Anyone know anything about schooling--circa 1850, Missouri?

The ages are too different. If you notice in 1860 Charles has a different wife. Although it could be the same one, but I don't think so. Polly in 1850 is born in Kentucky and Mary in 1860 is born in Tennessee. Something could of happened to Polly and the girls and Charles remarried. Harrison is still living with Charles. Also Mason Missouri is too far from Independence.