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I recently took an exam, and our professor told us that we should submit our question sheets since 2 other students in our class are going to take a make-up exam. We were also told that we were not allowed to talk about our exam while the other 2 are around. I presume this means that their exams are going to be identical to ours (For the sake of argument, let us assume that this is the case, and it is not in fact a strategy or something of our professor).

Our class is on weekdays (MWF for 1 section and TTh for another), but we had our exam on Saturday afternoon. Since we all have class on Saturday morning, it is okay to have an exam on Saturday afternoon since we would already be on campus. Apparently those doing the make-up exam have conflicts with their plans for Saturday afternoon which the professor accepts.

Essentially, we can't tell them the contents of the exam. Our professor claims that this is so as to not compromise the integrity of the exam.

So here's my first question:

Is it fair to the students taking the exam earlier that the make-up exams are identical to the original?

We are grad students of mathematical finance.

Expansion:

It seems to me that the fact that it is too easy for the two others to find out the exam questions should be reason enough for our professor to give a different and possibly even harder exam and that doing otherwise is in itself compromising the integrity of the exam.

If it's not compromising the integrity of the exam, why not just have the same exam every year and collect the question sheet from students (which, cmiiw, actually doesn't really do anything since we can just copy the questions on a bond paper and bring the bond paper home)?

See possibly related question.

Second question:

I seem to recall that department policy is that make-up exams are "generally" (exact word in undergrad syllabuses but not in our grad syllabuses which makes no mention of such) more difficult. If the answer to the first question above is yes, then does it follow that the "generally" should be removed?

P.S. I truly cannot imagine how difficult it must be to a mathematician: research, teaching, consultation, conferences, etc. Thus, I am aware that it is no easy task for a teacher to just come up with a make-up exam, but nevertheless for the sake of maintaining the integrity (maintain is not compromise?) of exams, I believe this should be done.

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    If the make-up test is harder than yours, it is unfair to them. If it is the same, it is unfair to you. So, the main question is: Why do you care about their exam? You did yours and that is all there is to know. – Alexandros Sep 1 '14 at 10:21
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    @Alexandros "If the make-up test is harder than yours, it is unfair to them." Explain please? – BCLC Sep 1 '14 at 10:22
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    I'm including that in an answer that I'm composing. :) – 299792458 Sep 1 '14 at 10:23
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    As a (math) instructor, I was once of the philosophy that make-up exams should be harder for the reason you gave. Then I realized, the students who tend to take make-up exams usually do worse than average even with the exact same exam (or one of similar difficulty). (I still don't have any way of knowing which students have a valid excuse for a make up, but it almost never happens that students who take a make-up do much better than I expect, so I no longer worry about this.) – Kimball Sep 1 '14 at 12:43
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    I'd like to strongly stress Alexandros point. In what way does the exam of other students affect you? You seem to have an misguided view of "fairness". Yes, other people will always have easier exams. Maybe next year, another lecturer teaches this course and has a much easier exam. Or the same course might be taught at other universities as well and will have a different level. Is that unfair to you as well? This has nothing to do with fairness. This also implies that you care a lot about grades; instead, you should care about learning things, good grades will follow automatically – dirkk Sep 1 '14 at 17:00
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Whether identical make-up exams are fair depends on the circumstances. The key point is that you can't eliminate all potential for cheating: there are too many ways to cheat, and you can't even try to rule them all out without brutal and expensive oversight. Ultimately, you have to make a trade-off, in which you take some anti-cheating steps but stop focusing on cheating once you reach the point of diminishing returns. [For example, if you are really concerned about cheating, then you can't use take-home exams, and you'll have to police restroom visits very carefully for in-class exams. These steps might be sensible under some circumstances, but counterproductive in others.]

So how does this apply to identical make-up exams? If you're teaching a required, low-level class to a large group of unenthusiastic students who desperately want good grades, then cheating sounds like a real worry, and giving the same exam twice would be a foolish decision. If you're teaching an advanced class to a small group of students you know and trust, then there may be no issue at all. Reasonable people could differ as to where to draw the line between these scenarios, and it depends on their judgment of the likelihood and consequences of cheating.

There's more to this than laziness, although writing a second exam is certainly a pain. Instead, there's a trade-off between several effects. If you write a new exam, then you've eliminated the possibility of learning the questions from a classmate. However, there's no way to calibrate the exams perfectly, so you've introduced the possibility that the make-up exam was inadvertently easier or harder, and the students may feel stress or bitterness over this. Both the cheating and the differing difficulty are bad, and there's no way to completely eliminate them both, so you have to decide how much they worry you and balance between them.

