National Education Association

The National Education Association, or NEA, is the largest labor union in the United States. It contributes heavily to the Democratic Party and other left-leaning organizations.

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Speech Relevance

In 'Encroaching Control', Reagan discusses the Federal government's slow, but steady, infiltration into controlling the schools, traditionally the role of the state and the local governments. One such area, he shares, is in integration:
The former president of the National Education Association spoke publicly on the probable need for temporary federal control of the school system in order to bring about integration in the South.
I can find no evidence of direct Federal control over any school systems in the enforcement of integration, only the use of Federal military troops to enforce the Brown v. Board of Education of Topeka decision.

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Source Links

National Education Association (Wikipedia)

Integration: 1954 to 1963