PLT TRAINEE OF SMA SEL ACFT DEVIATED FROM ASSIGNED TWR INSTRUCTIONS BY FLYING THE WRONG DOWNWIND TFC PATTERN AND NOT HOLDING SHORT AS INSTRUCTED AFTER LNDG RESULTING IN GND CONFLICT.

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I WAS FLYING WITH ONE OF MY PRIMARY STUDENTS; IN THE PATTERN; DOING TOUCH-AND-GOES ON RWY 27. AN SMA WAS ALSO DOING TOUCH-AND-GOES BUT FOR RWY 31. WE WERE BOTH IN L TFC. AFTER TKOF ON RWY 27; TWR TOLD US TO ENTER L DOWNWIND FOR RWY 31 FOR NOW; THEN HE WOULD GET US BACK FOR RWY 27. THE SMA WAS ON SHORT FINALL FOR RWY 31 WHEN MY STUDENT TURNED TO A HDG OF ABOUT 90 DEGS. (WE WERE NOW ON DOWNWIND FOR RWY 27; ABEAM THE APCH END.) I WAS NOT SURE IF HE WAS TURNING ON PURPOSE OR JUST WASN'T PAYING ATTN. I ASKED HIM IF TWR HAD TOLD HIM TO ENTER DOWNWIND FOR RWY 27; HE REPLIED THEY NEVER SAID THEY'D CALL OUR BASE SO HE COULD TURN. I TOLD HIM TO CALL TWR TO VERIFY THIS. THERE WAS OTHER TFC INBOUND FOR THE ARPT AND THE FREQ WAS REALLY CONGESTED. HE WAS UNABLE TO CONTACT TWR RIGHT AWAY. I TRIED TO TELL THE STUDENT HE SHOULD HAVE STAYED IN THE DOWNWIND FOR RWY 31; BUT DUE TO THE TWR TALKING HE WAS UNABLE TO HEAR ME. I TRIED TO TURN US BACK TO DOWNWIND ON RWY 31; BUT HE DIDN'T REALIZE THAT IT WAS ME AND OUGHT MY ACTION. I REPEATED TO HIM TO CALL TWR AND TOLD HIM I DIDN'T THINK WE SHOULD HAVE TURNED DOWNWIND FOR RWY 27. NOW HE STARTED TO TURN BASE FOR RWY 27. AT THIS POINT (THIS HAS ONLY TAKEN 2 TO 3 MINS) I GRABBED THE CTLS; AND CALLED TWR. I SAID 'WE ARE TURNING BASE FOR RWY 27.' TWR RETURNED WITH 'ROGER; BUT HE ADVISED YOU WERE SUPPOSED TO STAY ON DOWNWIND FOR RWY 31. CONTINUE FOR RWY 27; CLRED FOR TOUCH-AND-GOES RWY 27. SMA IS ON 1/2 MI FINAL.' (THE PLANE LNDG AHEAD OF US.) WE HAD THE TFC IN SIGHT. THE STUDENT IMMEDIATELY TURNED FOR FINALL. WE WERE A LITTLE CLOSE ON FINALL SO I TOLD THE STUDENT TO BE PREPARED FOR A GAR. TWR TOLD THE OTHER PLANE TO HOLD SHORT OF RWY 31. I WAS PREOCCUPIED WITH THAT PLANE STILL ON THE RWY AND ALSO HAD TO PAY CLOSE ATTN TO THE STUDENT'S XWIND LNDG. THE PLANE HAD JUST EXITED THE RWY AS WE BEGAN TO FLARE. WE DID THE TOUCH-AND-GO AND ENTERED L DOWNWIND RWY 27 WHEN TWR SAID WE HAD BEEN TOLD TO HOLD SHORT OF RWY 31 ON THAT LAST LNDG. I APOLOGIZED. I NEVER HEARD TWR TELL US TO HOLD SHORT OF RWY 31. AFTER WE FINISHED AND TAXIED TO THE RAMP; THE PLT IN THE PLANE THAT LANDED AHEAD OF US CAME OVER. HE STATED TWR TOLD HIM TO HOLD SHORT OF RWY 31 UPON LNDG; THEN TOLD HIM TO EXPEDITE EXITING RWY 27 DUE TO ACFT LNDG BEHIND HIM (US); THEN TWR TOLD HIM TO HOLD SHORT OF RWY 31 AGAIN. HE NEVER HEARD TWR TELL US TO HOLD SHORT OF RWY 31. POSSIBLY TWR USED THE WRONG CALL NUMBERS. THE FIRST PROB I FEEL I SHOULD HAVE BEEN MORE AGGRESSIVE WITH MY STUDENT. HE WAS ABSOLUTELY SURE HE COULD TURN DOWNWIND FOR RWY 27. THERE WAS SO MUCH CONGESTION ON THE FREQ THAT I THOUGHT I MIGHT HAVE MISSED IT. IT IS DIFFICULT SOMETIMES BEING AN INSTRUCTOR. YOU MUST ALLOW THE STUDENT TO MAKE DECISIONS; BUT YOU MUST ALSO BE READY TO STEP IN IMMEDIATELY IF IT IS THE WRONG DECISION. THE SECOND PROB; I AM NOT SURE IF WE MISSED TWR'S INSTRUCTION TO HOLD SHORT OR IF THEY MEANT US BUT USED THE WRONG NUMBERS. I KNOW I WAS VERY BUSY SUPERVISING THE APCH AND LNDG IN A XWIND; PLUS WORRYING ABOUT THE PLANE; IF IT WAS GOING TO EXIT THE RWY IN TIME SO I COULD HAVE MISSED THE INSTRUCTION.