The flight instructor was conducting an instructional flight in the airplane, which was owned by the student pilot. The flight instructor reported that he did not notice that the student pilot did not set the flaps to the appropriate position for takeoff, as required on the before takeoff checklist. Immediately after rotation, during the initial climb, the student pilot had difficulty maintaining directional control. The flight instructor took control of the airplane about 10 ft above the runway, the stall warning annunciator was audible, and the airplane began sinking. The flight instructor pushed the nose over but was unable to recover before the airplane landed hard and then departed the right side of the runway. The landing gear dug into the mud, the airplane then spun around and the nose gear and left main landing gear collapsed, which resulted in substantial damage to the elevator and vertical stabilizer. The flight instructor reported that there were no preimpact mechanical failures or malfunctions with the airplane that would have precluded normal operation.