The pilot reported that he was practicing take-offs and landings with an instructor during the accident flight. He stated that on the final landing, he crossed the runway numbers and made a hard landing. The flight instructor reported that when the airplane was about 2 feet above the runway the pilot made a down elevator input because he believed that the airplane had ballooned. The flight instructor stated that he had been guarding the flight controls and he immediately corrected by inputting up elevator, but the airplane impacted the runway in a flat attitude. Subsequent to the hard landing it was found that the airplane's firewall was buckled.