Although children at Pilot Mountain School memorized everything from basic reading words to presidents to state captials, the majority of stories I caught about memorization was connected to the yearly competition known as Recitation and Declaration.
The upper grade children would select a piece of literature to memorize and present to a panel of judges. They studied. They memorized. They practiced. When competition day arrived, they had one chance to do it right. One chance.
The schools I personally attended growing up never adopted this recitation tradition. Oh, I had to memorize, especially the Psalms in eighth grade, and the Gettysburg address in maybe fifth grade. But as far as competition, no.