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There's a lot of anecdotal stuff online about the myths of teaching/learning math. These "Twelve Math Myths" seem to come up again and again.

This list of "myths" written with a strong political bias. Take it in with a grain of salt. I like that they include references and links for why they believe what they do. This article would be good fodder for discussion.

I keep writing, in bits and pieces, about the middle way between the two approaches. For example, there should be enough discovery for every kid to firmly believe they could derive anything, if needed. This "just enough" will vary from student to student, too. In "The Glass Bead Game" Joseph took years to trace one short (highly abstract) game transcript to its very roots. He wanted to see for himself if the game was real. He did not do it for every game, though. The idea of "flow channels" between two opposite bad states comes to mind: http://www.secondlanguagewriting.com/explorations/elements/flow.jpg

"A major study into maths attainment has found that boys and girls perform equally in the subject, dispelling long-held myths around gender and education. The first UK-wide research of its kind for 13 years was carried out by Keith Topping, Professor of Educational and Social Research at the University of Dundee, and education assessment company Renaissance found differences in maths attainment between girls and boys to be almost negligible. The study also found that regular and high-quality maths practice improves outcomes across the board and that primary pupils outperformed secondary students, with better attainment scores."

A book by Reuben Hersh and Vera Johnson on the "hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians."