The flight instructor reported that, while abeam the intended touchdown point, he reduced power to idle for the student pilot to perform a simulated engine failure approach. The student pilot maneuvered for the runway and added full flaps (40°), decreasing airspeed to about 62 to 68 knots. The instructor asked the student if he believed he would be able to make the runway given his airspeed, and the student pilot retracted the flaps to 0° and then back to 25°. The airplane began to sink, the flight instructor added full flaps to "regain some lift", and he instructed the student pilot to recover. The student pilot put both hands on the yoke and pitched up. The flight instructor said, "my controls", applied full power, and attempted to lower the nose, but the student pilot froze and continued to pitch up. The flight instructor repeated the exchange of flight controls command, the student pilot released control of the yoke and retracted the flaps to 0°. The flight instructor put the flaps back to 25° and pitched the nose down in an attempt to recover. The airplane struck the top of a tree, the flight instructor reduced power and landed short of the runway; the nose landing gear collapsed. The airplane sustained substantial damage to both wings and empennage. The flight instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The Federal Aviation Administration inspector reported that, after conducting interviews, it was revealed that the flight instructor took control of the airplane "well below 500 feet from the ground". He also added that there may have been a communication barrier between the flight instructor and the student pilot. He reported that the student pilot paused for 20 to 30 seconds to comprehend each question before answering.