First, let's talk about your question. There are no Jewish public schools in the United States. If a school is Jewish, it must be a private school. If you are talking about a public school with a large population of Jewish children, that is another matter entirely.
The author says that his mother sent the children to "white schools to get the best education" (McBride 22). Later on in the book, the author states that she sent them to "predominantly Jewish public schools" (67). The author explains that his mother felt Jewish parents cared about scholastic success and raised their children accordingly. Since education was a priority for Jewish parents, they often settled in the same neighborhoods. This gave them a kind of "majority role" in their neighborhood public schools and made it easier for them to be involved in their children's education. There is good evidence to show that parents who are actively involved in their children's education have children who are more successful. Ruth was aware of this, and knew that her children would be most successful in an environment in which there were more interested parents and more successful children. There is a kind of ripple effect in a school, so that success breeds success for everyone, and sometimes failure breeds failure in the same way. Ruth was perfectly aware of this, and even though she cut herself off from the religious aspect of Judaism, she maintained the cultural goal of academic success.
I hope this helps!