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I am going to do an online exam next week. Since this will be done by students at home, there is no way to guarantee that they do not cheat. I am thinking of asking for a proof of work, i.e., photos of their sketch papers. It certainly cannot stop anyone from cheating, but maybe it can make it a bit harder.

On the other hand, this is an elective course. So students may not have too much incentives to cheat.

Update: I have decided to not to ask for this. Ultimately, there is no way in preventing cheating in home exams. It is better to save honest student the time.

As for the exam, I am teaching discrete mathematics, and I would like to ask students to apply theorems to solve problems. I don't really test computations because I allow them to use WolframAlpha to do the computation.

I also want to test their ability to discover mathematics, i.e., ask them to do a bit of counting, such as the number of binary trees, and discover a formula for these numbers, and prove it.

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    $\begingroup$ I think it may be in your interest to think specifically about techniques in creating exams to be taken remotely instead of cheating prevention. $\endgroup$
    – Andrew Chin
    Commented Sep 10, 2021 at 17:55
  • $\begingroup$ @AndrewChin Can you elaborate a bit? Thanks! $\endgroup$
    – user11702
    Commented Sep 10, 2021 at 23:34
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    $\begingroup$ What precisely are you testing your students? Ability to compute? Understanding and application of theory? What level of math is this exam for? $\endgroup$
    – Andrew Chin
    Commented Sep 12, 2021 at 8:36

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I also teach discrete mathematics, and do so online, including exams, in the last two years.

All of my test questions in that course are open-response, using the "essay" type of question on the Blackboard learning management system. Students are required to use either LaTeX or the built-in formula editor for any symbolic math statements.

To my understanding, learning logic, rules of inferences, and writing proofs (likely for the first time) is the chief goal of such a course. I don't see how justifying and explaining reasoning can be disentangled from that essential work. I'm not in favor of saying that answers are one thing, and justifications are another (both for conceptual and logistical purposes).

On the issue of cheating-deterence (for which I'm the head faculty expert on the issue), my understanding is that the best practice is to make test questions distinguished between different students. For me, this might mean programmatically altering some of the questions a bit so (a) answers might be a tiny bit different, and/or (b) someone posting a question to Chegg (et. al.) can be immediately identified.

For more on the anti-cheating issue, see this question:

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