I know nobody in the South cares how it was done in the North, but where I grew up we had neighborhood schools. IF your socioeconomic status caused your child to go to a school that you found to be unpleasant, you could go to the district office and put in an application (and I never knew of one to be denied) and have your child sent or bussed to a better school in a better community. But most of our 'city' schools had some special program of study or were a true magnet school; so many people from the suburbs would be bussed into the city schools as well. The city school district did ALOT to make the city schools better and offer many accelerated and special programs for students.
I'm not saying they did things the right way, but it's an idea and it gives people an option if they do not have option to move.
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