My goal is for students to discover as much as possible on their own. I am a fan of George Polya's method of letting them figure things out for themselves, and providing scaffolding as needed to help them. Math is all about problem solving, and we as a nation have turned it into rote memorization of routines, to our national detriment. Thankfully the common core is here, and hopefully we will be able to become a nation of problem solvers.