The student pilot was on the third leg of a VFR solo cross country flight. His intent was to do a touch-and-go landing and then return to his initial departure airport. During his first and second approaches, he executed go-around maneuvers due to what he described as turbulence when the airplane came into ground effect. During the third approach, he landed to the left of centerline and the airplane began to skid to the left. The student pilot stated that he applied the wrong rudder correction and the airplane went off the runway. He added power to try to pull up and the right wing stalled. The left wing hit the ground and the airplane came to rest nose down in a bean field adjacent to the runway. Both wings sustained substantial damage. The student pilot had a total of 25 flight hours in the airplane, with 4.2 hours as pilot-in-command (solo). The wind was calm at the time of the accident. Postaccident examination of the airplane did not reveal any evidence of preimpact mechanical malfunction or abnormalities.