The pilot of the tailwheel-equipped low-wing airplane received a taxi clearance from the tower air traffic controller for a planned departure and began taxiing toward the assigned runway. About 3 minutes later, the student pilot of the high-wing airplane requested and received a takeoff clearance while located stationary at the edge of the runup area. The student pilot then advised his flight instructor that the low-wing airplane was approaching from the left, heading toward their airplane. To avoid a collision, the flight instructor took control of the high-wing airplane and advanced the throttle in an attempt to taxi out of the path of the low-wing airplane. The low-wing airplane then impacted the high-wing airplane, resulting in substantial damage to the propeller of the low-wing airplane and to the left wing of the high-wing airplane. The pilot of the low-wing airplane reported that he saw other airplanes in the runup area but did not see the accident high-wing airplane until he was “underneath” its wing. The pilots of both airplanes reported that there were no preaccident mechanical malfunctions or failures with the airplanes that would have precluded normal operation.