While practicing touch-and-go landings, the student pilot unknowingly left the power in on landing. During the landing rollout, the student could not maintain directional control of the aircraft. The aircraft began to move left and right across the runway. He said he began to over correct, trying to keep the aircraft on centerline instead of pulling the power. The airplane left the runway edge and hit a distance marker sign. Examination of the aircraft was conducted with no abnormalities noted.