His goal was to break up what he saw as an educational monopoly that was controlled by public school systems. He hoped competition would drive under-performing schools out of business and provide an incentive for other schools to improve. His envisioned a system of schools that would be publicly financed but privately run. The equity model has come about more recently. We've also seen voucher programs come about in Cleveland, Milwaukee, and Florida that are not pure market model systems that Milton Friedman advocated, but are specifically designed to accommodate the needs of kids who are under-served in their public schools.
Charter schools are another piece of the equity model.
They are public schools. While not specifically designed to serve poor kids, there's open enrollment and in most cases the student body is reflective of the population of the local district. In those cases where they're not, there tends to be a slight over-subscription of poor and minority kids who are looking for alternatives. Between charter schools, voucher programs, and public choice programs, a lot has happened on the choice front, but good policy has been circumscribed by cynical politics and the result has been to stem competition and limit opportunities. The program Susan talked about is a case in point.