Methodology of Teaching Mathematics

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.

A marveilous newtrality have these things mathematicall and also a strange participation between things supernaturall, imortall, intellectuall, simple and indivisible, and things naturall, mortall, sensible, compounded and divisible.

I think time will show that the new approach, emphasizing emergent "macro" control, is equally valid in all the physical sciences, and that the behavioral and cognitive disciplines are leading the way to a more valid framework for all science. Although the theoretic changes make little difference in physics, chemistry, molecular biology, and so on, they are crucial for the behavioral, social, and human sciences. They don't change the analytic, reductive methodology, just the interpretations and conclusions. There seems little to lose, and much to gain.