Math should be taught and approached from a creative, reasearch-like perspective -- which is how it organically developed throughout history anyway. This will help children (and even adults) to know how to better approach problems and figure them out when they get to higher levels. Some of the "rote" memorization of forms and formulas is just silly, and in part is what is keeping anyone from learning any math created after the 18th century until they're a junior in college, by which point most have given up on mathematics entirely.

I maintain that part of the reason that 'geniuses' like Euler and Gauss 'discovered' so much of math is that there was a truly large amount of easy low-hanging fruit for them to find. There's no reason that students couldn't be 'led' to rediscover some of these types of areas for themselves.