INSTRUCTOR PLT UNABLE TO RECOVER DURING TOUCH-AND-GO WHEN STUDENT QUITS FLYING AFTER MAKING AN ERROR IN A COMPLEX ACFT.

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I WAS FLYING WITH A STUDENT (MULTI ENG). TOWARDS THE END OF THE LESSON; WE ENTERED THE OLV TFC PATTERN TO PRACTICE LNDGS. I INSTRUCTED MY STUDENT TO LAND ON THE 1000 FT MARKERS AND PREPARE FOR A TOUCH-AND-GO. AFTER THE LNDG; MY STUDENT RETRACTED THE FLAPS; ADDED FULL PWR AND BEGAN TO ROTATE. JUST AFTER LIFTOFF; MY STUDENT REACHED TO THE GEAR HANDLE AND BEGAN TO CYCLE THE LNDG GEAR. I YELLED 'NO' AND MOVED FOR HIS HAND. AS SOON AS I YELLED; HE LET GO OF THE CTLS AND THE LNDG GEAR HANDLE. AS THE PLANE SUNK TO THE GND; THE R MAIN GEAR BEGAN TO RETRACT. I ADDED BACK PRESSURE AND ATTEMPTED TO KEEP THE PLANE AIRBORNE. I WAS UNSUCCESSFUL. THE R PROP STRUCK THE GND AS WE SLID DOWN THE RWY. WE SLID TO THE R AFTER 100 FT OR SO BECAUSE THE L MAIN GEAR AND NOSE GEAR REMAINED EXTENDED AND LOCKED IN PLACE. WE SLID ON THE PROP AND FLAP HINGES INTO THE GRASS WHERE WE HIT A RWY LIGHT THAT DENTED THE LEADING EDGE AND BELLY OF THE R WING. WE CAME TO A COMPLETE STOP AND I SHUT EVERYTHING DOWN IN ACCORDANCE WITH THE EMER CHKLIST. EVEN THOUGH I SAW MY STUDENT PULL THE GEAR HANDLE; I DID NOT PREVENT THE SIT. I SHOULD HAVE MAINTAINED A CONTINUOUS VOCAL CHKLIST WITH MY STUDENT (MAKING HIM CALL OUT THE ACTION BEFORE HE PERFORMED THE ACTION). ALSO; I SHOULD HAVE MAINTAINED A PROPER OUT FOR THE SIT. I WILL NOW MAKE ALL STUDENTS OF A COMPLEX ACFT MAKE FULL STOP LNDGS.