INSTRUCTOR AND STUDENT PLT TAXI ON ACTIVE RWY 28L VICE RWY 28R AS CLRED.

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I WAS GIVING DUAL INSTRUCTION IN A DIAMOND DA20 AIRPLANE AT THE FCM ARPT. WE COPIED THE CURRENT ATIS INFO (WIND 310 DEGS AT 11; VISIBILITY 10 MI; SKY CONDITION CLR; 16 DEGS; DEWPOINT 7 DEGS; ALTIMETER 29.79. RWY 28L AND RWY 28R IN USE). WE THEN CONTACTED GND CTL INFORMING THEM THAT WE WERE ON THE NW RAMP WITH ATIS INFO XA READY FOR TAXI SBOUND. GND CTL STATED THAT ATIS INFO XB WAS NOW CURRENT AND GAVE US THE UPDATED WIND AND ALTIMETER SETTING. WE WERE INFORMED THAT PAINTING WAS IN PROGRESS AND TXWY A WAS CLOSED. WE WERE CLRED TO TAXI DOWN RWY 28R ALL THE WAY TO THE END FOR DEP ON RWY 28L. WE APPARENTLY MISUNDERSTOOD THE CLRNC AND BEGAN TO TAXI DOWN RWY 10R. THE GND CTLR ASKED US WHAT WE WERE DOING AND I STATED THAT I THOUGHT WE WERE CLRED TO TAXI DOWN THIS RWY. THE CTLR STATED THAT WE WERE CLRED TO TAXI DOWN THE OTHER PARALLEL RWYS. NEXT THE CTLR SAID 'STOP.' THEN THE CTLR SAID TO TAXI AHEAD AND TAKE THE NEXT R OFF THE RWY. AFTER WE EXITED THE RWY; WE WERE ASKED TO COPY DOWN THE TELEPHONE NUMBER TO CALL THE TWR ABOUT A POSSIBLE DEV AT THE COMPLETION OF OUR FLT. AT THE COMPLETION OF THE FLT LESSON; I CALLED THE TWR AND THE MGR SAID THAT THEY NEEDED TO FILE A RPT AND HE NEEDED MY NAME; ADDRESS; AND CERTIFICATE NUMBER. I GAVE HIM THE INFO THAT HE REQUESTED AND I WAS ADVISED THAT I MAY WANT TO OBTAIN SOME LEGAL COUNSEL. THE COM WITH GND CTL WAS DIFFICULT BECAUSE MY STUDENT IS A NATIVE OF ANOTHER COUNTRY AND HE WAS ATTEMPTING TO MAKE HIS FIRST COM WITH ATC. I BELIEVE THERE WOULD BE LESS CHANCE FOR PLTS TO MISINTERP TAXI INSTRUCTIONS IF THE CTLRS WOULD ISSUE TAXI CLRNCS BY REFERRING TO THE RWYS IN THE DIRECTION THAT THEY WANT YOU TO TAXI. A PLT IS NEVER ISSUED A TKOF OR LNDG CLRNC BY REFERRING TO A RWY AS ITS RECIPROCAL. WE WERE ON THE W END OF THE ARPT AND NEEDED TO TAXI TO THE E END FOR TKOF. THE TAXI INSTRUCTIONS WOULD HAVE BEEN MUCH CLRER IF THE CTLR WOULD HAVE SAID 'TAXI DOWN RWY 10L.' FROM THE PLT VIEW THE RWY SIGNS ON THE W END OF THE RWY SAY 10L AND 10R.