"A teacher of Mathematics has a great opportunity.
If he fills his allotted time with drilling his students with routine operations
he kills their interest, hampers their intellectual development, and misses his
opportunity. But if he challenges the curiosity of his students by setting
them problems proportionate to their knowledge, and helps them to solve their
problems with stimulating questions, he may give them a taste for, and some
means of, independent thinking." (Polya, 1971)
Real Mathematics involves problem solving, creating ideas and representations, exploring puzzles, discussing methods and many different ways of working, it is not copying methods from the board and reproducing them accurately time and time again.