Is there a preference, in Torah/Talmud, between sending a child to a large (Jewish traditional) school, vs. the parents (assuming they are frum, and have the time and resources), and a hired rebbe educating the children?
The context is home schooling and modern school system. It is not about private schools vs. public schools, nor is it about secular schools vs. religious schools.
A good answer will cite sources in the Talmud and other traditional works, and relevant halachot, and give examples that take into account the history of our people. I would like to build a case for both positions.