Edgefield County had a total population of 42,438 of which 12.897 were designated white, 16,863 Black and 2,062 mulatto according to ancestry.com. The numbers don't add up. This may be because not all transcribers included racial designation in their transcriptions.
There are twenty three people with the occupation 'teacher' in Edgefield. Checking back through the original Census returns one by one there are five teachers with a designation of Black or mulatto in Edgefield:
Jno Guardiner, born c1843, residence Hamburg, Edgefield
Milligan Jones, born c 1852, residence Blocker, Edgefield
Stephen Miles, born c1838, residence Gray, Edgefield
Sumter Simms, born c1842, residence Hamburg, Edgefield
John S Simms, born c1839, residence Schultz Township, Edgefield
Sources
Population of SC 1870 bit.ly/2JsAYsq
Racial designations and occupation results from ancestry.com