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.
There has to be evidence of their process for me to accept it as evidence of understanding/ability. I have made it clear to them that this is necessary. Their job is to convince me that they know what they're doing. (But... I'm teaching HS Mathematics). So .. I'd mark it wrong/incomplete. I'm also working on student understanding of consequences of their actions, so wouldn't give them another opportunity on that exam. They would need to improve things on the next exam.