SMT TRAINING IN PROGRESS. PLT NON ADHERENCE TO ATC INSTRUCTION LANDED WRONG RWY.

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APPROX 10 MI OUT I INSTRUCTED THE STUDENT TO CALL OWB TWR AND TELL THEM WE WERE INBOUND FOR LNDG. WHEN STUDENT CALLED HE RPTED OUR POS AS 10 MI W OF ARPT; AND ADDED OTHER INFO NECESSARY FOR LNDG. WHEN HE RELEASED THE MIKE; (XMIT BUTTON) HE PAUSED FOR APPROX 2-3 SECONDS THEN CORRECTED HIMSELF BY SAYING HE WAS NOT W OF THE ARPT BUT IN FACT 10 MI E. WHEN HE RELEASED THE XMIT BUTTON A SECOND TIME WE IMMEDIATELY HEARD THE TWR TELL US TO RPT R BASE FOR RWY 18. MY STUDENT REPLIED BY SAYING 'RPT R BASE FOR RWY 36.' HE (STUDENT) DID NOT HEAR THE TWR TELL US RWY 18 AND EXPECTED TO BE CLRED FOR RWY 36. I; HOWEVER; DID HEAR THE CLRNC FOR RWY 18 YET DID NOT SAY ANYTHING TO EITHER THE STUDENT OR TWR BECAUSE SINCE WE WERE USING MULTIPLE RWYS THIS PARTICULAR DAY AND TWR DID NOT CORRECT US ON READ BACK I FIGURED WE WERE UNDERSTOOD FOR RWY 36. AS WE ENTERED BASE LEG FOR RWY 36 MY STUDENT RPTED HIS POS AS 'R BASE FOR RWY 36.' HE THEN RPTED FINAL AND WAS CLRED TO LAND BY THE TWR. AFTER LNDG; WE CLRED RWY 36 AND TWR MADE A COMMENT ABOUT WHY WE LANDED ON RWY 36. I THEN TOLD THEM THAT THERE WAS A MIX UP IN COMS AND WE FIGURED THAT SINCE THEY DIDN'T CORRECT US FOR RPTING FOR RWY 36 WE WERE IN FACT UNDERSTOOD BY THEM THAT WE WERE TO LAND ON RWY 36. THE TWR THEN SAID SOMETHING TO THE EFFECT THAT HE WAS 'DOWNSTAIRS' AND DIDN'T SEE US SET UP AND COME IN ON RWY 36. AFTER WE TAXI TO THE RAMP I TELEPHONED THE TWR AND EXPLAINED WHAT HAPPENED. I TOLD HIM THAT AFTER MY STUDENT MADE HIS FIRST RPT OF 10 MI W HE IMMEDIATELY CORRECTED HIMSELF THUS BLOCKING OUT THE TWRS XMISSION. I ALSO TOLD HIM THAT SINCE WE RPTED THAT WE WERE SETTING UP FOR RWY 36 AND HE DIDN'T CORRECT US; I FIGURED IT WAS UNDERSTOOD BY BOTH PARTIES WHAT RWY WE WERE USING. NO CONFLICT RESULTING IN ANY EVASIVE ACTION WAS REQUIRED; AND NO OTHER TFC WAS IN THE TFC PATTERN AT THE TIME. THE TWR DIDN'T INDICATE THAT HE WOULD FILE ANY COMPLAINTS YET I WANTED TO DOCUMENT THE EVENT. IF ANY OF THIS SEEMS UNCLR OR THE NEED OF MORE INFO IS NECESSARY; PLEASE CONTACT ME ANY TIME. NEXT TIME I WILL MAKE IT CLR TO THE TWR AND STUDENT WHAT RWY WE ARE TO USE.