I gave my students a take home exam over spring break. (This is normal where I teach) One of the questions was particulary difficult. It came down to a factor of three in the solution. That factor inexplicably appeared with no justification on many of their exams. I intend to have the students I suspect of cheating come to my office to solve the problem on the board. What would you do?
Edit: I gave them the Tuesday before spring break until the Thursday after. I didn’t want it to be right before or right after.
When I say normal I mean giving take home exams.
I think getting them to show their work is appropriate and for any that can’t replicate their work explain to them the downfalls of cheating. The other comments here justifying likely haven’t ever been in an academic setting. Relying on cheating is setting yourself up for failure if you intend to continue studying at a tertiary level.
I don’t think a punishment is necessary for cheaters just a lecture. Let them know people can and have had their degrees rescinded years after the fact when their cheating was detected with newer methods.