The certificated flight instructor (CFI) and student pilot of the Cessna 150M completed at least three touch and go circuits at another airport before returning to Reigle Field Airport (N58), Palmyra, Pennsylvania. The airplane flew the complete left hand traffic pattern. The pilots intended to make a full stop landing on runway 31, a 1,950 feet long, 40 feet wide, asphalt runway. The flaps were set to the maximum extension of 40 degrees. According to the CFI, the airspeed was "a little high" on the final approach leg. The airplane floated, touched down "hard," and then bounced back into the air. The airplane touched down a second time, exited the runway to the left, and struck a cornfield located approximately 150 feet from the runway edge. On impact with the cornfield, the nose gear collapsed and the airplane nosed over. Both pilots were uninjured, and exited through the window on the right (co-pilot) side of the airplane. The recorded weather at an airport approximately 12 miles east of the accident site, about the time of the accident, showed winds from 260 to 280 degrees, at 5 to 7 knots. The temperature was approximately 31 degrees Celsius, with a dew point of 18 degrees Celsius. The CFI had approximately 720 hours of total flight experience, and the student pilot had approximately 30 hours of total flight experience. After the accident, the CFI reported that the accident could probably have been avoided if a go around had been initiated early in the sequence.