C172 INSTRUCTOR LANDED ON THE WRONG RWY DUE TO POSSIBLE CTLR ERROR.

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I WAS APCHING THE ATW ARPT FROM THE W AND MADE MY INITIAL CALL AT; I BELIEVE; 8 MI W. I WAS DIRECTED TO RPT 3 MI W AND PLAN LNDG ON RWY 29. AT 3 MI W; I CALLED TWR AND WAS CLRED TO LAND ON RWY 3. (THERE WAS NO OTHER TFC ANYWHERE AT THE TIME.) I REPEATED 'CLRED TO LAND RWY 3' AS I ALWAYS REPEAT THE RWY. I THOUGHT IT KIND OF STRANGE THAT I WOULD BE CLRED TO LAND ON RWY 3 AFTER BEING TOLD TO EXPECT RWY 29; BUT I CONSCIOUSLY THOUGHT THAT BY REPEATING THE LNDG CLRNC; IF THE CTLR DIDN'T REALLY MEAN TO SAY '3' HE WOULD CATCH IT. I CONSIDERED QUESTIONING HIM TO SEE IF THAT WAS WHAT HE REALLY WANTED; BUT I DID NOT. I NOW WILL QUESTION ANY SIT WHERE QUESTIONS MAY ARISE. BUT; I CONCLUDED THEN THAT HE WAS CLRING ME TO LAND ON RWY 3 BECAUSE IT WAS MOST EXPEDITIOUS FOR ME. I INSTRUCT OUT OF THIS ARPT AND WE RECOGNIZE EACH OTHER'S VOICES. AFTER LNDG; I STOPPED SHORT OF RWY 29 AND ASKED FOR 'TAXI TO PARKING.' I WAS CLRED TO DO SO. WHILE TAXIING; THE CTLR ADVISED ME TO GIVE THE TWR A CALL AFTER PARKING. I DID THIS; WONDERING WHAT I COULD POSSIBLY HAVE DONE WRONG. HE SAID; 'I CLRED YOU TO LAND ON RWY 29' AND I IMMEDIATELY SAID; 'NO SIR; YOU CLRED ME TO LAND ON RWY 3 AND I CONSCIOUSLY REPEATED THAT CLRNC.' HE WAS OPEN MINDED AND UNDERSTANDING AS I BELIEVE I WAS; TOO. WE CONCLUDED THAT HE MAY HAVE MADE THE ERROR OR I MAY HAVE THOUGHT I HEARD '3.' BUT HE DID NOT REALLY LISTEN TO MY VERIFICATION CALL BACK. WE DECIDED WE EACH NEED TO HELP EACH OTHER ALWAYS; AND THAT NO HARM WAS DONE (THERE WERE EXCELLENT VISUAL CONDITIONS; AND NO OTHER TFC). I WOULD CERTAINLY HAVE DONE SOMETHING IF ANY CONFLICTS HAD ARISEN. FINALLY; I SHOULD HAVE AND FOREVER AFTER WILL QUESTION A SOMEWHAT 'IFFY' RWY CLRNC. HE SHOULD HAVE CAUGHT MY READBACK BUT DID NOT. WE WILL BOTH; I BELIEVE; BE MORE CAREFUL AND PRECISE. THIS CTLR IS EXCELLENT; CALM; AND VERY COURTEOUS AND HANDLED THE SIT WELL.