I recently read the book "Peak: Secrets from the New Science of Expertise" by Karl Anders Ericsson and Robert Pool. Ericsson is a respected researcher in the field of expertise formation, this is why I take his words as valuable. In a paragraph of the book it reads:
Some activities, such as playing music pop in music groups, solving crossword puzzles, and folk dancing, have no standard training approaches. Whatever methods there are seem slapdash and produce unpredictable results. Other activities, like classical music performance, mathematics and ballet, are blessed with highly developed, broadly accepted training methods. If one follows these methods carefully and diligently, one will almost sure become an expert.
I´ve written him an email, but, in the mean while, do you have any idea what "highly developed, broadly accepted methods" is he talking about? A simple reference to a book, article or website to start with might suffice.
The purpose of my question is that I feel I'm learning maths without any "highly developed" approach, just by following my intuition. If such approach existed I would really like to know about it, to improve my learning, and perhaps teaching, in the future.