I want young children to develop their mathematical thinking and their mathematical memory skills through the use of pattern, relationships, reasoning and puzzlement. I want them to study fractals and all kinds of wonderful geometric relationships that can all be used to enhance the remembering of math facts and the more mundane aspects of math that have to be learned. I want arithmetic to be made obsolete, or at least to be made relevant to the problems solving skills it is designed to accompany.
I've just read a wonderful article in the Harvard Education Letter that speaks far more eloquently than can I to what I am trying to say and do. Changing the Face of Math is a wonderful plea to make math less "cold-blooded", to give students the warm fuzzies when they learn it. It is a plea to make math personally-identifiable-with in the same way that students identify with their favorite reading genre and their creative writing interests. Everyone who teaches math in any way whatsoever should read this article and be resolved to act upon what they discover.