There are also matters of educational philosophy. I'm not fond of any approach that tells students I don't trust them or that challenges them to see if they can slip anything by me. That doesn't mean I won't take countermeasures against cheating, but it means I consider the countermeasures to be problematic in and of themselves, so I try to use them as sparingly as I reasonably can.

In practice, how I design make-up exams differs from course to course. Sometimes I write a new exam from scratch (while allowing some possibility of overlap with the previous exam, so students can't be sure something won't be on the make-up just because it was on the original exam). In other cases, I just fiddle with some of the details or replace a few questions, while warning students not to discuss the exam until after the make-up exam.

Regarding outcomes, I find that students who take similar make-up exams rarely do surprisingly well, and on average they do a little worse than I would have expected. Of course I don't know what's happening behind the scenes, and perhaps cheating saved them from scoring even lower. However, I'm at least confident that students aren't using this as an opportunity to rack up lots of undeserved points.

If it's not compromising the integrity of the exam, why not just have the same exam every year and collect the question sheet from students?

It's not a matter of absolutes, but rather of how much the integrity is compromised and what the consequences are. Re-using the same exams every year offers much more scope and temptation for cheating than a single make-up exam does. The longer you re-use an exam, the more likely it is that unscrupulous students will piece together and circulate a list of questions, even if you collect the question sheets. If you do this for all the exams in the course, then the potential benefits of cheating are quite a bit higher than in just one make-up exam. (If I saw the same student repeatedly requesting make-up exams, I would wonder why and might become suspicious.) If the ease of cheating in every exam is known, then the course will attract dishonest students who might never have taken it otherwise. There's a big difference between possibly being able to learn about one exam if you convince someone else to help you cheat, and being able to learn about every exam by downloading a file from the internet. It's reasonable to draw a distinction between these scenarios.

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Assuming that your professor is really going to put forward the same questions in the re-exam (which I doubt he will), he's only saving his labor. There is no way he can ensure that out of all people who took the exam, not even a single person will disclose the contents to the two gentlemen. That's why, most sensible people in this situation would prefer to have a different set of questions over for exam no. 2.

As regards the difficulty level, the reason why we have these kinds of exams is the following: suppose they missed on the original exam because of genuine medical circumstances - that can happen to anyone. There is generally a provision for this at most universities, i.e. show medical records and you can appear in a repeat exam. You might argue that if the record-demand (or the verification of record part) isn't too firm, there will always be people who will use this rule to buy some extra time to prepare. Assuming someone's not genuinely unwell, he would have gone half-prepared into the exam and would have fared badly. But because he 'bought' more time, he may be better prepared now, and therefore may fare better than what he would have originally. Perhaps, this reasoning prompts your comment, and I reckon you would expect your instructor to make the re-exam tougher than the original. But, you see, all possibilities need to be covered here. If someone was genuinely unwell, and hence missed out on the exam, there is a possibility that he may be well prepared for the exam, and would have done as well as you, if he could appear in the exam. But he couldn't, for reasons beyond his control. In this situation, if the instructor is deliberately increasing the difficulty level for the exam, it is unfair to the ill guy. Here, he certainly did not have the benefit of extra time, as the detractors were imagining.

For this reason, sensible instructors will generally go for nearly the same difficulty level only - just to ensure that genuine cases don't get wronged. But of course, there has to be a different set of questions. Identical paper is absolutely wrong.

  • Let us continue this discussion in chat. – 299792458 Sep 1 '14 at 11:17
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    Unless you have personal knowledge of the students involved, I would not jump to conclusions about the nature of their conflict. You seem to be assuming that they had plans to go to the beach or something. My first guess when someone says they have a conflict on a Saturday would have been religious observance; and at least around here (US), such conflicts are accorded great deference, as a matter of university policy. My point is that we do not know the nature of the conflict, and it's probably none of our business. (continued) – Nate Eldredge Sep 1 '14 at 11:22
  • It sounds like the professor is, quite rightly, being vague about it in order to protect their privacy. – Nate Eldredge Sep 1 '14 at 11:23
  • @NateEldredge - OK. I was ignorant of this religious thing, but if you find my 'generous' comment unjustified, I assume others also will, so I'm removing it. I never meant it to be insensitive. :) – 299792458 Sep 1 '14 at 11:30
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    @bclc: To be honest, I'm not really interested in second-guessing your professor here. These situations are difficult to handle; Anonymous Mathematician has done a great job of summarizing the issues involved. (I was considering writing an answer but he/she has made it unnecessary, as that answer matches my thoughts almost exactly.) I would say, though, that even if the exams are not identical, there could be valid reasons for asking you not to discuss the exam until after they take it. – Nate Eldredge Sep 1 '14 at 19:11

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