1) The adjustive or adaptive function. Schools are to establish fixed habits of reaction to authority. This, of course, precludes critical judgment completely. It also pretty much destroys the idea that useful or interesting material should be taught, because you can't test for reflexive obedience until you know whether you can make kids learn, and do, foolish and boring things.
2) The integrating function. This might well be called "the conformity function," because its intention is to make children as alike as possible. People who conform are predictable, and this is of great use to those who wish to harness and manipulate a large labor force.
3) The diagnostic and directive function. School is meant to determine each student's proper social role. This is done by logging evidence mathematically and anecdotally on cumulative records. As in "your permanent record." Yes, you do have one.
This part makes some sense (and reminds me of a claim I heard that the philanthropist Andrew Carnegie was behind the modern education system's emphasis on unstructured rote memorisation of facts rather than critical analysis; the former makes useful worker drones, whereas the latter can breed revolutionaries and troublemakers. Mind you, it wouldn't surprise me if the source of the claim was some Marxist or anarchist pamphlet.)
Point 5, however, is a bit more paranoid.
5) The selective function. This refers not to human choice at all but to Darwin's theory of natural selection as applied to what he called "the favored races." In short, the idea is to help things along by consciously attempting to improve the breeding stock. Schools are meant to tag the unfit - with poor grades, remedial placement, and other punishments - clearly enough that their peers will accept them as inferior and effectively bar them from the reproductive sweepstakes. That's what all those little humiliations from first grade onward were intended to do: wash the dirt down the drain.
Granted, school is a brutal, high-intensity pressure-cooker environment that brings out the worst in its inmates, and I can buy the theory that it conveniently serves the purpose of instilling conformity and social cohesion (though, these days, TV, short attention spans and medication also help); however, the claim that it's designed to act as a system of psychological eugenics to keep the unfit from breeding is a bit harder to swallow.