Where I grew up there was -
Government run school (aka "Public School")
Charter Schools (funded by taxpayers as an alternative to the government run school)
Independent studies (You are enrolled in a government run school. Work is done at home. Tests taken on campus once a week.)
Home Schooling (this is where mom, dad, or both are teaching their children)
My next door neighbors home school their kids up to high school. Then they send their kids to government run school. Mom holds a degree in education and is certified to teach in government run school. I see how that would work well.
With my own children I saw indoctrination at an early age - kindergarten. Starting in kindergarten the students are indoctrinated by the teachers and faculty that all students attend a University. Each grade had to learn a different University fight song and sing those songs at schoolwide assemblies.
My middle son would tell me that he was going to attend a prestigious University. I head this every year. Finally, when he was in the 5th grade I asked him: "Who is going to pay the $200,000.00 so you can attend that college?" My son was stunned speechless. I asked my son to ask his teachers if they would pay the tuition. My son never again brought up going to that college.
That is just one example of indoctrination that government run education imposes on our children. Fortunately my wife and I encourage critical thinking with our children. Our children usually see the truth of things.