The flight instructor said he was not on the flight controls as the student pilot made a stable approach to the runway for a full stop landing. The student pilot initiated a flare over the runway but did not follow thru and the airplane bounced about 20-30 ft back into the air. The flight instructor took control of the airplane and tried to save the landing; however, the airplane stalled and landed hard resulting in substantial damage to the firewall and fuselage. The flight instructor said there were no mechanical issues with the airplane and the accident could have been prevented if he had executed a go-around.