At about 1136 Eastern time, a Cessna 172S experienced a hard landing at the Daytona Beach International Airport. Visual conditions prevailed. The airplane was substantially damaged and the Student pilot was not injured. The pilot stated that he did not apply adequate back pressure to the control yoke during the landing flare, and because of this, I bounced very roughly. He further stated that he executed a go-around after the hard landing, flew another traffic pattern and landed without further incident. Postflight examination of the airplane revealed damage to the firewall.