The flight instructor/pilot was conducting an introductory flight for the passenger and was landing on a 2,770-foot-long, asphalt runway. Upon landing, the airplane began to bounce. After the third touchdown, the nose gear collapsed, which resulted in substantial damage to the underside of the fuselage. The airplane's second touchdown was described as "rough" by the pilot, and "much more forceful than the initial touchdown" by the passenger. The pilot further stated that he considered aborting the landing after the first bounce, but elected to continue the landing attempt. Postaccident examination of the airplane, which included a metallurgical examination of nose landing gear assembly, did not reveal any preaccident malfunctions or failures that would have precluded normal operation. The pilot reported about 440 hours of total flight experience, which included about 8 hours in the same make and model as the accident airplane, of which, 1.2 hours were accumulated during the previous 90 days.