On September 2, 1996, at 1400 central daylight time (cdt), a Cessna 172, N65785, piloted by a private pilot, was substantially damaged during a hard landing onto runway 36 (3,904' X 150' dry asphalt) at the Merrill C. Meigs Airport, Chicago, Illinois. Visual meteorological conditions prevailed at the time of the accident. The 14 CFR Part 91 flight was not operating on a flight plan. The pilot and three passengers reported no injuries. The flight departed Waukegan, Illinois, at 1330 cdt. The pilot said she flew the final approach with full flaps extended and the engine at RPM. She said she was surprised when the airplane bounced into the air after touching down on the runway. The pilot said the airplane bounced into the air two more times before coming to a stop without its nosewheel after the third touchdown. During an interview with the pilot landing procedures were discussed. She was asked if she had ever heard of a runway touchdown point. She said "No." When asked if she were familiar with the use of an aiming point during final approach the pilot said she was not. She was asked to explain how she would check the airplane's descent rate when it neared the runway and where she would begin the airplane's roundout, or flare, for landing touchdown. Her response was, "I extend my vision to the runway's end to see if my angle is correct." She explained the "angle" in the following manner: "You engage the visualized angle with your glidepath." The pilot asked, "Are you talking about final approach?" The answer, "Yes," was given by the interviewer. The pilot said, "I don't know then, I don't know if there is anything you can use to judge the final approach or the roundout aspect." While reviewing the pilot's logbook and during the discussion centered on landing it was revealed the pilot had not received dual instruction in the recovery from "bounced landings. The pilot was asked why she did not go-around after the first bounced landing. She said she wasn't sure if the go-around would work because the airplane's nose was too high. According to the pilot's logbook, she had received 13 hours of dual instruction in the Cessna 172 during February and May, 1992. After receiving her private pilot certificate she received an additional 1.6 hours of dual instruction in the Cessna 172 during March 10 and April 6, 1996. The pilot's logbook entries for the Cessna 172 instructional flights did not show instruction in go- around from a landing or recovery from a bounced landing event. The last Cessna 172 dual instructional flight was on April 6, 1996. Her total pilot-in-command time in the Cessna 172 was 2.6 hours, excluding the accident flight. Her logbook showed August 5, 1996, as her last flight before the accident flight. This flight was in a Cessna 172.