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In the book Why Don't Students Like School ( http://www.amazon.com/Why-Dont-Students-Like-School/dp/04705...) Daniel Willingham argues that people need to have a good vocabulary of mechanics, basic concepts, and skills in order to be able to move on to higher order knowledge. Children should learn how to calculate not necessarily to do calculations instead of a computer, but to help their brains develop.

Besides, until kids hit puberty, their brains aren't ready for higher orders of thinking. What they are good at is memorization and mechanics. The more mechanics they learn and the more they memorize as little kids, the better equipped they will be for higher order thinking as teens and adults.

However, we are still teaching and emphasizing arithmetic and memorization in high school — even in the advanced classes. That's the problem, really.

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