Courant, in his book "What is mathematics?", says the field historically seems to go through alternating phases, from wild, creative, adventurous phases in which new things are discovered -- often inspired by "real-world" problems in physics or engineering -- to more sober, rigorous phases in which another generation takes over and basically cleans up the findings of their predecessors (making proper definitions, constructing and refining the proofs etc.).
But this is far from what math _education_ can be about.
The biggest obstacle to math education is the meme that mathematics is "only for intelligent people". Mathematics at the basic, cleaned up level has almost nothing to do with "intelligence" and a lot to do with memory. I know this first-hand because I used to be really bad at maths and then one day decided to learn it anyway (and did). Most often, when someone doesn't get some result or can't figure out the derivation, it's because he doesn't remember or has never learned the relevant facts. [EDIT: Also, if you think you need to be "intelligent" (however defined) to do math, you will give up sooner when you don't understand sth because you think "uh, I'm too dumb" instead of asking "what am I missing".]
Mathematics is a kind of language, and as in any language, most people will actually need to sit down and memorize vocabulary. It's mundane, it's not fancy-creative, it's a pain in your behind, but once you succeed in automating certain things, the process takes on a momentum of its own.
This "dragon mom" stuff I occasionally read about in the NYT is silly IMHO but it's just as silly for a 22 year-old, who by her own admission doesn't even know the standard curriculum of a plain vanilla mathematics education, to want to be "the ambassador of mathematics" (http://www.nytimes.com/2011/01/18/science/18prof.html). First you do the hard work, then you can fly.