Does fractal geometry make mathematics more interesting and less intimidating to children?
Mathematics has a great strength that also leads to a great weakness. The monumental strength is that established mathematics can be taught from top down in a way that allows no doubt about the validity of the result. In this approach, the principles are simple — but also very far from real — shapes and things. They are not inspiring in themselves and can be called dull, dry, cold. Students must learn something very unnatural: to dominate boredom and recall those principles very exactly. Gratification is endlessly postponed and cannot be found in the end product as much as in quirks of the proofs that lead to that end product. In limited but significant ways, fractal geometry is the opposite. Of the mathematical topics that can be taught in schools, fractals are the only concept that was developed by someone who is still alive. Moreover, fractals have the romance of being beautiful and involving two forms of drama: the drama that is provided by recent resistance to their acceptance a
