SMA TWIN HAS NMAC WITH SMA IN TFC PATTERN.

Narrative

THE STUDENT IN THE L SEAT OF THE ACFT HAD THE ONLY PUSH- TO-TALK SWITCH. IT HAD BEEN 2 MONTHS SINCE HIS LAST FLT; AND HE WAS HAVING TROUBLE WITH HIS XMISSIONS. AS WE ENTERED THE DOWNWIND; EITHER THE OTHER ACFT; A CESSNA 210; WAS 'STEPPED ON.' (XMITTED OVER); OR DID NOT MAKE A POS RPT. IN ANY CASE; THE OTHER ACFT WAS NOT ACQUIRED VISUALLY BY EITHER MYSELF OR MY STUDENT. WHEN WE OBSERVED THE OTHER ACFT; IT WAS 500 FT AHEAD AND TO OUR R; AND SOMEWHAT BELOW US. JUDGING BY THE FLT PATH OF THE OTHER ACFT; IT WAS PROBABLY EXECUTING A DOWNWIND DEP AFTER TKOF. IT IS POSSIBLE THAT THE DEPARTING ACFT MADE A XMISSION ON THE RWY STATING HIS INTENTION TO TKOF AND DEPART ON THE DOWNWIND; AND BOTH MYSELF AND THE STUDENT DID NOT HEAR IT; DUE TO MY GIVING INSTRUCTION TO THE STUDENT ON THE EXTENDED '45' TO THE DOWNWIND. THE LARGEST CONTRIBUTING FACTOR WAS MY FAILURE TO PERSIST IN GETTING THE STUDENT TO STABILIZE THE HIGH PERFORMANCE; MULTI-ENG ACFT WELL BEFORE ENTERING THE PATTERN; THIS RESULTED IN A GREAT DEAL OF COCKPIT DISTR AND COM AT A CRUCIAL TIME FOR TFC AWARENESS AND AVOIDANCE. IF A PUSH-TO-TALK SWITCH OR HAND MICROPHONE HAD BEEN AVAILABLE; I WOULD HAVE RELIEVED THE STUDENT OF COM DUTIES ON THAT PARTICULAR OCCASION. IT IS MY BELIEF THAT THE PLT OF THE OTHER ACFT BOTH SAW AND AVOIDED US; BUT I CANNOT BE CERTAIN. A CONTRIBUTING FACTOR IN THE STUDENT'S PERFORMANCE WAS NERVOUSNESS OR UNEASE AT THE PROSPECT OF LNDG AT THIS ARPT; WHICH WAS SOMEWHAT SMALLER THAN THE ARPTS HE HAD LANDED THIS ACFT AT PREVIOUSLY. THE NET RESULT WAS A NEAR MIDAIR; A FRUSTRATED STUDENT AND A GAR.