THE STUDENT PILOT STATED THAT AFTER A NORMAL APPROACH AND LANDING, HE EXPERIENCED A NOSE WHEEL SHIMMY AND THE AIRPLANE PULLED TO THE LEFT. HE STATED THAT HIS ATTEMPTS TO RAISE THE NOSE WHEEL OFF OF THE RUNWAY RESULTED IN THE AIRPLANE BECOMING AIRBORNE ONCE OR TWICE, AND THAT ON THE SECOND OR THIRD TOUCHDOWN THE NOSE GEAR COLLAPSED. HE SAID THE AIRPLANE HAD A HISTORY OF NOSE WHEEL SHIMMY AND THAT IT HAD OCCURRED ON THE PREVIOUS TAKEOF. A CFI WHO OBSERVED THE ACCIDENT SAID THE APPROACH WAS NORMAL BUT, INSTEAD OF FLARING, THE AIRPLANE NOSED DOWN AND HIT THE RUNWAY IN A 'CLASSIC WHEELBARROW NOSE WHEEL FIRST CONFIGURATION.' THE THEN SAW THE AIRPLANE BOUNCE AND COME DOWN ON THE NOSE A SECOND TIME AND THE NOSE GEAR COLLAPSED. NO EVIDENCE OF PRE-IMPACT FAILURE OR MALFUNCTION WAS FOUND AND THE OPERATOR'S RECORDS DID NOT INDICATE A HISTORY OF NOSE GEAR SHIMMY.