On Edspresso, “John Dewey,” who’s studying to become a math teacher, observes that education professors value “divergence” (more than one answer exists for a question) and regard “convergence” (only one answer exists) with disdain.
I think ed school teachers take an oath to uphold these beliefs as part of an attempt to turn math into a “divergent thinking” type of subject like social studies or English. Such thinking reflects a significant and depressing lack of understanding of what math is about.
More emphasis on teaching students to solve proofs might help, but geometry has become proof-light.
The proofs that exist in today’s high school geometry courses are trivial; many textbooks have turned most theorems into postulates so that geometry has become a collection of “taken on faith” propositions with no proofs offered. Geometry classes have become nothing more than memorization of formulae (areas, volumes, surface areas of volumes) and very few proofs.
I remember asking my geometry teacher why the “given” was given. He couldn’t explain the underlying thinking. He just knew how to march us through the process.