What makes for a high quality education?
A positive context
A social environment & positive cultural context that prizes educational values such as growth, curiosity, learning, wonder.
This is because Humans preferentially learn from those we consider high status and specifically Children use age as a proxy for status. If children have slightly older role model that embody educational values, they will imitate and learn from them.
Because Public schools don't enforce a specific educational culture, they may or may not be able to provide this positive context.
See Techniques to scale an opinionated educational culture for ways to build this.
Personalization
A teacher/mentor/guide that champions the culture while paying an insane amount of attention to each child, personalizing their education & overall development as a human being.
Such a teacher will make sure to Design your environment as scaffolding towards creating the world you want to see.