A C172 INSTRUCTOR AND STUDENT; WHILE MAKING A VOR DME APCH; PREMATURELY STARTED THEIR DSCNT TO THE INITIAL ALT; AFTER ATC HAD CLRED THEM TO MAINTAIN 4000 FT.

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I WAS FLYING A C172. THE FLT WAS ON AN IFR CLRNC. I WAS SITTING R SEAT PROVIDING INST INSTRUCTION TO A STUDENT PLTING THE PLANE FROM THE L SEAT. WX WAS VMC -- HIGH THEN OVCST WITH VISIBILITY +10 MI. WE WERE FLYING DIRECT GRAND STRAND (CRE) VOR AT 4000 FT MSL AND WERE APPROX 15 MI FROM CRE WHEN WE RECEIVED INSTRUCTION TO 'DSND TO 3000 FT; MAINTAIN 3000 FT TO THE CRE VOR; CLRED FOR THE TWIN CITY (5J9) VOR/DME-A APCH.' I ACKNOWLEDGED 'LEAVING 4000 FT FOR 3000 FT; MAINTAIN 3000 FT TO THE VOR; CLRED FOR THE APCH.' WE DSNDED TO 3000 FT. WHILE LEVEL AT 3000 FT; I BRIEFED MY STUDENT ABOUT THE TURNS AND DSCNTS THAT WOULD BE REQUIRED ONCE XING CRE TO BEGIN THE APCH. BEFORE REACHING CRE; HOWEVER; WE WERE INSTRUCTED TO CLB AND MAINTAIN 4000 FT TO THE VOR. HOW THIS CLB INSTRUCTION WAS ISSUED AND HOW WE ACKNOWLEDGED THE INSTRUCTION ARE THE KEY ELEMENTS THAT CREATED A MISUNDERSTANDING THAT LED TO AN ALTDEV. WE WERE ON APPROX A 120 DEG HDG. TO BEGIN THE APCH; WE NEEDED TO TURN L TO INTERCEPT AND TRACK THE 340 DEG RADIAL OUTBOUND FROM CREW. THE INITIAL APCH SEGMENT HAS A MINIMUM ALT OF 1800 FT. WE CROSSED CREW; AND I INSTRUCTED MY STUDENT TO TURN L TO 320 DEGS. HE DID SO; AND AS WE WERE INTERCEPTING THE RADIAL TO TRACK OUTBOUND FROM CRE TO THE 5J9 ARPT; I INSTRUCTED MY STUDENT TO INITIATE A DSCNT TO 1800 FT. WHILE PASSING THROUGH ABOUT 3300 FT; THE CTLR INFORMED US THAT WE HAD BEEN INSTRUCTED TO MAINTAIN 4000 FT UNTIL CLRED FOR LOWER. APPARENTLY HE HAD SOME TFC AT 3000 FT. I STOPPED OUR DSCNT AT 3200 FT AND INITIATED A CLB BACK TO 4000 FT. AFTER JUST A FEW (10-15) SECONDS; THE CTLR CLRED US TO CONTINUE THE DSCNT. APPARENTLY THE TFC WAS NOT NEARBY; AND NO TFC CONFLICT WAS IMMINENT.