> if you are well be enough to send your child to a private school

This is a similar but separate effect. Rich, uncaring parents can raise unachieving idiots.

It’s easier to be caring with resources. But plenty of public school difference-in-outcome studies have found a signal from parental participation that I believe remained after adjusting for income.

I have friends who have a kid in one of those schools on financial aid

It's both.

My kids went to a free charter school, with similar setup and care from parents. The outcomes were notable and it wasn't really about privilege imho. (Though some activist type folks I know who count "parents who care" as a form a privilege.)

Which it is? From the child's pov obviously, not from the parent's.

In my experience in private schooling only about half the kids come from money. The rest are on financial aid.

I grew up quite poor.

My parents cared enough to find ways to get me into private schools on grants and scholarships.

My neighbors had just as many if not more opportunities to do so but did not care enough to do so for their children.

Yes, it’s caring. Education as a top priority for poor families is the number one way a parent can give their kid a better life than they had. Most do not even try.

Isn’t Montessori considered kind of weird by many people, though? Like you have to be into child education and actually critically assess the available options to realize it’s probably better than the standard one. Or has Montessori achieved Eternal September?