I just wanted to say that I like the way the article refers to "great teachers" in the plural, and to "the one" bad teacher in the singular. Also, to misconcep

I just wanted to say that I like the way the article refers to "great teachers" in the plural, and to "the one" bad teacher in the singular. Also, to misconception #4, I just finished reading Gowers' "Mathematics: A Very Short Introduction", where he tangentially makes the point that sometimes putting too much effort into trying to get students to understand "the meaning" behind some piece of mathematical technique may be misguided, in part because a given piece of math can represent multiple meanings (he uses the example of xa + xb = x(a+b), which can perhaps be taught more easily axiomatically, instead of teaching "exponentiation is really repeated multiplication").