Communist, Socialist, and Capitalist School

Communism and capitalism seem to be two extremes of economic systems while socialism is somewhat of a compromise.  In communism, the school would reflect the economy in that the government would make all decisions for its students.  All schools would need to be public and your course of action as far as your career would also be chosen by the government.  On the opposite end of the spectrum, capitalism would only have private schools leaving the cost of education to those who could afford it.  Only some people would be able afford to send their kids to schools, so, in a way, your career options are being chosen for you in a capitalistic economy as well.  Smaller factors such as classes and amount of education would also be up to the student and his/her family.  Socialism is a balance in that, although many things would be provided by the government such as education, their still is not as much choice as in a capitalist school system.  Many classes would be chosen for you, but some might not be.  Amount of education would be a choice after a certain point, yet the government may make it mandatory for a certain amount of years.