INSTRUCTOR WITH SPI ON FINAL APCH HEARS SECOND ACFT ANNOUNCE DEP ON 'SAME' RWY. GAR EXECUTED.

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THE CONFLICT AROSE AS WE WERE ON FINAL APCH TO LAND AND ANOTHER ACFT WAS TAXIING INTO POS FOR TKOF. WE EXECUTED A GAR AND THERE WERE NO PROBS. HOWEVER; THE SIT DISTURBED ME AND THERE COULD HAVE BEEN A MUCH MORE SERIOUS SIT. OUR ACFT CROSSED OVER X04 (ORL COUNTY) MIDFIELD AT 1500 FT; WHICH I BROADCASTED OVER UNICOM (123.05). I ALSO CALLED ENTERING DOWNWIND FOR RWY 33 AND LEFT BASE FOR RWY 33. ON SHORT FINAL ANOTHER ACFT BEGAN TO TAXI ONTO RWY 33. HE BROADCASTED THAT HE WAS TAKING OFF RWY 33. I INSTRUCTED MY STUDENT TO GAR; WHICH HE DID. I THEN CALLED THAT WE WERE GOING AROUND. THE OTHER ACFT CALLED THAT HE WOULD MOVE OVER OFF THE RWY (INTO THE GRASS; I GUESS). I CALLED BACK THAT WE WERE ALREADY 'ON THE GO.' WE DEPARTED THE PATTERN; WHICH I BROADCASTED; AS A L DOWNWIND DEP. WE NEVER HEARD OR SAW THE OTHER ACFT MAKE ANY MOVES AFTER WE WENT AROUND. THINGS THAT CONCERN ME: WE TURNED A SHORT FINAL; WHICH I DID NOT CALL. SINCE THE RWY HAS ACFT PARKED ALL AROUND THE ARR END; WE PROBABLY WOULD NOT HAVE NOTICED HIM UNLESS HE CALLED. I THOUGHT HE WAS PARKED LIKE THE REST OF THE ACFT. HE (THE OTHER ACFT) MUST NOT HAVE CHKED THE PATTERN; BEEN MONITORING THE FREQ; OR CHKED FINAL BEFORE TAXI. I WAS TOO INVOLVED IN THE APCH AND SHOULD HAVE BEEN CHKING THE RWY AND PATTERN MORE CLOSELY. I ALLOWED MY STUDENT TO ENTER AT MIDFIELD RATHER THAN A 45 DEG TO DOWNWIND. MORE TIME MIGHT HAVE HELPED.