WRONG XPONDER CODE USED DURING AN APCH TO DEST ARPT WITHIN THE DC ADIZ; 2 NM N OF GAI; MD.

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ON APR/FRI/04; I WAS THE FLT INSTRUCTOR FOR AN INSTRUCTIONAL FLT ORIGINATING FROM GAI ARPT. THE ARPT IS LOCATED WITHIN THE WASHINGTON ADIZ. I OBTAINED A STANDARD BRIEFING AND FILED 2 ADIZ FLT PLANS. AFTER DEPARTING GAI AT APPROX XA20 LCL; WE PROCEEDED TO EXIT THE ADIZ TO THE NW. THE INCIDENT OCCURRED ON THE RETURN TO GAI. AFTER COMPLETING OUR FLT MANEUVERS OUTSIDE OF THE ADIZ; I CONTACTED POTOMAC APCH REQUESTING OUR DISCRETE XPONDER CODE FOR OUR FLT BACK TO GAI. THE APCH CTLR ASSIGNED A CODE AND INSTRUCTED ME TO RPT 10 MI FROM GAI. DURING THIS TIME; I WAS PROVIDING INSTRUCTION TO MY STUDENT ON GPS NAV AND LANDMARKS. WHEN WE WERE ABOUT 10 MI FROM THE ARPT; I RPTED TO THE APCH CTLR AND CALLED THE ARPT IN SIGHT. HE INSTRUCTED ME TO 'CHANGE TO CTAF AND REMAIN ON THE SQUAWK.' I READ BACK HIS INSTRUCTIONS AND THANKED HIM FOR HIS HELP. THE CTLR SAID 'YOU'RE WELCOME.' AT THIS POINT; I INSTRUCTED THE STUDENT TO BEGIN A DSCNT AND TO MANEUVER FOR THE 45 DEG ENTRY TO RWY 14. WHEN WE WERE TURNING DOWNWIND; I NOTICED THAT THE XPONDER WAS SQUAWKING 1200. I IMMEDIATELY REENTERED OUR DISCRETE XPONDER CODE. I BELIEVE THAT MY STUDENT ACCIDENTALLY HIT THE VFR BUTTON ON THE XPONDER AS WE STARTED OUR DSCNT. THE VFR BUTTON IS ABOVE THE PWR CTL. OF COURSE; THERE IS THE POSSIBILITY THAT I NEVER ENTERED THE CORRECT DISCRETE XPONDER CODE. I FEEL THAT DUE TO THE ATTN I WAS GIVING MY STUDENT ON GPS NAV AND SHOWING THE IMPORTANCE OF SMOOTH CTL INPUT; I BECAME TOO DISTR. ALSO; THE FACT THAT THE APCH CTLR NEVER QUERIED ME ON WHAT I WAS SQUAWKING LED ME TO ASSUME THAT I WAS SQUAWKING THE CORRECT CODE. THE CTLRS SHOULD USE A STANDARD PHRASE TO LET US PLTS KNOW THAT THEY SEE OUR XPONDER. POTOMAC APCH CTLRS USE DIFFERENT PHRASES SUCH 'PROCEED ON COURSE;' OR 'BEACON CODE OBSERVED.' I FEEL THAT IF THEY HAVE A STANDARD PHRASE THAT IS IN USE WOULD ALLOW EVERYONE TO MINIMIZE ERRORS. I HAVE ALSO STARTED TO INSTITUTE A MORE STERILE COCKPIT ENVIRONMENT BEFORE ENTERING THE ADIZ. I WILL NEVER ASSUME THAT THE CTLR'S LACK OF QUERY OF MY XPONDER CODE MEANS THAT I'M SQUAWKING THE CORRECT CODE. AND I WILL MONITOR THE XPONDER MORE CLOSELY WHILE IN THE ADIZ.