I've taught a lot of enrichment seminars on Saturdays. They involve "clock arithmetic," or Fermat's little theorem and the basics of RSA encryption for older st

I've taught a lot of enrichment seminars on Saturdays. They involve "clock arithmetic," or Fermat's little theorem and the basics of RSA encryption for older students, or fractals and ways of computing fractal dimension (and exploring polynomials and iteration and Newton's method), or the differences between geometry on a beach ball, a paper towel center tube, and a piece of paper, or even a bit of Mill and Frege's ideas on how to define a number... Kids love this stuff and they get really excited and they start asking questions about infinity and making connections with their other learning. They have fun, but the topics aren't fun -- they are important and useful! Learning about solids has applications (if that's what you value) to proteins and polymers and all sorts of funky stuff. Check out http://phys.org/news/2014-02-years-mathematicians-class-solid.html http://phys.org/news/2014-02-years-mathematicians-class-soli... for some new solids mathematicians have just discovered, inspired by biological research. Seems better than just learning to hate math. Our current system is certainly not effective in teaching young people to add fractions, which I see as the single greatest indicator for competence in college mathematics (sigh). Ok, after another moment's thought your argument seems similar to "Why should kids read stories and books? To succeed in writing dissertations they need grammar. All that extra reading of literature should be confined to the side..."