'You should have seen the shock on their faces! Some started complaining. So I said, "No, seriously. You will all prove this. Just wait and see. It will work."'
Are people really that timid when all they're being asked to do is try?
Furthermore they were staring at a theorem that was complicated and abstract enough that none of them had any idea why it was true. They had just been given a method of attack, but had no particular reason to have any confidence in it.
I expected and wanted this surprise. I wanted them to take this handout seriously. I thought that the experience of seeing how easy an apparently impossible problem really was would make them pay attention.
When I taught 11th grade English, I started the year by asking students to write a two-page composition (and gave them a concrete, well-defined topic), due the following Monday. They panicked, hardcore: "How do you expect us to do this? That's 2 whole pages! How can we ever get that muc done?"
Now, even when I substitute teach, I have to spend a decent amount of time hand-holding.
Particularly in classes, it feels like there are not many teachers who take the "Let's try this out and see what happens. It's okay if it doesn't work this time, because we're learning a new skill. It might take a few tries," approach. It's a necessary approach, I think, when learning higher-level thinking, particularly systematized thinking.