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Long division was taught as a set of rules from a cookbook, with no explanation of how a particular sequence of short divisions, multiplications, and subtractions got you the right answer. In high school, extracting square roots was offered reverently, as if it were a method handed down from Mt. Sinai. It was our job merely to remember what we had been commanded. Get the right answer, and never mind that you don't understand what you're doing.

Carl Sagan
The Demon-Haunted World--Science as a Candle in the Dark, 1995