A Mooney pilot reported an NMAC at FCM when a student pilot failed to follow Tower instructions.

Narrative

I was on a right base for [Runway] 18 and clear to land. An [aircraft] was on a left base cleared to land on 18 following me. We had visual contact with each other. A [small plane] was told earlier by the Tower that they would call his crosswind and he should not be on a left downwind yet. I did my final landing gear and fuel check before turning final. I looked up to my left to make sure I still had clearance from the [other aircraft] - probably 2 miles - I looked straight ahead and saw another airplane at my altitude right in front of me. I immediately made a sharp right turn and dropped 300 FT as fast as I could. This placed me about 200 FT AGL and below the VASI. As I was doing this; I tried to inform the Tower of the conflict and my actions. The smaller plane announced 'turning final' as I went under it. The Tower told him to go around and he should not be there. The pilot informed the Tower he was a student pilot. I was re-cleared to land and the [other aircraft] was also re-cleared. I landed poorly; but safely. I failed see the conflicting traffic because I was at a Tower (controlled) airport and had built the visual picture in my mind of where the aircraft were based on the ATC calls. I was not expecting to see the [small plane] right in front of me and had not identified them in the pattern. This is something I had done at a non-towered airport earlier while doing airwork practice. I need to remember to make a more concentrated effort to identify all traffic in the pattern; even at Tower controlled [airports]. I might have seen him before the near miss.