BE76 ON TRAINING FLT EXPERIENCED NOISE GEAR COLLAPSE DURING LNDG ROLL; INSTRUCTOR UNSURE IF STUDENT MANIPULATED GEAR HANDLE.

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WHILE PRACTICING SHORT FIELD LNDGS AT ZZZ ARPT; THE NOSE GEAR CAME UP WHILE ON THE ROLLOUT ON THE THIRD LNDG. THEREFORE; THE NOSE HIT THE RWY ALONG WITH THE PROPS WHILE THE THROTTLES WERE AT IDLE. THE STUDENT HAD CTLS AND WE BOTH VERIFIED 3 GREEN WHILE TURNING OR ON THE BASE AND FINAL LEGS. THERE WAS ALSO A WITNESS ON THE GND WHO SAW ALL 3 LNDG GEAR DOWN. I ALSO REMINDED THE STUDENT TO DO THE FINAL CHK SINCE I NOTICED THE PROP LEVERS WERE NOT IN THE FULL FORWARD POS AND; THEREFORE; I DID THE FINAL CHK SINCE WE WERE CLOSE TO SHORT FINAL. SINCE WE WERE PRACTICING SHORT FIELDS; THE STUDENT WAS TAUGHT TO BRING THE FLAPS UP; USE MAX BRAKING AND AERODYNAMIC BRAKING. NOW WHILE ROLLING OUT; THE STUDENT STARTED TO APPLY AERODYNAMIC BRAKING AND MAX BRAKING; BUT I REMINDED THE STUDENT THAT HE FORGOT THE FLAPS AND; THEREFORE; I REACHED FOR THE FLAPS TO BRING THEM UP TO AVOID SKIDDING OF THE TIRES. THEN AS SOON AS I BROUGHT THE FLAPS UP; I NOTICED THE ACFT'S NOSE SINKING BELOW NORMAL AS IF THE NOSE GEAR WAS COLLAPSING AND PULLED BACK ON THE CTLS TO GET THE NOSE UP BUT THERE WAS NOT ENOUGH AIRSPD OR TIME TO KEEP THE NOSE UP AND PREVENTING THE ACCIDENT. THUS; THE ACFT'S NOSE WAS DAMAGED; THE GEAR DOORS; AND ALSO BOTH PROPS HIT THE GND. AS FOR THE STUDENT; I WAS UNABLE TO SEE HIS HANDS WHEN I BROUGHT UP THE FLAPS BECAUSE MY EYES WERE CONCENTRATED ON THE FLAP LEVER TO MAKE SURE IT WAS THE RIGHT LEVER AND OUTSIDE TO OBSERVE AND MAKE SURE THE STUDENT DOES NOT LOSE DIRECTIONAL CTL. THUS; I AM UNSURE ON WHETHER OR NOT THE STUDENT ACCIDENTALLY BROUGHT THE GEAR HANDLE IN THE UP POS; BUT THE STUDENT SAYS THAT HE DID NOT PUT THE GEAR HANDLE IN THE UP POS. AS FOR CORRECTIVE ACTION; I CAN MAKE SURE TO START SIMULATING FLAPS UP UNTIL AFTER LNDG TO ELIMINATE THE FACTOR OF THE STUDENT OR THE INSTRUCTOR FROM ACCIDENTALLY PULLING THE GEAR HANDLE INTO THE UP POS.