THE FLT INSTRUCTOR ALLOWED THE INST TRAINEE TO TURN TO THE WRONG HDG.

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WHILE ON AN IFR TRAINING FLT; AN ASSIGNED HDG WAS MISSED BY BOTH MYSELF AND MY STUDENT. THE STUDENT READ BACK THE CLRNC; HOWEVER; I MISSED IT. AFTER HAVING TURNED APPROX 120 DEGS; I ASKED MY STUDENT TO TELL ME WHAT HDG WE WERE ASSIGNED AND HE REPLIED; 'I'M NOT SURE.' I THEN TOLD HIM TO CHK WITH ATC TO FIND OUT. THE CTLR RESPONDED BY TELLING US TO TURN IMMEDIATELY TO 330 DEGS (WE WERE CURRENTLY FLYING 030 DEGS AFTER HAVING TURNED R FROM A HDG OF W). THE CTLR THEN INFORMED US OF TFC AT 12 O'CLOCK AND A MI AT AN ALT BELOW US (I BELIEVE IT WAS 1500 FT). WE NEVER SAW THE TFC DUE TO CLOUDS AND LOW VISIBILITY DUE TO RAIN. THE CTLR THEN QUESTIONED US ABOUT WHY WE WERE FLYING THE HDG WE WERE. I BELIEVE THIS SIT WAS CAUSED BY 3 FACTORS. 1) MY STUDENT'S BLIND FAITH IN THE FACT THAT I WOULD TELL HIM WHERE TO STOP HIS TURN; EVEN AFTER HE HAD FORGOTTEN WHAT HDG HE WAS ASSIGNED. 2) COMPLACENCY ON MY PART. HAVING FLOWN MANY PRACTICE APCHS IN THIS AREA I ASSUMED OUR TURN WOULD BE TO THE NE; AS IS USUALLY THE SIT. BY NOT QUESTIONING THE STUDENT UNTIL HAVING PASSED OUR HDG I ALLOWED THIS SIT TO OCCUR. 3) LAST; AND MOST IMPORTANT; IS THE AMOUNT OF ATTN I WAS PAYING. BY ALLOWING MY ATTN TO SLACKEN MOMENTARILY AND MISSING A RADIO CALL; I POTENTIALLY PUT OUR FLT IN JEOPARDY. IN THE FUTURE; AS SOON AS A RADIO CALL IS MISSED; I WILL CONFIRM IT WITH MY STUDENT OR ATC IMMEDIATELY; BEFORE A POTENTIAL 'SIT' CAN DEVELOP.