AN INSTRUCTOR PLT IN AN SMA MISUNDERSTOOD HIS IFR CLRNC. HEADING TRACK DEV. ALT DEV.

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I WAS ON A IFR XCOUNTRY TRAINING FLT. MY STUDENT FILED THE IFR FLT PLAN UNDER MY NAME FROM GXY TO GLL; V220/AKO. THE OPPOSITE WAS FILED FOR THE RETURN TRIP. WE RECEIVED THE CLRNC ON THE GND AT GXY. THEY GAVE US RADAR VECTORS TO AKO. WE ASKED TO FLY THE AIRWAYS FOR TRAINING AND THAT WAS APPROVED. OUR CTLR AT AKO FROM ZDV WAS BUSY WITH ARRIVING DEN TFC. SO HE CLRED US FOR THE VISUAL APCH AT AKO. WE ASKED FOR THE VOR APCH AND OUR RETURN CLRNC TO GXY. HE CLRED US FOR THE VOR APCH AND ASKED US TO CALL FSS TO GET OUR RETURN CLRNC TO GXY. WE CALLED DENVER RADIO ON 122.55 TO GET OUR CLRNC AND THEY SAID THEY WOULD BE HAPPY TO HELP US; BUT IT DIDN'T MAKE ANY SENSE TO GET OUR CLRNC FROM THEM BECAUSE THEY WOULD HAVE TO CALL ZDV TO GET THE CLRNC. WE SAID WE WOULD CALL CTR AFTER WE FINISHED THE APCH. AFTER FLYING THE APCH; WE STARTED BACK TOWARDS GXY INSTEAD OF FLYING THE MISSED APCH PROC. WE CALLED CTR AT ABOUT 7000 FT MSL; (MISSED APCH ALT WAS 6000 FT MSL) AND CTR ADVISED US HE EXPECTED US TO FLY THE MISSED APCH PROC AND NOT FLY BACK TOWARDS GXY. WE THOUGHT HE WANTED US TO CALL HIM AFTER THE APCH AND ON OUR WAY BACK TO GXY. CTR TOLD US THAT THE AIRSPACE WAS PROTECTED FOR OTHER POSSIBLE TFC AND HE WANTED TO MAKE SURE WE UNDERSTOOD THAT. WE THANKED HIM AND CONTINUED BACK TO GXY ON OUR IFR FLT PLAN. THE OUTSIDE CONDITIONS WERE VFR AND WE SHOULD HAVE CANCELED IFR BEFORE THE APCH AND THEN GOTTEN A NEW CLRNC ON OUR WAY BACK TO GXY.