The true purpose of a school follows from the true purpose of human life (to know, love and serve God in this life and to be happy forever with him in the next). The central purpose of a true education then is to aid a child in learning to know, love and serve God in this life and to be happy forever with him in the next.
You know that, and I know that, but you could never have that as a mission statement for a public school. The closest secular equivalant would be to help the students grow to their greatest human potential (which IS to know, love and serve God in this life and to be happy forever with him in the next!)
Or to simply achieve "happiness," in the sense that Aristotle would have used the term. Unfortunately, the phrase "greatest human potential" can mean just about anything these days.
And that's my point. A public school cannot in principle provide a true education. Therefore, the problem is public schooling itself. The system must be destroyed or replaced.
A good first step toward better education for all children would be the implementation of a voucher program where at least all parents could choose a true education for their children.