I think you are in the right idea in terms of extending the public system, but I would say that entire system needs an overhaul. Just like most bloated govt run enterprises, the dept of education is a massive failure. What’s the point of extending hs past yr 12 when the failing rates and drop out rates are so high? Why pump more money into a system more focused on new edition textbooks for cost increases on students/parents (while billions sent to printing companies) over simple concepts like charter schools and school choice. Just like everything controlled by big govt and unions, they will fail due to greed and graft of the institution.
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