Thank you for writing a terrific criticism on how math is taught today. In part because it's one of the oldest taught subjects, I think the field has gotten aw

Thank you for writing a terrific criticism on how math is taught today. In part because it's one of the oldest taught subjects, I think the field has gotten away with how it teaches. In every other field we have an escalation ladder of abstraction that starts from tangible descriptions that a motivated learner could understand all the way up to symbolic jargon that is only accessible to insiders. Math doesn't have this at all. It goes from arithmetic straight into symbolic manipulation with only a sideways glance at describing three dimensional shapes. It's lazy and the field needs to acknowledge that it has practical dimension as well as a theoretical one and each needs to be taught and described differently.