His seems to advocate that children should be taught to explore math problems and make discoveries rather than memorize and practice given truths. My layperson's read of your comment finds some commonality between your positions.
I used to teach math and reading Lockharts Lament was deeply satisfying. He is much closer to the light than our current system, but in retrospect I think he's got his head in the clouds a little.
http://www.maa.org/devlin/LockhartsLament.pdf
His seems to advocate that children should be taught to explore math problems and make discoveries rather than memorize and practice given truths. My layperson's read of your comment finds some commonality between your positions.