> think that cheating is bad
I don't think that cheating is bad.
> recognize that it happens frequently,
Naturally. If you give people stupid chores they will almost universally try to find a way to avoid them.
> don't think that cheaters should be punished.
Even if I bought into everything else ie: that testing is good and cheating is bad, I would still not punish cheaters. As I said, I cheated that one time because I had other issues that made school difficult. Punishing would have done nothing except add additional stress, making me retreat further from my education. But of course, as I just said, I don't buy into all of that other stuff, so it's not only an ineffective and cruel way to approach education, but it serves no purpose.
> It's not clear to me what your point is regarding cheating.
My point is that most tests are stupid, and a lot of what "cheating" is is just making them less stupid. For example, I remember students would hide their notes during a test so that they could reference them. That's just good sense - in what real world situation do you need to have instant recall for arbitrary information? It teaches kids to memorize shit, which is damaging.
Two students checking each others answers? Sounds a lot like any normal adult problem solving.
So you can try to "tweak" the system until cheating is impossible or so scary that people will rarely try, or you can "give up" and let people cheat... or you can take a step back and realize that you've made up a problem with no solution.
As I said, school should focus on the three things I mentioned. Nonsensical testing strategies and finding ways to trick kids for doing what is, frankly, the sane thing to do, is purely damaging.