The flight instructor reported that with the student pilot on the controls for the landing, the airplane floated down the runway and eventually touched down on the first third of the runway. As the airplane bounced the second time, the instructor announced that he was assuming control of the airplane; simultaneously advancing the throttle to full. The students hand position on the throttle prevented full throttle application as the instructor attempted to gain altitude without stalling the airplane. The airplane subsequently struck a fence near the departure end of the runway. Power was reduced and the flight instructor initiated a forced landing to an open field.
The airplane sustained substantial damage to the left side horizontal stabilizer.
The instructor reported that there were no mechanical malfunctions or failures that would have precluded normal operation.