'On Harkness teaching: "I love it! Students are the ones who do all the work!"'
I think the Harkness method used at Exeter
http://www.exeter.edu/admissions/109_1220.aspx makes less sense for math and science than history or literature, and a gifted student may prefer to listen to a knowledgeable instructor than to participate in lengthy discussions with classmates that are slower and less informed than he is.
Exeter teaches math through problem sets , available at
http://www.exeter.edu/academics/72_6539.aspx , and does not use textbooks. I don't favor this approach either. It is true that many Exeter students do well on math competitions, and the school deserves credit for sharing its materials.
Zuming Feng, Exeter math teacher and coach, also teaches at Idea Math , where some of the same materials are used
http://www.ideamath.org/LexCourse.htm .
My 9yo boy has enjoyed playing with "Peanut Software" produced by an Exeter teacher
http://math.exeter.edu/rparris/ .