The Road to Desegregation
In 1954, the Supreme Court ruled in the case Brown v. Board of Education that separate educational facilities were unequal. However, Eleven Oaks School remained segregated due to the "Massive Resistance" movement in Virginia, coordinated by white authorities in state and local governments, churches, private businesses, and neighborhoods. Eleven Oaks was eventually integrated but only in 1965, when the students there were reassigned to another school. 
Virginia Senator and newspaper publisher Harry F. Byrd led the Massive Resistance movement, which aimed to restrict state educational funds and close integrated public schools. Some schools altogether shut down in order to prevent integration. All-white private schools benefited from these closures; their revenues increased with larger enrollments.  In some cases, Black students had to suspend their education because they were not allowed or could not afford to attend white private schools.
In 1965, first graders at Eleven Oaks were assigned to other schools near their homes, but grades second through sixth remained segregated in the original building.  The next year Eleven Oaks was partially closed and adapted for re-use as an integrated kindergarten. The annex of the building was used for school staff and certain program offices, including Head Start. By 1968, Eleven Oaks had become an educational administration center. 
Here is one student's reflection on the process of school integration in Fairfax County:
“On a personal note, in the fall of 1965, I was a white first grader at nearby Green Acres Elementary School. I was oblivious to the historic events happening around me. As a child, I naturally assumed that white and black children had always attended school together. One of my classmates that year was Verne Quinn. Verne, who is now Verne Butz, just happens to be African American. She and I remain friends to this day." 
Eleven Oaks students were reassigned to Burke, Centreville, Clifton, Fairview, Lorton, and Westmore elementary schools.  Below, the map shows the proximity of these various schools; the chart also highlights the number of Black children integrated into each school. Newspaper articles further discuss the desegregation process.
By Alexis Massenburg
 A new library and two classrooms added to Eleven Oaks in 1959 shows that Fairfax County had no intention of integrating certain "colored schools" after the Brown v Board of Education decision was handed down by the Supreme Court. Close to $52,000 in construction money was invested in Eleven Oaks, one of the last two schools that was supposed to be integrated after 1954: William Johnson, “African American Education in the Town/City of Fairfax,” The Fare Facs Gazette. (2006). http://www.historicfairfax.org/wp-content/uploads/2012/05/HFCI41-2006.pdf. Interesting new scholarship on the "Massive Resistance" movement in Virginia from the perspective of its opponents: Brian J. Daugherty, "'Those Who Were on the Other Side': The NAACP and the Rise of Massice Resistance, 1956," in Deborah E. McDowell, ed. On Keeping On: The NAACP and the Implementation of Brown v. Board of Education in Virginia (Charlottesville: University of Virginia Press, 2016 ), 44-58; Matthew D. Lassiter and Andrew B. Lewis, eds. The Moderates' Dilemma: Massive Resistance to School Desegregation in Virginia (Charlottesville: University of Virginia Press, 1997). Massive Resistance and national civil rights: Charles W. Eagles, "Toward New Histories of the Civil Rights Era," The Journal of Southern History 66, no. 4 (2000), 818, 821; Gary Gerstle, American Crucible: Race and Nation in the Twentieth Century (Princeton: Princeton University Press, 2001), 281-2.
 Byrd and Massive Resistance: James W. Ely Jr. The Crisis of Conservative Virginia: The Byrd Organization and the Politics of Massive Resistance (Knoxville: University of Tennessee Press, 1976); Robert Pratt, "New Directions in Virginia's Civil Righs History," The Virginia Magazine of History and Biography 104, no. 1 (1996), 149-54.
 William Johnson, “African American Education in the Town/City of Fairfax,” The Fare Facs Gazette. (2006). http://www.historicfairfax.org/wp-content/uploads/2012/05/HFCI41-2006.pdf
 “Where were the African-American schools in Fairfax, County,” Desegregation: The Schools. Fairfax County Public Schools, Accessed July 12, 2021. https://www.fcps.edu/about-fcps/history/records/desegregation/schools#eleven-oaks