APPARENT MISCOM BTWN TWR AND FLC ON PATTERN ENTRY AND LNDG RWY. FROM RPTR'S DESCRIPTION; THE FLC FOLLOWED ALL CORRECT PROCS; BUT TWR DIDN'T UNDERSTAND WHAT THEY WERE DOING.

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12 MI W OF ARPT AND AFTER LISTENING TO ATIS; THE VERY COMPETENT PRIMARY STUDENT; FLYING HIS PERSONAL ACFT; RPTED HIS POS AND REQUESTED ENTRY INTO THE TFC PATTERN FOR THE PURPOSE OF MAKING TOUCH-AND-GO LNDGS. (IT WAS OUR PLAN TO TERMINATE OUR PRACTICE LNDG PROGRAM WITH A FULL- STOP FOR LUNCH.) ATIS INDICATED THAT RWY 24 WAS THE ACTIVE RWY. SINCE WE WERE APCHING FROM THE W WE WERE SURPRISED TO HAVE THE TWR CTLR REQUEST WE RPT A L DOWNWIND FOR RWY 24. (AT LEAST; WE BOTH UNDERSTOOD 'L'.) (SEE DIAGRAM.) I SUGGESTED TO THE STUDENT THAT HE REQUEST A R-TURN DOWNWIND ENTRY FOR OUR INITIAL LNDG; WHICH HE DID; AND THE CTLR SAID; 'I GAVE YOU A R DOWNWIND.' AFTER RPTING A R DOWNWIND WE WERE REQUESTED TO RPT A R BASE; REFING A JET ON FINAL. THE STUDENT RPTED THE R BASE AND WAS CLRED FOR A TOUCH-AND-GO; IMMEDIATELY FOLLOWED BY A REQUEST TO LAND ON RWY 29; DUE TO TFC ON RWY 24. THE STUDENT TURNED L TO ENTER A R DOWNWIND FOR RWY 29. IMMEDIATELY THE CTLR COMMENTS WERE; TO THE BEST OF OUR UNDERSTANDING; AS FOLLOWS: 'WHY ARE YOU DOING A 360 DEG; IS THERE AN INSTRUCTOR ON BOARD? IF SO; HE SHOULD TAKE OVER WHEN A STUDENT IS CONFUSED; CLRED TO LAND ON ANY RWY; SINCE I DON'T KNOW WHAT YOUR INTENTIONS ARE!' AT THIS POINT MY STUDENT HANDED ME A HAND MIKE. SINCE I WAS AS CONFUSED AS HE WAS; I SIMPLY ASKED THE TWR WHAT HE WANTED US TO DO. HE SAID 'LAND ON ANY RWY -- CLRED TO LAND ON RWY 24.' I ACKNOWLEDGED THIS AND WE PROCEEDED TOWARD RWY 24; WHICH WAS BY NOW RIGHT IN FRONT OF US. AS WE CAME OVER THE FENCE; THE CTLR SAID SOMETHING ABOUT 'LNDG CLRNC' WHICH WE DISREGARDED AND LANDED. I INSTRUCTED THE STUDENT TO FORGET THE TOUCH-AND-GO AND ADVISED THE TWR WE WERE FULL-STOP AND REQUESTED TO PROCEED TO THE TERMINAL FOR LUNCH. WE WERE REQUESTED TO DEPART THE RWY AT 'CHARLEY' AND PROCEED TO GATE. DURING LUNCH WE DREW DIAGRAMS; ETC; TRYING TO DETERMINE WHAT ALL OF THIS WAS ABOUT. WE WERE UNABLE. THERE WAS NO OTHER TFC EXCEPT THE JET THAT WAS NEVER A FACTOR. THE WHOLE THING WENT FROM A HO-HUM ROUTINE TFC AND LNDG PROC TO THIS PECULIAR SIT. THE CTLR APPEARED TO BE ALL ALONE; AS HIS VOICE WAS ON ALL FREQS. THERE WAS NEVER A CONFLICT WITH OTHER ACFT. WHEN WE LEFT EVERYTHING WAS ROUTINE AND NO MENTION OF THE PREVIOUS ACTIVITY WAS MADE BY US OR THE CTLR; WHO APPEARED TO BE THE SAME FELLOW.