Ideally, how would math be taught?

Rather than "memorize formula, solve problems, tommorow add more to formula, solve more problems, repeat," how should math ideally by taught?  What kind of teacher would you need?  What kind of student interaction would there be?  And are there any close examples from other countries or societies, past or present?

Math shouldn't be taught at all.  Guidance should be available to help people who need a certain amount of math to learn it by themselves and also for the few people who like it to learn as much as they like, again for themselves on the topics they prefer.  Stop wasting resources on the fuck ups who will never use what's being forced down their throats and things will go much better.