On November 9, 1998, at 1215 eastern standard time, a Cessna 337C, N2655S, operated by a private rated student and a commercial rated instructor pilot, sustained substantial damage during a hard landing on runway 7 (3,128' X 40' dry/asphalt), near New Hudson, Michigan. The student received serious injuries, while the instructor reported no injuries. The 14 CFR Part 91 instructional flight was operating in visual meteorological conditions. No flight plan was on file. The flight departed Brighton, Michigan, about 1200. In his written statement, the instructor pilot said that on initial touchdown the airplane bounced, at which time full power was applied in an attempt to abort the landing. He said the airplane began turning left until the left wing impacted the terrain followed by the fuselage. He did not indicate any power interruption. He said that it is possible that the landing gear doors may not have closed after the gear extended because they were extended after the accident. He said that the there had been problems with the operation of the doors two times since the last inspection and had received maintenance.