The airplane landed hard in a field adjacent to the airport during an attempted takeoff. The purpose of the solo flight was for the student pilot to perform practice touch-and-go takeoff and landings. After completing a normal takeoff, he continued around the traffic pattern and then preformed a normal landing. During the landing rollout he retracted the flaps, input full throttle, and pushed the mixture control partially forward, leaving it out about 7/8 inch. The airplane lifted off the runway surface and climbed to about 50 to 100 feet above ground level (agl), with an airspeed of about 60 knots. The airplane was not able to maintain the airspeed and the student pilot thought the engine was only producing partial power. He opted to perform a precautionary landing in an open field adjacent to the runway. The airplane landed hard and the left main landing gear broke off. Damage to the airplane included the left main landing gear, firewall, and underside of right wing. Post accident examinations by both the operator and Federal Aviation Administration (FAA) inspector revealed no evidence of engine or airframe anomalies that would have precluded normal operation. The FAA inspector stated that the signatures on the spark plugs indicated a very lean condition. An engine run was conducted the day following accident and the FAA inspector attempted to power the engine to about 2,000 revolutions per minute (rpm); he did not want to apply full power due to the instability of the airplane from the damaged left main landing gear. The engine ran normally with no discrepancies noted.