INSTRUCTOR; GIVING DUAL INSTRUCTION; DIRECTS THE STUDENT TO MAKE A L TURN AFTER AN INTXN TKOF; CONTRARY TO TWR CTLR'S INTENTIONS FOR A R-HAND PATTERN.

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AT THE TIME OF THE INCIDENT I WAS USING RWY 17 AND 2 OTHER ACFT WERE IN THE PATTERN FOR TOUCH-AND-GOES ON RWY 24. I HAD ALSO BEEN USING RWY 24 AND INTENDED TO RETURN TO USING RWY 24 AFTER USING RWY 17. THE TWR CTLR ADVISED ME AND MY STUDENT TO MAKE A STOP-AND-GO LNDG ON RWY 17 AND HOLD SHORT OF RWY 24. WE MADE THE FULL STOP LNDG AND ATC ASKED IF WE COULD REMAIN N OF RWY 24 IF WE STARTED OUR TKOF ROLL FROM OUR PRESENT STOPPED POS ON RWY 17. ATC WAS ALSO TALKING TO THE OTHER ACFT AND I QUESTIONED ATC ABOUT HER INSTRUCTIONS AND SHE REPEATED SHE WANTED US TO REMAIN N OF RWY 24 AND MAKE R TFC. I THOUGHT SHE WANTED US TO MAKE R TFC FOR RWY 24 AND AFTER BEING CLRED FOR TKOF I MADE A SHARP L TURN TO REMAIN N OF RWY 24 AND ENTERED R TFC FOR RWY 24. ATC IMMEDIATELY QUESTIONED MY L TURN AND ADVISED ME I HAD BEEN TOLD TO MAKE R TFC. I RESPONDED THAT I THOUGHT I WAS TO MAKE R TFC FOR RWY 24. I THEN CONTINUED R TFC AND LANDED ON RWY 24. I FELT RUSHED BY ATC AND SHOULD HAVE CLARIFIED THE TURN OUT DIRECTION AND PROPER RWY OR EVEN BETTER; I SHOULD HAVE ADVISED ATC THAT I WAS UNABLE TO MAKE THE TIGHT TURNOUT AND REQUESTED TAXI TO RWY 17 OR RWY 24. ATC COULD HAVE AVOIDED THE ENTIRE SIT ALSO BY SIMPLY ADDING THE RWY NUMBER TO HER DIRECTIONS. SHE COULD HAVE SIMPLY STATED; 'REMAIN N OF RWY 24; MAKE R TFC FOR RWY 17.' I THINK IT SHOULD BE STANDARD PROC FOR ATC TO USE RWY NUMBERS EACH TIME THEY GIVE A DIRECTION TO AN ACFT AND THERE IS MORE THAN 1 RWY IN USE.