The flight instructor and the pilot receiving instruction were practicing short field landings. After an initial unsuccessful approach, the pilot conducted a go-around and set up for another landing approach. The flight instructor described that after passing over obstacles while on short final approach to the runway, the flight instructor told the pilot to reduce engine power to idle so that they would not overshoot the touchdown point again. The pilot complied, and as they descend the pilot continued to increase the airplane’s pitch attitude as if engine power had not been reduced. The flight instructor noted this, directed the pilot to decrease the airplane’s pitch, and then “nudged” the control stick forward to reduce the airplane’s angle of attack. As the flight instructor released his forward pressure on the control stick, the airplane’s pitch again increased along with its descent rate, as the pilot continued to pull back on the control stick. The airplane subsequently touched down “hard” on the runway, resulting in substantial damage to the right wing. The operator reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation, nor did the pilot or flight instructor report any.