I don't know about point 1. My parents paid me for good grades, and my attitude towards learning is a little warped now, to say the least. (They were also Tiger

I don't know about point 1. My parents paid me for good grades, and my attitude towards learning is a little warped now, to say the least. (They were also Tiger Parents, though. Motivation is a tricky thing to get right.) For point 2, definitely. I asked my math teacher once what a rigorous definition for a tangent was, and she couldn't give me one. Blah. All these unhappy postdocs and grad students should teach high school.