When Theoneste Mutabazi started teaching at Umuco Mwiza School in Kigali in 2008, he marveled at everything its students had. There was an art room, a music room, and a library “with many books,” he says during a phone call from his office in the Rwandan capital. Since then, Umuco Mwiza, whose name means “good culture” in the Kinyarwanda language, has added more classrooms and even a large recreation area. Mr. Mutabazi, who is now the school’s principal, notes in an excited voice that “Our...