to throw one other, maybe-less-obvious, spin on it:
When you take a class, you see one wrong way to do things. When you teach a class, you see fifty wrong ways to do things.
Puzzling through all the different wrongs ways to think about a problem really helps cement the core ideas... And first-year calc students are masters of creating interesting-but-wrong interpretations.
When you take a class, you see one wrong way to do things. When you teach a class, you see fifty wrong ways to do things.
Puzzling through all the different wrongs ways to think about a problem really helps cement the core ideas... And first-year calc students are masters of creating interesting-but-wrong interpretations.