STUDENT PLT DOES NOT TRACK AIRWAY.

Narrative

DURING A VOR A APCH TO NEW HAVEN ARPT WHILE ON AN IFR FLT PLAN (WX WAS BETTER THAN 10000 FT AND 10 MI VISIBILITY); THE STUDENT MISREAD THE APCH PLATE AND DEPARTED THE MADISON VOR ON THE 047 DEG RADIAL IN LIEU OF THE PROPER PUBLISHED TRANSITION. AT THE ALT WE WERE AT WE HAD BEEN INFORMED THAT RADAR SVC HAD BEEN LOST. I WANTED TO ALLOW THE STUDENT SUFFICIENT TIME TO ANALYZE THE SIT SINCE WE WERE NOT GETTING ANY INDICATION OF CLOSURE ON THE DESIRED INTXN. I FELT IT WAS IMPORTANT TO MONITOR HIS REACTION. I HAD TO POINT OUT THE ERROR AND HE PROCEEDED TO TURN TO THE PROPER HDG AND TWIST IN THE PROPER RADIAL. APCH THEN CALLED AND ASKED FOR AN UPDATE ON OUR POS. UNFORTUNATELY; HE REPLIED WE WERE N OF THE VOR TO WHICH APCH REPLIED WITH A SMALL ESSAY ON PROTECTED AIRSPACE AREAS DURING THE APCH. WHEN I COULD FINALLY GET TO TALK ON FREQ; I INFORMED APCH THAT WE WERE S OF THE VOR ESTABLISHED ON THE PUBLISHED TRANSITION. HE (APCH) CONFIRMED WHAT I HAD INFORMED HIM OF; RELATIVE TO OUR POS; AND I INFORMED HIM OF THE ERROR THE STUDENT HAD MADE. HE EXPLAINED HIS INITIAL CONCERN AND REQUESTED THAT I INFORM ATC OF ANY DEVS FROM PUBLISHED PROCS. I CERTAINLY WOULD HAVE ADVISED ATC IF THERE WAS A MEANS TO TALK DISCRETELY TO ATC WITHOUT THE STUDENT BEING ABLE TO HEAR THE CONVERSATION. WASN'T THAT WHY THE 'OPTION' APCH WAS DEVISED? (SO THE STUDENT WOULD NOT HEAR AHEAD OF TIME?) AN OBVIOUS SOLUTION FOR THIS SIT WOULD HAVE BEEN TO SHOOT THE APCH VFR; HOWEVER; HERE IN THE NE THE PHRASE 'UNABLE PRACTICE APCHS; STATE YOUR INTENTIONS' IS ALL TOO OFTEN THE RESPONSE TO SUCH A REQUEST.