INSTRUCTOR PLT OF A PIPER PA44 ENTERED A RESTR AREA DUE TO A MISUNDERSTANDING OF APCH CTLR'S RESPONSE OF 'RADAR CONTACT' THAT HE WAS CLRED TO ENTER THE RESTR AREA AS REQUESTED TO ATC.

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MY STUDENT AND I WERE FLYING OVER X21 FROM DAB TO FPR; DUAL XCOUNTRY DAY. OVER X21 I CONTACTED DAB APCH ON 134.95 AND ASKED FLT FOLLOWING TO FPR AND TO FLY FIRST OVER KENNEDY VISITOR CENTER; MAKE 2 TURNS; THEN CONTINUE TO FPR (SPACE TOUR). THE CTLR GAVE ME SQUAWK CODE AND AFTER A FEW MINS; HE CALLED 'SMA RADAR CONTACT.' THAT IS WHERE I MADE A MISTAKE AND STARTED TO FLY TOWARD THE VISITOR CENTER. IT IS NOT MY FIRST TIME THAT I DID THIS TYPE OF TOUR; BUT AS WE GOT CLOSE TO THE VISITOR CENTER; THE CTLR CALLED ME AND ASKED 'WHAT ARE YOU DOING?' I ASSUMED THAT 'RADAR CONTACT' WAS OK BECAUSE I DIDN'T ASK TO FLY OVER NASA RWY. HE TOLD ME TO TURN IMMEDIATELY R 190 DEGS BECAUSE I WAS ENTERING R-2934 ABOVE 1200 FT (I WAS AT 2000 FT). I TURNED BACK S AND LEFT THE AREA AND CONTINUED TO FPR. THAT WAS BAD JUDGEMENT FROM ME TO NOT WAIT FOR HIM TO SAY 'CLRED FOR THE TOUR' OR HAND ME OFF TO NASA TWR. I THINK THAT WAS A MISCOM FROM BOTH SIDES. NEXT TIME I WILL BE MORE SPECIFIC IN MY REQUEST; EVEN THOUGH I KNOW THE AREA WELL; NEVER NEED TO TAKE THINGS FOR GRANTED.