When I was in school majoring in math we always thought back to how poorly motivated the subject was growing up. So we decided to explain some pretty basic group theory (permutations, etc) to our friend's dad who taught elementary school.
When he brought in the topic with some basic shapes to illustrate the concepts to his kids (4th grade, I think), they all went crazy for it. We then gave him other concepts from a geometry class, which they loved as well (http://www.gang.umass.edu/~kusner/class/462hw).
I think catching them at an early age -- sparking their natural curiosity and giving them confidence in the subject -- is most important, before they're disheartened by all the years of computation and applying algorithms.
When he brought in the topic with some basic shapes to illustrate the concepts to his kids (4th grade, I think), they all went crazy for it. We then gave him other concepts from a geometry class, which they loved as well (http://www.gang.umass.edu/~kusner/class/462hw).
I think catching them at an early age -- sparking their natural curiosity and giving them confidence in the subject -- is most important, before they're disheartened by all the years of computation and applying algorithms.