CROSS COUNTRY TRAINING FLT; THOUGHT WAS CLEARED FOR ADF APCH ENROUTE AND CONTINUE.

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A STUDENT AND I WERE ON AN IFR TRNING FLT FOR HIS LONG CROSS COUNTRY. WITH 3 LEGS IN THE CROSS COUNTRY; WE HAD 2 FUEL STOPS AND WERE REQUIRED TO PICK UP 3 SEPARATE CLRNCS. ON OUR FIRST STOP WE FUELED AND PICKED UP OUR CLRNC FROM THE FSS WHICH WAS AS FOLLOWS: CLRED DIRECT HVR V430 CLB AND MAINTAIN 2000'; CONTACT CENTER ON 133.40; 30 MI E OF THE CTB VOR. WE HAD FILED FOR AN APCH AT AN ARPT BTWN US AND OUR NEXT FUEL STOP; SO THE CLRNC WE HAD RECEIVED SHOULD HAVE TIPPED ME OFF AS TO SOMETHING BEING WRONG. THEY HADN'T CLRED US FOR THE APCH AND WANTED US TO CONTACT CENTER 30 MI E. MY INITIAL REACTION WAS THAT WE WOULD BE TOO LOW IN THE AREA WE WERE IN TO RECEIVE CENTER UNTIL WE WERE THROUGH WITH THE NDB APCH (LOW APCH) AND CLBING BACK OUT TO OUR ASSIGNED ALT. WE COULD ONLY CLB OUT AT 250 FPM AND WITH A 25 KT TAILWIND AT 5000'; WE WOULD NEVER HAD MADE 7000' IN ORDER TO CONTACT CENTER AND GET A CLRNC TO SHOOT THE APCH. THERE WAS CONFUSION ON BOTH PARTS; ON MY PART AS TO THINKING I WAS CLRED FOR THE APCH AND ON THE PART OF THE FSS AS TO NOT UNDERSTANDING THAT WE HAD WANTED AND HAD FILED FOR AN APCH WHILE ENRTE TO OUR SECOND STOP. IT COULD HAVE BEEN RESOLVED IF WE WOULD HAVE BEEN INSTRUCTED TO STAY ON FREQ WITH THE FSS UNTIL WE HAD COMPLETED THAT APCH; AND HAD GAINED SUFFICIENT ALT IN ORDER TO CONTACT CENTER. IT COULD ALSO HAVE BEEN CLRED UP QUICKLY IF I WOULD HAVE QUESTIONED MY CLRNC BEFORE OUR DEP. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: WX CONDITIONS WERE VFR; NO CLOUDS AND UNLIMITED VIS. NO CONFLICT RESULTED FROM THE ADF APCH TO SHELBY. CTLR WONDERED WHY THEY HAD NOT CONTACTED THEM AS PER HIS CLRNC AND IT WAS THEN POINTED OUT THE MISUNDERSTANDING. FSS WAS ALSO PARTLY TO BLAME BUT HE CONCURRED HE SHOULD HAVE REQUESTED CLARIFICATION WHEN THE CLRNC DID NOT INCLUDE THE ADF APCH SHELBY. DISCUSSED WITH THE CTLR AFTER THE FLT AND THAT IS THE LAST INFO ON THE INCIDENT.