How about attach the money spent on a school to the child, and let the teachers/administrators compete just like everything else. You can create specialized roles, pay more, focus on X, whatever you want.
The school system is a failing monopoly that should be broken up.
This has been used successfully in long-term care. The concept is called "Money Follows the Person."
Money Follows the Person (MFP) Rebalancing Demonstration is part of a comprehensive, coordinated strategy to assist U.S. states, in collaboration with stakeholders, to make widespread changes to their long-term care support systems. This initiative will assist states in their efforts to reduce their reliance on institutional care, while developing community-based long-term care opportunities, enabling the elderly and people with disabilities to fully participate in their communities.
The school system is a failing monopoly that should be broken up.