Harper Lee never reveals whether there is a school in Maycomb for the black children or not. Although she does not suggest it, it is a certainty that Jem's and Scout's school is segregated--for whites only. All schools in the Deep South during the 1930s were separated for whites- or blacks-only. If there is a separate school for African-American children, it is never mentioned. We know that Calpurnia, who is one of "about four folks in First Purchase" who can read, never attended school: When Jem asks her
"Where'd you go to school, Cal?"
she responds, "Nowhere." The vast majority of the members of Calpurnia's church are illiterate--eliminating a need for hymnals. There also is the mention of "tiny children" who sit in the shade of trees while their parents work in the fields. We can assume that the older children either join their parents at work; are left at home; or (possibly) attend a school in the Quarters. So, if there is a school for black children, it must be fairly new, since most of the older members of the church cannot read or write.