Conrad Wolfram gives a thought provoking talk on a different way to teach Mathematics in schools.
We've had the biggest transformation of any ancient subject that I could ever imagine with computers. Calculating was typically the limiting step, and now often it isn't. I think in terms of the fact that math has been liberated from calculating. But that math liberation didn't get into education yet. See, I think of calculating, in a sense, as the machinery of math. It's the chore. It's the thing you'd like to avoid if you can, like to get a machine to do. It's a means to an end, not an end in itself, and automation allows us to have that machinery. Conrad Wolfram
Mathematics is a tool that we use to solve problems. We should enthuse children with its the power to do precisely this: solve problems, answer questions and build things.