The flight instructor reported that, with the pilot receiving instruction at the flight controls, during the landing roll, the airplane veered to the left and the instructor took the flight controls. He added full power, reduced flaps, and the airplane continued to veer left. The airplane exited the runway to the left, impacted a ditch, the nose landing gear collapsed, and the airplane came to rest inverted. The airplane sustained substantial damage to the left wing. The instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The instructor reported that the wind was from 170° at 8 knots. The automated weather observation station located on the airport reported that, about 15 minutes after the accident, the wind was from 140° at 4 knots. The pilot landed the airplane on runway 19.