DA20 INSTRUCTOR AND STUDENT AND A C172 HAD AN NMAC AFTER A STUDENT GAR BECAUSE OF AN UNSTABILIZED APCH.

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ON AUG/FRI/03; I WAS CONDUCTING A PRE-SOLO STAGE CHK WITH A STUDENT. WE HAD BEEN IN THE NORTHERN PRACTICE AREAS; AND WANTED TO RETURN TO THE AIRFIELD TO DO TOUCH-AND-GOES. WE WERE APPROVED FOR A STRAIGHT-IN APCH TO RWY 16L. THE STUDENT CAME IN HIGH AND FAST; THUS DECIDED TO EXECUTE A GAR. WE WERE TOLD TO GO AROUND ON THE L SIDE; AND DID SO. WHILE WE WERE GOING AROUND; A C172 WAS CLRED FOR TKOF. AT THIS TIME; WE ARE BOTH ON UPWIND FOR RWY 16L. MY STUDENT AND I WERE TOLD TO FOLLOW ANOTHER DA20 (DIAMOND FALCON) ON DOWNWIND; BUT WE WERE NOT CLRED TO MAKE L CLOSED TFC (AT MIL ARPTS; ONE MUST RECEIVE CLRNC TO TURN XWIND). WHILE MY STUDENT WAS TRYING TO CALL TWR TO REQUEST L CLOSED TFC (THE PATTERN WAS VERY CONGESTED; AND MY STUDENT WAS HAVING A HARD TIME GETTING A WORD IN); THE TWR CTLR CLRED THE C172; WHO WAS ABOUT 30 FT BELOW AND SLIGHTLY AHEAD AND R OF US AND CLBING; FOR L CLOSED TFC. THE CTLR DID NOT ADVISE THE C172 OF US; AND I DOUBT IF THE 2 PLTS ON BOARD THAT C172 KNEW WE WERE THERE. WHILE THEY WERE IN A CLBING L TURN FOR THE XWIND; I QUICKLY TOOK THE CTLS FROM MY STUDENT; APPLIED FULL PWR AND PULLED THE NOSE UP TO ABOUT 20 DEGS IN PITCH TO AVOID HITTING THE C172. IF THE TWR CTLR WANTED US TO EXECUTE THE L TURN FOR THE XWIND AND FOLLOW THE OTHER DA20 THAT WAS ON DOWNWIND; SHE SHOULD HAVE TOLD US THAT WE WERE CLRED FOR L CLOSED TFC. SHE DID NOT DO SO; AND IT IS MY BELIEF THAT IF I WOULD HAVE MADE THE XWIND TURN WITHOUT CLRNC; I WOULD HAVE BEEN VIOLATED.