By definition, Libertarians advocate the complete separation of education and State. They propose that government public schools lead to the indoctrination of children, while simultaneously interfering with the free choice of individuals. They, therefore, strongly suggest that government ownership, operation, regulation, and subsidy of schools and colleges should be ended to achieve true liberty. In other words, Libertarians call for the repeal of the guarantees of tax-funded, government-provided education. Libertarians advocate free-market education where parents, teachers, and students, not the government, should make their own choices on education.
i.e., remove all (or as much as possible) government involvement (complete separation of education and State), while giving additional choice selection and power to the parents of students/citizens.