A grammar school was a type of school.
In grammar school, a classmate of B'Elanna Torres, Daniel Byrd, bullied her about her Klingon heritage and called her "Miss Turtlehead". (VOY: "Juggernaut")
In grammar school, Deanna Troi had to memorize a speech Jonathan Archer gave in 2161. (ENT: "These Are the Voyages...")