HDG TRACK DEV IN NON ADHERENCE TO ATC CLRNC INSTRUCTION.

Narrative

UPON DEPARTING EYW RWY 09; I HEARD THE CTLR CLR US FOR TKOF AND MY ITALIAN COPLT (WHOSE ENGLISH IS FAR FROM FLUENT) READ BACK CLRNC. I; HOWEVER; DID NOT REGISTER AN ASSIGNED HDG AND SOMEHOW HAD IN MY HEAD THE USUAL 360 DEG HDG. AS WE LINED UP ON THE RWY AND READ THE CHKLIST; I INSTRUCTED COPLT TO HOLD THE BRAKES UNTIL PWR SET AND HE'D PROBABLY BE TURNING TO 360 DEGS. I WENT AHEAD AND SET MY HDG BUG. HE STILL DID NOT ADVISE ME OF AN ASSIGNED HDG. (I HAD PICKED UP RTE CLRNC IN WHICH NO HDG WAS ASSIGNED). AFTER DEP AT 300-400 FT I TOLD HIM CLR L AND WE STARTED TURN AS WE CONTACTED DEP. UPON CONTACTING HIM IMMEDIATELY AFTER INSTRUCTED TO DO SO; HE TOLD ME TO FLY 090 DEGS. I ANSWERED WE WERE TURNING BACK TO 090 DEGS. (WE WERE NOW PERHAPS ROLLING THROUGH 040 DEGS) SO WE STARTED BACK TO 090 DEGS. THEN THE CTLR TOLD US TO STOP TURN AT 030 DEGS WHICH IS WHERE WE WERE. A FEW MOMENTS LATER HE TOLD ME I HAD BEEN INSTRUCTED BY TWR TO FLY RWY HDG AND ASKED WHY I FLEW 360 DEGS. I TOLD HIM I'D UNDERSTOOD 360 DEGS AND I'D JUST BEGUN TURN WHEN I CONTACTED HIM. I SAW NO CONFLICT FROM THE SIT AND HE CAUGHT ME OFF GUARD AS I WAS UNAWARE OF THE MISTAKE. AS I DISCUSSED WITH THE COPLT HIS CLRNC; HE SAID HE THOUGHT HE REMEMBERED RWY HDG. I THINK IT'S A REAL PROB IN THE COCKPIT WHEN LANGUAGE/COM BTWN CREW AS WELL AS ATC IS A PROB. I FELT ALL DAY AS I WAS BASICALLY OPERATING A SINGLE PLT ACFT AND SAFETY IS COMPROMISED WHEN I CAN'T CLRLY AND EASILY COM WITH CREW AND HE WITH ME. I KNOW NOW THAT I REALLY CAN'T RELY ON SOMEONE ELSE FOR INSTRUCTIONS THAT I AM RESPONSIBLE FOR AND TO LISTEN TO CTLR; NOT WHAT MY HABITS ARE TELLING ME. SINCE I DIDN'T HEAR OF A TURN MYSELF I SHOULD HAVE VERIFIED BEFORE TURNING.