Best practices when allowing exam cheat sheets Context: I am an assistant professor of mathematics at a small liberal-arts college in the US.

I am currently teaching an applied mathematics course for about thirty students with business-related majors, and I want to give them the opportunity to use a sheet of notes (a.k.a cheat sheet) on their first exam.  I am concerned about the implementation of this policy; specifically, I want to ensure the following:


This policy is as beneficial to student learning as possible.
I close any loopholes that could lead to unfairness or some other unforeseen problem on test day.


Some things I have already anticipated:


I will give the students some starter material that they should include on their note sheet—important formulas, critical concepts, examples they should definitely be prepared to see, etc.
Rules regarding the size of the notes are precise: Students may have a single sheet of 8.5" × 11" paper (or smaller), and they may write on either side of it.
The notes must be handwritten as this requires the students to process the material. (See this question for more discussion on why I believe that ultimately helps my students.)
I will not give a student their exam until they have removed everything from their desk except their note sheet and calculator. (I do not want them searching in their bag/book/folders once they have begun the exam.)


That leaves me with the following questions:


Should I require students to turn in their notes to me before the exam?  After the exam?  Is their anything to be gained by me reviewing their notes?
Would it be better for me to simply give them a formula sheet that I’ve prepared?  I know that this will help the students who are too lazy to bring a notes sheet, but I feel like that’s on them.
Are there other problems I should be prepared to confront?  I want to do everything possible to avoid difficulties on the day of the exam.
Is there research that supports/discourages the allowance cheat sheets?  Am I actually doing something that’s ultimately beneficial to my students?
There is no way to cover every eventuality, but what helps is to have a clear paradigm as to what cheat sheets are supposed to achieve.
Then view every decision you make regarding your exam in this respect.
My paradigm (which may align with yours) is:


  I do not want to gauge the students’ ability to blindly memorise stuff and recall it in a stress situation because it is not relevant to their lives and not what my course is about.
  The cheat sheet thus replaces the procedure of blindly memorising certain stuff.
  Moreover, what they write on a cheat sheet is a good emulation of what they have available through Internet searches, reference books, and similar in their non-exam future. (After all, they may just keep the cheat sheet.)


Applying this, I would add to your points and answer your questions and concerns raised in the comments:


Memorising is your benchmark for fairness.
You cannot avoid slight unfairness to some students (see below for some examples), but as long as your process is more fair than relying on memory, you have won.
Communicate your paradigm to the students.
This way, you avoid that students use the cheat sheet in misguided way that is detrimental to them.
Moreover, by teaching them the spirit of the rule, you reduce the chance and strengthen your position in case of any rule disputes and allow the students to answer certain questions about the rules themselves (do not rely on any of this though).

  Would it be better for me to simply give them a formula sheet that I’ve prepared?


The most important part of memorising before a classical exam is structuring and reiterating the relevant knowledge as this strengthens the actual understanding of concepts (which is what your exam should be about).
Making the cheat sheet handwritten replaces this.¹
Provided cheat sheets are not good for this.
The same applies to machinally created cheat sheets, as they can simply be created by copying and pasting.
In a perfect world, restricting the cheat sheet in size would not be necessary – you cannot prevent students from blindly learning the entire textbook either.

However, it does prevent students from wasting their time – before and during the exam – with an overly extensive cheat sheet.
Moreover, it may increase the perceived fairness of the process.
Finally, there will always be some idiot who manages to blindly copy the solution to every exam task ever given for the subject.

On the other hand, make sure that whatever size limit you give suffices for the content the students should need, so you do not inadvertently reward those with a smaller handwriting, better eyesight, finer pen, etc.
Giving them slightly more space than they need is not a problem; giving them much more space is.
You cannot avoid that some student just fills the cheat sheet with solutions to exercises or previous exam tasks.
However, such a behaviour should not be rewarded:
Make sure that the pool of possible tasks is sufficiently large.
If you cannot do this (e.g., certain parts of theoretical physics have a notoriously low number of exam-suitable tasks), your exam may not be suited for handwritten cheat sheets – but then it is not suited for eliminating the advantages of memorising either.
Handwritten cheat sheets will pose problems to some handicapped students. (Just like memorising is bad for people who have issues with memorising or anxiety.)
Ensure beforehand that every student can voice such problems so that a reasonable alternative can be found for them.

  Should I require students to turn in their notes to me before the exam? After the exam? Is their anything to be gained by me reviewing their notes?


This does not agree with the above paradigm:
You cannot control what students memorised for the exam either.
It may be helpful to verify and helpful to evaluate your approach to cheat sheeting by collecting the cheat sheets anonymously, but this deprives the students of re-using their cheat sheets².





¹ In fact, my own memorising process for exams (that required me to do this) was to write a cheat sheet for everything I had not memorised yet, check my memory with this cheat sheet a few times, write a new cheat sheet with the remainder of what I had not memorised, and so on.
² My cheat sheets¹ are probably the most useful written thing I kept from my own studies, but then I have not revisited them yet.