The airplane collided with terrain during a soft-field takeoff. In a written statement, the certified flight instructor (CFI) reported that the purpose of the flight was for the student pilot to practice soft-field takeoffs and landings, which he had briefed the student for prior to departure. After rotation, with the airplane about 10 to 15 feet above ground level (agl), the student pilot raised the nose of the airplane high, akin to a short-field takeoff configuration. The airplane yawed about 15 degrees to the right of the runway centerline and the CFI momentarily waited for the student pilot to make corrective action. The CFI directed the student pilot to input left rudder, but the airplane yawed an additional 15 degrees to the right. The CFI further stated that he assumed the airplane controls. He applied left rudder, and lowered the nose in an effort to maneuver the airplane back to the runway. The left wing contacted the ground about 5 feet from the right edge of the runway and the tail subsequently impacted a grassy median to the right of the runway. The CFI believed that the airplane's main landing gear had contacted the ground and continued with the initial takeoff climb. Shortly thereafter, the CFI and student noticed the damage to the left wing and returned to the airport for an uneventful landing. The CFI noted no preimpact mechanical malfunctions or failures with the airplane or engine that would have precluded normal operation.