On November 9, 2013, about 1039 central standard time, a Piper PA-28-150 airplane, N5790W, was substantially damaged during an off-field landing near Blosser Municipal Airport (CNK), Concordia, Kansas. The flight instructor and student pilot were not injured. The airplane was registered to a private individual and operated under the provisions of 14 Code of Federal Regulations Part 91 as an instructional flight. Day visual meteorological conditions prevailed for the local flight, and no flight plan had been filed. The student and flight instructor stated a takeoff on Runway 17 was performed utilizing 'soft field' procedures. After lifting off, a high pitch attitude was utilized to clear a simulated obstacle. The flight instructor recalled that flaps were set to 10 degrees during the climb, whereas the student recalled that flaps were set to 25 degrees. Both stated the airplane struggled to climb with the high pitch attitude and subsequently observed the airplane approach a stall. The flight instructor performed an off-field landing, which substantially damaged the left wing. The weather observation station at CNK reported the following conditions at 1055: wind 010 degrees at 8 knots, visibility 10 miles, clear skies, temperature 15 degrees Celsius (C), dew point 1 degree C, altimeter setting 30.18. Based on the recorded temperature and dew point near the time of the accident, the engine was in the range of susceptibility for carburetor icing during glide and cruise power settings. Examination of the airframe and engine by Federal Aviation Administration personnel revealed no evidence of mechanical malfunctions or failures that would have precluded normal operation.