Absolutely, from kindergarten all the way through university. Boys and girls learn differently, and would be best served by schools that cater to their learning styles. However, schools would also be expected to coordinate with each other and arrange a large number of chaperoned recreational activities that involved both boys and girls in order to teach them to relate to the opposite sex in a proper, respectful, and positive fashion.
Boys and Girls would be taught an identical curriculum for the first ten years focused on math, science, physical education, and a social studies education that glorifies the cultural and material accomplishments of western civilization.
15 year olds would take a series of tests to determine scholastic, vocational, and physical aptitude. Boys who did poorly on these exams would be sent to a vocational high school to learn whatever trade they would be best at. Physically gifted boys could either go to the vocational school or attend a military-style academy focused around sports and discipline, with the ultimate goal of producing superior soldiers, police, and professional athletes. Boys who did well on the scholastic part of the test could attend vocational school, go to the military school as long as they met certain physical minimums, or could attend an exclusive university prep school, which would endeavor to give them a complete high school education but also allow them to specialize in certain subjects to an extent. Universities would only be open to graduates of these schools.
Girls would take the same aptitude tests. Those who received high scores could attend a university prep school similar to the boys. All the rest would be sent to a school focused on teaching domestic skills, instilling them with a good cultural education, and keeping them strong and healthy.
Men's and Women's universities would teach similar curricula with the intent of instilling students with a true classical liberal arts education. The first two years would focus exclusively on math, philosophy, music, rhetoric, history and a few introductory science classes. After that, students would specialize, with the expectation being that most would focus on STEM, medicine, or law. Degrees in history, physical anthropology, music, and philosophy would also be available, however the student would have to pass a murderously difficult entry exam to prove that they actually have something worthwhile to offer their field and aren't just going after an "easy" degree.
By putting all the kikes in the oven along with their books, of course. Really though, I think that if schools focused on providing a rigorous classical education, the problem would basically solve itself. There's nothing the Jew fears more than the classics, because they remind the white man just how noble, wise, and beautiful his birthright is.
Already covered.
The military will be exclusively male, as it should be. There will be no other explicit prohibitions, but children will be taught proper gender roles from a very young age, so most jobs will likely become de facto segregated as well.