During the landing roll, the student pilot, who was performing a series of touch-and-go landings, allowed the airplane to veer slightly to one side. While attempting to get the airplane realigned with the runway, he overcorrected. In his attempt to compensate for the overcorrection, he overcorrected in the opposite direction. This sequence of events resulted in a series of overcorrections, followed by a loss of directional control, which was followed by the airplane departing the side of the runway. After departing the runway, the airplane made an abrupt turn of about 90 degrees, whereupon the left main landing gear collapsed and the left wing impacted the terrain. The impact with the terrain resulted in structural damage to the wing. The pilot reported that there was no mechanical malfunction associated with the accident.