Traditionally both America and Europe segregated their schooling by class but in very different ways. In America technically all people had access to the same sort of schools that could lead to a higher education. Of course in practice certain school districts were very good, others very bad. In Europe on the other hand what you got was a three track system - university track, middle track, and apprenticeship track.  Admission to the top track was open to all, but some were more equal than others. Like everywhere in the world, the children of the well educated (and thus generally better off) were more likely to get into the university track high schools. Plus it was typical for borderline bourgeois students to get in while borderline working class kids were steered to lower tracks. And the wealthy and upper middle class used private schools as a fallback option if their kids were too dumb to get into public ones. The result - excellent quality public high schools open to all in theory, but mainly populated by the children of the bourgeoisie and a perpetuation of the class system.  Over the past couple decades there has been a shift, formal or de facto, to universal high school education. At the same time I've seen increasing complaints that schools in poor areas are worse quality than those in better off ones.