Did Dame schools prepare boys for college?

No, dame schools did not prepare boys (or girls) for college. Dame schools were informal, basic schools, typically run by women in their homes, that primarily focused on teaching very young children (ages 4-8) the rudiments of reading, writing, and sometimes arithmetic. Their curriculum was extremely limited and nowhere near the level of education needed for university entrance. Colleges required a much more advanced education, typically obtained through grammar schools and later private tutoring or attendance at a university preparatory school.