I'll be teaching Calculus I at Emory University this fall, so I found this TED talk to be particularly interesting and useful. TED is a small nonprofit devoted to ideas worth spreading. In this TED talk, Dan Meyer, a Math educator, proposes a Mathematics curriculum makeover in America. He breaks down Mathematics into two categories: computation and math reasoning.
He claims while computational methods may be easily forgotten, as educators, we should focus on math reasoning. He outlines successful procedures to promote mathematical intuition and discussion in the classroom to foster math reasoning. This, in turn, will help students get involved in the formulation of the problem, a useful skill for students who continue to study math, and those who don't.
Can't wait to incorporate his suggestions in my classroom! Have a look and get inspired: