The student pilot was practicing touch and go landings. During the first approach she felt her approach was too high, so she pitched down slightly, leveled off, and landed on the main landing gear. After landing the airplane porpoised twice and then landed flat and hard. The pilot taxied back to the hangar and had the airplane examined for damage. None was found, so she took off again and continued her training. Sometime after the flight the firewall was found buckled. The student pilot's recommendation for preventing the accident was to add power and go around.