The flight instructor and student pilot were practicing short field landings when the student pilot landed hard on the nose landing gear. The flight instructor took control of the airplane and performed a touch-and-go. The flight instructor held the nose landing gear off the ground on the full stop landing; however, the nose landing gear collapsed, and the airplane veered off the runway and into the grass. Post flight examination revealed buckling and wrinkling of the lower fuselage. The examination of the airplane found no mechanical malfunctions or failures that would have precluded normal operations. The flight instructor reported that the student pilot was low on the approach, but the flight instructor did not intervene because the student pilot was going to take his private pilot checkride later that day and could perform short field landings. Neither the flight instructor nor the student pilot returned the National Transportation Safety Board 6120.1 Pilot/Operator Aircraft Accident/Incident Report.