nat Feb 6 '18 at 7:43
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I ran into this question, writ large, in high school, so my perspective may be skewed.

In 7th and 8th grade I took a 2-year course on American History. We used a standard textbook pair, and our tests were the generic ones from the teacher's guides, though as I was in an honors class the answers for matching and multiple choice questions were blanked out and we were expected to supply our own answers. (Our grades were also based on a fair bit of supplemental work.)

I moved to another state between 8th and 9th grade. In my new school, 9th and 10th graders took a two-year course of... American History. From the same textbooks. My teachers administered... the standard tests from the teacher's guide.

Every exam I took in History class during 9th and 10th grade was the exact duplicate, in much easier form, of a test I had taken 2 years before.

I saw zero ethical problems in studying for my tests by reviewing my own graded papers from tests I had taken at a lower academic level.

In your case, you are being assigned for homework problems that you have already done during your own independent learning. If they are well-known problems then the solutions are probably available online, as well. I'd suggest that you attempt to solve them again from scratch, so that the skills and techniques are fresh in your mind (the true underlying goal of most homework), and only refer back to your previous solutions if you get stuck, but I see no ethical issues in applying work that you previously did while satisfying your own intellectual curiosity.

  • If you made your teachers think you were really good at the tests, rather than that you had studied all the material before, then what you did was unethical, although in a context where the consequences are smaller. – Jessica B Feb 5 '18 at 18:22
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    @JessicaB I had actually complained about the usefulness to me of the class in 9th grade and was told by the school administrators to STFU. The school knew I had already studied the material from the same textbooks. – arp Feb 12 '18 at 22:36

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