The student was conducting a period of circuits. On his second approach, he was requested to make a full stop landing due to a problem with a following aircraft. He reported that the aircraft touched down normally on the main wheels just beyond the threshold. When he lowered the nose wheel, the nose of the aircraft seemed to sink too far. He applied braking as the aircraft pulled to the left, off the centreline, towards the grass. The aircraft came to rest with the nose landing gear collapsed rearwards. Examination showed the nosewheel tyre had been in very poor condition. It is possible that the tyre crept on the rim during touchdown, resulting in the valve stem being torn off, deflating the tyre.