A correction is worth making before answering, since the existing response attributes the Association to W. E. B. Du Bois and an essay called "The Negro and the Constitution." The Association for the Study of Negro Life and History was founded by Carter G. Woodson in 1915, along with several colleagues, and its solution to what was then called the race problem comes out of Woodson's own thinking rather than Du Bois's. The quotations in that earlier answer do not match the documented sources, so I would set them aside.
A note on the name itself. "Negro" was the standard and respectful term in 1915 and remained so for decades, which is why it appears in the Association's original name and across Woodson's work, and the organization kept it until 1972 before becoming the Association for the Study of Afro-American Life and History and later the Association for the Study of African American Life and History. Using "Negro" when naming the Association or quoting Woodson is accurate to the period, while "Black" or "African American" is the right choice for your own discussion of the history.
Woodson built the Association around a specific diagnosis. He argued that the central problem was the systematic erasure of Black history and achievement from education, an erasure that compounded the legal and economic oppression Black people already faced. It taught Black and white Americans alike that Black people had contributed nothing worth recording. He founded the Association in 1915 to correct that erasure through the scientific study and publication of Black history, and he created the Journal of Negro History the next year and Negro History Week in 1926 to carry that work to scholars and schools.
The solution that follows from this diagnosis is education, but in a particular sense. Woodson did not mean access to existing schools, since he argued in The Mis-Education of the Negro that the standard curriculum trained Black students to admire others and dismiss themselves. He meant a corrected education grounded in accurate Black history, one that would give Black Americans knowledge of their own past as a foundation for self-respect, leadership, and economic independence, and would force white Americans to recognize a record they had been taught to ignore (Woodson, The Mis-Education of the Negro). The Association's work of research and publication was the engine for producing that corrected knowledge.
So the Association's answer to the race problem was the recovery and teaching of Black history as the precondition for everything else. Woodson treated accurate history as the ground on which political claims, economic self-determination, and genuine mutual respect could be built, since a people written out of the record could not be valued by others or fully empowered to act on their own behalf.
Source:
Woodson, Carter G. The Mis-Education of the Negro. Washington, DC: Associated Publishers, 1933.