INSTRUCTOR WITH STUDENT GIVING RECURRENT TRAINING HAS GEAR UP LNDG.

Narrative

A FRIEND AND A STUDENT WANTED TO FLY AN SMA TO GET SOME RECURRENCY TRAINING. WE LIFTED OFF FROM ADDISON ARPT ABOUT XA00 FOR MESQUITE FOR SOME TOUCH-AND-GOES. WE SUCCESSFULLY COMPLETED 1 TOUCH-AND-GO AND A GAR. ON THE SECOND TOUCH-AND-GO THE STUDENT LANDED THE AIRPLANE AND ON THE ROLLOUT I TOLD HIM; 'LET'S GO AGAIN.' HE GAVE THROTTLE AND RAISED THE FLAPS TO 15 DEGS (FLAP TKOF SETTING). WHILE THE FLAPS WERE COMING UP I QUICKLY LOOKED OUT ON THE WING TO VERIFY FLAPS SET; THEN AS I LOOKED BACK THE NOSE PITCHED DOWN AND THE PROP STRUCK THE GND HARD. I TOOK OVER CTL OF THE AIRPLANE; PITCHING UP AND GIVING FULL THROTTLE AS A REFLEX AND GOT IN THE AIR. KNOWING THAT THE PROP WAS SEVERELY DAMAGED; I SMOOTHLY SET THE AIRPLANE BACK ON THE RWY. AS WE HAD BEEN IN THE AIR A BRIEF MOMENT THE MAIN GEARS HAD RETRACTED. THIS WAS NOT OBVIOUS TO ME AT THE TIME SINCE THE INCIDENT FELT MORE LIKE A FLAT TIRE OR A MALFUNCTION OF THE NOSE GEAR. IT IS OBVIOUS THAT THE STUDENT SELECTED GEAR UP WHILE I WAS VERIFYING THAT THE FLAPS WERE SET AT 15 DEGS; AS ALSO IS CONFIRMED BY HIS STATEMENT TO FAA. MY DECISION TO PUT THE AIRPLANE BACK ON THE RWY; INSTEAD OF TRYING TO MAKE IT AROUND THE TFC PATTERN WITH A DAMAGED PROP AND MAYBE A DAMAGED ENG; RISKING TO LOSE THE ENG SOMEWHERE IN PATTERN; WOULD STILL BE THE SAME IF I KNEW THE GEAR WAS UP.