One of my recent assignments was as more of a tutor than a teacher. The teacher sent me out with a student that completely didn’t understand the previous day’s lesson. Basically, rounding to the nearest ten and adding. 76+49=80+50=130. That sort of thing. The girl was having a really, really hard time understanding the concept. So I sat with her for a half-hour and got it to the point where she very reliably narrow it down to two options (64 rounds to either 60 or 70) and gets the right answer about 80-90% of the time.
She was quite proud of herself. So was I!
So we went back into the classroom and the teacher asked if she got it. I said, half-jokingly, that she either got it or was very good at faking it.
She burst into tears. “I WAS NOT FAKING IT!”