[dragonwriter]

> Most private schools do better only because they weed out the expensive problems and force them back to the public system.

The single biggest factor is that private schools, as non-default choices, automatically filter for parental engagement in education, even before considering the filters they put in place in terms of admissions criteria.

Students with parents engaged in their education do better.

[frabbit]

> Students with parents engaged in their education do better

IMHO this is the crucial thing. And it is one of the aspects of Montessori that some parents who are simply aspirational-consumers are a bit thrown by initially.