APEC, the awkwardly named Asia Pacific Economic Cooperation, has established among its educational priorities developing "21st century competencies and skills". Disregarding the near redundancy in that term, the international group has done a good job in defining what those abilities are, building on the basis laid down by the Partnership for 21st Century Skills. So we have a reasonably good idea of what these (learning and innovation, career and life, digital literacy) skills look like; what about the schools that will develop them?
My expertise is in secondary education, so I will confine myself to that level, rather than primary school, here (if you want to see 21st century universities and polytechnics, we already have those in abundance in America; it's the K-12 system that most needs attention). But a 21st century secondary school should build upon a firm foundation laid down during primary school, and might be considered an extension of it, like the middle school portion of a Nordic comprehensive school providing nine years of high quality basic education for everyone. But that middle school would be better transformed into a side-by-side pair of modern single sex middle schools, where boys and girls inhabit their own sections of a common campus and learn the same curricula under separated, optimally pedagogically adapted conditions, an ideal perhaps best executed in east Asia (I taught such students in South Korea). But these middle schools should connect in turn to a three-year coeducational upper secondary school, one providing a high quality general academic education preparing its students for university in the manner of a French-German lycee (Gymnasium) preparing its students for a qualification entitling them to a university education at public expense: let's call it an American baccalaureate certificate, or an international Matura. And such a publicly funded, privately managed school (each of these two factors as independent variables being associated with higher student achievement) might ideally conclude in a magnet school resembling a United World College.
Such a secondary school, operating under a federal charter on a state-of-the-art campus (part of the definition of "state-of-the-art" including the fact that it could be built and operated on ordinary, rather than extraordinary, capital funding levels for contemporary public school campuses), would be optimally designed as a flagship to make America's schools truly competitive and able to "win the future" in the present-day world. Its description also describes what I am trying to create now.