Mathematics is inherently sequential and most of the fundamentally important discoveries have already been made. Though Pure Mathematics has led to useful discoveries, much of the impetus has come from the physical sciences. In the last couple of decades there has been an explosion in new mathematical knowledge. One learns mathematics by practicing logical reasoning on traditional problems. The essentials of a mathematics curriculum is pre-defined.
People learn by interacting with reality.
We must develop new course content and approaches in which students learn to use contemporary tools to apply contemporary mathematics to contemporary problems. I believe present school mathematics curricula reflect objectivistic perspectives of mathematics. We make little or no provision for students to play an active and generative role in learning mathematics and we teach mathematics as if we expect that students will never have occasion to invent new mathematics. We don't teach language that way. If we did, we would never require students to write an original piece of prose or poetry.