According to the student pilot, while landing, the airplane “bounced back up into the air.” The student pilot was "trying to ride it out," but when the airplane touched down again, the propeller struck the runway, and the nose landing gear collapsed. An examination of the airplane by the student pilot revealed that the airplane sustained substantial damage to the firewall. The student pilot also reported that there were no mechanical malfunctions noted prior to the accident, and that the winds were calm.