The flight instructor reported that, during a soft field takeoff, the student kept the stick back and allowed the nose of the airplane to come up. The airplane drifted to the left and he reminded the student to apply right rudder and right aileron. He added that it seemed like the student applied too much right aileron and the right wing was close to dragging on the runway. The flight instructor prepared to take the flight controls and the student overcorrected to the left and the left wing impacted the ground. The flight instructor took control of the airplane, reduced power, and taxied to park without further incident. The student pilot reported that, during a soft field takeoff, about 30 to 35 knots, the airplane lifted off the ground and encountered a crosswind that rolled the airplane to the right. The right wing dragged on the ground, he rolled the airplane to the left, and the left wing impacted the ground. The airplane sustained substantial damage to the left aileron. The chief flight instructor of the school reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.