NMAC. SMT TWIN ENG ACFT OVERTAKES AN SMA SEL TRAINING ACFT ON SHORT FINAL AT AN UNCTLED ARPT.

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AFTER COMPLETING 3 SUCCESSFUL PATTERNS AND MAKING THE NECESSARY RADIO CALLS; WE CALLED 'BOCA TFC (SMA X); L DOWNWIND RWY 5 BOCA RATON.' AS WE APCHED APPROX MIDFIELD L DOWNWIND RWY 5; THE SMT Y REQUESTED TA; HE RECEIVED 'RWY 5; L TFC.' WE THEN PROCEEDED TO SET UP FOR THE TOUCH-AND-GO. ABEAM THE NUMBERS; WE BEGAN OUR DSCNT. AS WE BEGAN TO TURN L BASE TO RWY 5; I MADE THE CALL; 'BOCA TFC (SMA SEL X) TURNING L BASE RWY 5 BOCA RATON.' AT APPROX 600 FT WE BEGAN THE TURN TO FINAL; 'BOCA TFC (SEL X) TURNING FINAL RWY 5 BOCA RATON.' AFTER THIS XMISSION; THE SMT RPTED 'SMT NUMBER; L DOWNWIND RWY 5 AT BOCA.' AT THIS POINT; I FOUND IT STRANGE THAT THE SMT HAD ENTERED A L DOWNWIND SO QUICKLY AFTER HIS INITIAL RADIO CALL. I LOOKED FOR HIM ON DOWNWIND BUT COULD NOT SEE HIM. APPROX 10 SECONDS LATER HE CALLED 'FINAL RWY 5 AT BOCA.' NO BASE LEG CALL. AT THIS POINT; A RADIOED 'BOCA; SMA SHORT FINALS RWY 5 AT BOCA; SMT POS RPTS.' NO ANSWER. I FRANTICALLY LOOKED TO THE REAR IN THE SMT SEL TO SEE HIM APCH OVERHEAD AT NOT MORE THAN 5 FT. LUCKILY; MY STUDENT HAD DROPPED SLIGHTLY LOW ON THE GLIDE PATH. IF NOT; A MIDAIR COLLISION WOULD DEFINITELY HAVE RESULTED. I BELIEVE THIS EXACERBATED THE SIT: 1) PLTS DO NOT MAKE THEIR TA CALLS FAR ENOUGH FROM UNCTLED FIELDS. 2) MAKE WRONG ENTRIES. 3) DO NOT MONITOR CTAF WELL ENOUGH. HE ALSO BROKE FAR 91.113(G) LNDG ACFT. SEVERAL WITNESSES ALSO FOUND THE SAME FAULT WITH THE SMT.