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."
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.
