Interesting Ted Talk by Conrad Wolfram (2010):
He argues that we act like calculating is all there is to math, so that we spend too much time teaching students how to calculate by hand and not nearly enough time teaching them to ask the right questions, frame the questions mathematically, and evaluate the results. (He does not say we should throw out all calculations. It's useful to be able to do some mental arithmetic to make estimates, for example.)
If you've never seen wolframalpha.com, by the way, take a look. It's very useful for statistics (e.g., area of the U.S., population of L.A.), formulas (volume of a cylinder, quadratic equation). You can also use it to check your answers for algebra (and other) math problems.
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