SMA X HAD NMAC WITH ACFT Y ON FINAL APCH. EVASIVE ACTION TAKEN. SEE AND AVOID CONCEPT.

Narrative

SMA X ENTERED THE RWY 9R PATTERN AT MLB AND WERE TOLD TO MAKE A SHORT APCH. WE COMPLIED; AND AS WE WERE ON SHORT FINAL THE TWR CTLR CLRED A SEMINOLE FOR TKOF ON RWY 9R. SHE THEN ISSUED A GAR TO US FOLLOWED BY INSTRUCTIONS TO ENTER R TFC FOR RWY 9R. WE FLEW A NORMAL RIGHT HAND PATTERN FOR RWY 9R. AS WE WERE ON BASE; I NOTICED AN ACFT ON FINAL FOR RWY 9L. I ADVISED MY STUDENT TO 'CLR FINAL.' WE COMMENCED OUR TURN TO FINAL; BUT HAD NOT RECEIVED LNDG CLRNC (WHICH IS NOT UNUSUAL DURING CONGESTED TIMES AT MLB). I SAID; 'X SHORT FINAL RWY 9R;' ABOUT THE SAME TIME MY STUDENT SAID WE HAD ANOTHER ACFT OFF OUR L WING. I WAS NOT CONCERNED; THINKING IT WAS THE TFC I SAW GOING TO RWY 9L. A VERY CONFUSED CTLR CAME ON AND ASKED WHO WAS ON SHORT FINAL. WE THEN SAW ANOTHER ACFT Y SLIGHTLY BEHIND AND BELOW US TO THE L. BOTH ACFT INITIATED IMMEDIATE GARS. WE RECEIVED NO TA'S WHILE MAKING R TFC. TFC EVIDENTLY; LCL CTL HAD EXPERIENCED A SHIFT CHANGE AND WE WERE FORGOTTEN. A VALUABLE LESSON WAS LEARNED IN OUR COCKPIT ABOUT THE IMPORTANCE OF SCANNING FOR TFC (AT EVERY TURN IN THE PATTERN; ESPECIALLY) AT UNCTLED OR CTLED FIELDS.