Best practices when allowing exam cheat sheets
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.
I had one professor who would routinely give open-book, closed-note exams. He also said that we were allowed to (in fact, encouraged to) write whatever notes we wanted on the pages of the book.
His reasoning? He figured that most students would discard their notes at the end of the term, but some would at least keep their textbooks. And pertinent formulas and such would be scrawled inside the front and back covers.
I’ve not adopted this practice myself, but you mentioned the benefits of having students assemble their cheat sheets. This allows them to do so, but in a way that might be beneficial even beyond your class.
Of course, this means your questions will need to be suitable for an open-book test – but that’s another can of worms.
Why don't you include the students a bit more in the process, rather than just providing a dictum?
Start out by explaining the pedagogical virtues of having them prepare a note sheet. Avoid the word "cheat sheet", as it gives poor connotations. They are, in fact, not cheating.
Tell them that the written exam will be adapted to the length of the note sheet. If the length of the sheet allows them to copy the book verbatim, the exam will essentially be like an open book exam.
Ask, in class, for suggestions: How long would you like the note sheet to be? Write down all suggestions, and set up an online poll with a deadline. Pick the one with most votes by the deadline, no extensions or excuses.
Have the students prepare the sheet a week before the exam, and organize a Q/A session based on the sheets. Have the students prepare sheets, and perhaps bring your own suggestion to how you would make a sheet, but tell them that sheets organizing knowledge are per definition individual. Allow the students to compare sheets (in groups if there are many students) and discuss among themselves.
In this way you will have facilitated a process where the students feel ownership themselves, and they will hopefully also learn a lesson in organizing knowledge.
I have tried the above procedure with success.