Reminds me of the shortcuts I use to do math quicker. The catch is that I can make shortcuts because I understand the underlying basic math. If this is advanced material taught after the basics have been learned then I don’t have a problem with it. If it’s being taught instead of the basics then that’s a problem.
You are right.
I think they are trying to keep things at 10 and under, so kids can count on their fingers.
(Which I do, as part of my shortcuts, sometimes.)
Same here. If I'm doing it on paper, I'll use the carrying method, but if I'm doing it in my head, this is exactly the method I use. I didn't learn it in school, though. I do it instinctively.