A PA44 ON LNDG THE NOSE LNDG GEAR CAME DOWN VERY ABRUPTLY. FRACTURING THE JOINT BTWN THE FRONT AND REAR DRAG LINK.

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THE APCH WAS FINE; BEFORE LNDG CHKLIST WAS PERFORMED AND THE GEAR WAS CONFIRMED DOWN WITH 3 GREEN LIGHTS. HOWEVER; DURING THE LNDG; THE STUDENT -- UNCHARACTERISTICALLY -- CHOSE HELD-OFF A LITTLE HIGH; AND THOUGH HE DID NOT REACT TO MY INSTRUCTIONS TO ADD PWR; I DECIDED TO LET HIM CONTINUE WITH THE LNDG; AS I WAS CERTAIN WE WERE ONE -- OR FEWER -- FT OFF THE GND; AND THE RESULTING HARD LNDG WOULD PROVIDE BETTER FEEDBACK TO THE STUDENT; THAN AN INSTRUCTION TO 'GO ROUND' FROM ME. AS ANTICIPATED; THE LNDG ON THE MAINS WAS HARD BUT NOT -- IN MY OPINION -- SO HARD AS TO CAUSE DAMAGE. I WOULD SAY IT WAS NORMAL FOR AN AB INITIO STUDENT IN A C172. HOWEVER; IMMEDIATELY AFTER TOUCHDOWN THE NOSEWHEEL CAME DOWN VERY ABRUPTLY -- MORE SO THAN IS USUAL EVEN IN THE PA44; ACCOMPANIES BY TIRE SQUEALING; AS THOUGH THE BRAKES WERE ON. THE ACFT STARTED VEERING GENTLY TO THE R; AND AT THAT POINT I INTERVENED AND DISCOVERED IT WAS ALMOST IMPOSSIBLE TO ROLL OUT STRAIGHT. I; THEREFORE; ALLOWED THE ACFT TO MAKE A R TURN OFF RWY 23; ONTO RWY 29; AND TAXIED PAST THE HOLD SHORT MARKINGS. I CALLED THE TWR AND INFORMED THEM THAT I NEEDED ASSISTANCE; AND THAT I THOUGHT I HAD A FLAT R TIRE. AFTER SHUTDOWN; IT BECAME APPARENT THAT THE ACFT HAD SUFFERED A MERCIFULLY PARTIAL NOSE GEAR COLLAPSE; OWING TO A FRACTURE OF THE KNUCKLE JOINT BTWN THE FRONT AND REAR DRAG LINK. THE NOSE GEAR WAS; IN FACT; RESTING ON THE BROKEN STUMP OF THE REAR DRAG LINK. THE PROB AROSE DUE TO A COMBINATION OF POOR JUDGEMENT ON THE HT OF FLARE ON THE PART OF MY STUDENT; MY INABILITY TO PREDICT THE SEVERITY WITH WHICH THE NOSEWHEEL CAME DOWN. A CONTRIBUTING FACTOR WAS THE GUSTY WINDS; WHICH MIGHT HAVE AGGRAVATED WHAT WOULD ALREADY HAVE BEEN A HVY LNDG. I SUSPECT BUT CANNOT PROVE THAT THE STUDENT WAS RIDING THE BRAKES ON LNDG; THIS WOULD CERTAINLY HAVE AGGRAVATED THE SEMINOLE'S PRONOUNCED TENDENCY TO DROP THE NOSE DOWN AFTER THE MAINS HAVE TOUCHED DOWN; IN ANY BUT THE FASTEST LNDGS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE AIRPLANE WAS LANDED ON THE MAIN LNDG GEAR BUT NOT CONSIDERED A 'HARD' LNDG BUT THE NOSE GEAR CAME DOWN HARD AND WAS DAMAGED. THE NOSE GEAR WAS PARTIALLY COLLAPSED AND RESTING ON THE BROKEN REAR DRAG LINK. ON THE NOSE GEAR TOUCHDOWN THE JOINT BTWN THE FRONT AND REAR DRAG LINKS SNAPPED.