PLT INADVERTENTLY PUT THE GEAR HANDLE IN THE UP POS DURING A TOUCH AND GO LNDG TKOF RESULTING IN THE GEAR COMING UP CAUSING DAMAGE TO THE PROP AND ENG.

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MY STUDENT AND I WERE DOING TOUCH AND GO LNDGS. WE WERE ON OUR 4TH TKOF ROLL; WHEN THE STUDENT MISTAKENLY RETRACTED THE LNDG GEAR HANDLE INSTEAD OF RESETTING THE ELEVATOR TRIM FOR TKOF. THE 3 PREVIOUS TKOFS; I WATCHED THE STUDENTS HAND RETRACT THE FLAPS THEN SUCCESSFULLY RE- SET THE TRIM WHEEL. HOWEVER; ON THE 4TH TKOF ROLL; I SAW THE STUDENT PLT RETRACT THE FLAPS; BUT I DID NOT FOLLOW HIS HAND TO THE TRIM STATION. INSTEAD; I RETURNED MY EYES 'DOWN THE RWY.' THE PLT CALLED OUT 'TRIM; RE-SET;' BUT ACTUALLY RETRACTED THE GEAR HANDLE. MOMENTARILY THE GEAR WARNING 'HORN' SOUNDED UNTIL THE STUDENT APPLIED FULL PWR. IN THOSE PASSING SECONDS; MY PERIPHERAL VISION CAUGHT A RED ANNUNCIATOR LIGHT (GEAR UP). I THEN TURNED MY EYES DIRECTLY TO THE GEAR HANDLE AND REALIZED THE STUDENT HAD SELECTED IT TO THE UP POS. BY THIS TIME THE STUDENT PLT HAD ROTATED (ROTATION OCCURRED PRIOR TO VR); AND THE GEAR MOTOR BEGAN TO CYCLE THE GEAR INTO THE WHEEL WELLS (AS I TOOK OVER THE FLT CTLS). THE ACFT THEN SETTLED BACK ONTO THE RWY. NONE OF THE CREW OF 3 WERE INJURED IN ANY WAY. THE ACFT SUSTAINED ONLY SUPERFICIAL DAMAGE. THE PROP BLADES WERE DESTROYED. THE ENG WILL HAVE TO BE RE-BUILT. AS THE PIC; I FEEL THAT IT IS MY RESPONSIBILITY TO ENSURE THAT THE STUDENT MANIPULATES THE CTLS/LEVERS IN A PROPER AND TIMELY FASHION. IT IS MY OPINION THAT HAD I ACTUALLY SEEN THE STUDENT PLACE HIS HAND ON THE GEAR HANDLE INSTEAD OF THE TRIM WHEEL; THAT THIS MISFORTUNE COULD HAVE POSSIBLY BEEN AVOIDED.