Paul Lockhart, from an essay written way back on 2002:
Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity—to pose their own problems, make their ownconjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs—you deny them mathematics itself.
It is not necessary that you learn music from a professional composer, but would you want yourself or your child to be taught by someone who doesn’t even play an instrument, and has never listened to a piece of music in their lives? Would you accept as an art teacher someone who has never picked up a pencil or stepped foot in a museum? Why is it that we accept math teachers who have never produced an original piece of mathematics, know nothing of the history and philosophy of the subject, nothing about recent developments, nothing in fact beyond what they are expected to present to their unfortunate students?
The more I read about mainstream education, the more convinced I become that it serves primarily as a babysitting service and mandatory social club. Imagine if kids actually spent their first two decades doing something they were really passionate about.