Memorization kills intuition, and should be banned.

Very interesting! I would have loved to hear his talk. I have secretly subscribed to this idea for a while now, but it's so exciting to hear an expert state it.

The whole reason I pursued DYS for DS now 9 (then just turned 6) was that he "terrified" me with his math intuition. He could calculate problems significantly faster than I could. I was convinced he was this rare talent that needed nurturing. After a couple more years in elementary school working through 6th-7th grade math curricula, I saw he could no longer calculate as fast or as accurately because he was "bogged down" by the methodical, multi-step process taught and his compulsion to show his work, crooked columns making errors and he didn't automatically check to see if the answer made sense. I was very disturbed. Last summer we did Mental Math in hopes of regaining his intuition.

I pressed for advanced math (algebra 1) this year and the teachers denied us. So we signed him up for AoPS and he's really enjoyed it. I find the instructor and classmates exude the "love of math" mentality and are not "bogged down" by the process. Many times the instructor asks them to "Guess! Don't think about it--first thing that comes to mind" type stuff. I feel that continued enrollment in advanced math classes, even if it's just for exposure to concepts, instructor/mentor, and excited peer group, rather than for credit and grades, is the needed solution for DS9.

I have also seen that my oldest DS (13) cannot problem solve like DS9 unless it resembled recipe from his textbook. I really believe that DS13's Alg 2 class has not taught him anything new except the discipline of doing assigned problems every night. His math reasoning has not been strengthened--and may have been weakened by fall-asleep mode for a year.