Originally a comment at Philosoraptor.
If you don't get children thinking as they learn from as early an age as possible, they'll never shake off the rote regurgitation of factoids or, at best, the ability to solve exactly the class of problem that you've taught them. They'll never grasp the meaning in the equation.
Teachers matter, but for the most part parents are decisive. If they permit their children to follow the truth, their children may try to understand how things work instead of how their parents and teachers want them to work. The academically free approach is perfectly encapsulated in Richard Feynman's title, What Do You Care What Other People Think?. I was blessed with a mom who introduced me to Darwin at age eleven (me, not her!). (She was a public school educator and also an exceptional mentor.)
None of my teachers were going to do this. They were too conservative (in the South a long time ago), too unable themselves to question their social conditioning.
I went to college with a botanist who told me that in no case could a blackberry be considered a berry because botany classified blackberries as drupes (actually, an aggregate of drupelets, but nevermind). No amount of lexicography could move her off that dogma to a more open-minded view that words have different and still legitimate senses. She teaches high school science now, hopefully with a little more perspective.
Since I knew this botanist at Harvard, for chrissake, my result matches jimbales's for elite institutions. Critical thinking appears to be as damn rare in them as everywhere else.
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