According to the student pilot, he landed at his second destination airport, performed a full stop, and taxied back to runway 13 for departure. He lined up on runway centerline and applied a left crosswind correction by turning the yoke to the left. After applying takeoff power and starting his ground roll the right wing rose upwards. The pilot responded by applying right aileron, right rudder, and brakes; however, the airplane departed the left side of the runway and struck a thousand foot marker. Postaccident examination of the wreckage revealed right wing spar damage. The pilot reported no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.