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Football players lift weights because it is known to be one of the more effective ways to build muscle strength. Do we have evidence to support the claim that learning calculus is particularly effective at improving general cognitive ability?

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Good question. Maybe rigorous mathematical expositions should be replaced with visual metaphors or explanations that will get the idea across without children going through tiresome process of manipulating symbols and calculations.

"The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols."

http://worrydream.com/KillMath/

Most people can’t do more than the simplest derivations in their head, the symbols are just a notational placeholder, and also used to communicate with others.

The abstraction is the what you have to have a knack for, not the symbols themselves.

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