The student pilot was performing touch and go landings while his instructor monitored at the airport. He performed two touch and go landings without incident and approached the runway to perform a full stop landing to pick up his instructor. During the landing rollout, the student pilot reported a gust of wind picked up the right wing and the airplane began to veer left. The student pilot attempted to correct with opposite aileron; however, the airplane exited the runway, and the nose landing gear collided with a runway sign. The nose landing gear collapsed and was torn from the airplane as it skidded to a stop. The airplane sustained substantial damage to the forward fuselage. The student pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. At the time of the accident, the student pilot was landing the airplane on runway 14 with wind from 080° at 9 knots.