Most original discussions about the application of the 14th amendment ended with the courts interpretation that it was up to the state to decide the segregation imposed upon the African race
In 1896 the doctrine of "Separate but Equal" was introduced in the case of Plessy v. Ferguson- Although having to do with transportation, this doctrine became applicable across the board.
At the time the 14th Amendment was ratified, the idea of tax funded public education was still fairly new and not yet implemented fully everywhere. Where it was implemented, there were still many short comings...
Only by looking at modern Public Education can it be truly decided if the imposed segregation is a violation of the 14th Amendment's equal protections clause.
Where the state has taken it upon itself to provide public education, education becomes a right for every citizen within that state. By law this right must be made available to all equally.
It is believed that Segregation of the public school system based on Race, even with all tangible factors equal, still deprives those effected of equal educational opportunity.
A finding in a Kansas Case that: Segregation of colored and white children negatively impacts colored children, specially when the segregation is enforced by law.
To separate students of similar age and mental ability based only on race breeds a sense of inferiority when it comes to social standing and achievement
The notion of Separate but Equal is impossible, because separate facilities are inherently unequal. The segregation of schools based on race is a direct violation of the 14th Amendment.
Finding in Sweatt v. Painter; found that a segregated law school for Blacks could not provide equal educational opportunities. This finding was based on non tangible factors to play a part in the education of students.
Finding in McLourin v. Oklahoma State Regents: Black individuals admitted to white graduate schools should be treated the same as any other student. Based on intangible factors, such as ability to study and converse with peers.
Northern Public Schools (although by comparison somewhat better), were not where they are today. At the time of ratification, Northern schools also faced issues as far as regulation and equality in service.