On July 23, 2001, about 1745 eastern daylight time, a Mooney M20J, N4223H, was substantially damaged while landing at the Freeway Airport, Mitchellville, Maryland. The certificated private pilot, and certified flight instructor (CFI) were not injured. Visual meteorological conditions prevailed and no flight plan was filed for the instructional flight conducted under 14 CFR Part 91. According to the CFI, the pilot was receiving instruction on high performance airplanes. While landing on runway 18, the pilot, who was at the controls, began to flare the airplane about 20-30 feet above the runway. The CFI informed the pilot that they were too high and he should lower the nose; however, the pilot did not respond. Before the CFI could take corrective action, the airplane touched down hard on the main landing gear, and bounced back into the air. Deciding that she wanted to see if the pilot could regain control of the airplane, the CFI elected not to take corrective action. The pilot added full power and pulled back on the yoke until the airplane entered a stall. The CFI assumed the flight controls and pushed forward on the control yoke with both hands. When the CFI took her left hand off the control yoke to adjust the trim setting, the nose of the airplane began to rise again, and the airplane entered another stall. With the trim in the "full nose up" position, the only way for the CFI to keep the airplane out of a stall condition was to push on the control yoke with both hands. The left wing of the airplane then struck the ground, and the CFI aborted the go-around. The airplane touched down hard on the runway again, and the right main and nose landing gear collapsed. The airplane departed the left side of the runway, and came to rest in a grass field. The CFI reported that the pilot had accumulated about 3 hours of total flight experience in the accident airplane. The pilot had also accumulated about 8 landings, and demonstrated go-around procedures in the past. The winds reported at a nearby airport, at 1755, were from 240 degrees at 15 knots, gusting to 22 knots.