Anonymous wrote:No. Socialism is the ideal and unfortunately Communism is the interpretation and twisting of the idea.
But to answer your question OP, no of course there would not be one type of school in a truly socialist society there would be "education for all" in the truest sense.
Gawd, you people are so poorly educated it's sad!
Communism is the ideal, not socialism. Socialism is an intermediate stage between capitalism and communism characterized by one decisive factor: the collective ownership of the means of production. Translation: you can't own an enterprise that brings in profits. You can own personal property, though. Education - primary, secondary and higher -- is entirely run and funded by the state.
Private schools DO NOT exist in true socialism. That said, there aren't many true socialist countries left nowadays - Cuba and Vietnam come to mind, and that's about it.