Jackson historian Byron Farwell went into detail on the school.
"School began promptly at three o'clock each Sunday, and there were no latecomers. Jackson locked the doors. Service began with a hymn, invariably "Amazing Grace," for this was the only song he could manage to make recognizably tuneful. (Dr. White, peaking of Jackson's ignorance of "the science of music," declared that he had "neither the ear or the voice for singing.") Jackson then led the school in prayer, which was followed by relating a story or reading passage from the Bible, after which the pupils were turned over to teachers for lessons drawn from the Shorter Catechism or perhaps Charles Colock Jones's A Catechism for Colored Persons. When called together again they sang, said a prayer, and were dismissed. Under Jackson's supervision the entire session lasted exactly forty-five minutes."
There were no lessons in reading and writing in any of that. Anyone who has read up on Jackson knows that he was a disciplined man with a strong feeling of right and wrong and a respect for authority. The idea that he would break the law by teaching slaves to read or write is nonsense. Likewise, the idea that he would interfere with another man's property by teaching their slave to read and write is equally hard to believe. Jackson would not sit back and allow another to do that to his slaves, why on earth would he do it to someone else's?
It would appear there is a difference between the historians and the matter is unresolved to me.