> It holds a monopoly because mathematics teachers teach things by rote and procedure, not the underlying concepts from experience. Really? That was never my e

> It holds a monopoly because mathematics teachers teach things by rote and procedure, not the underlying concepts from experience. Really? That was never my experience. Indeed, algebra got a lot easier once I just started memorizing it. Years later I learned that portions of our system of algebra is largely an agreed upon system for ease of communication and that other algebras also exist for working in other domains. (Taking formal logic also helped explain things a lot! Having to prove the commutative property from a couple of basic axioms is enlightening.) All in all, the entirety of my public school math education in the US was highly focused on concepts and theory.