C172 IN IFR FLT TRAINING HAS VACUUM PUMP FAILURE RESULTING IN HDG DEV WHILE NO-GYROSCOPE.

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IFR TRAINING FLT WITH 2 STUDENTS. FIRST LEG AHN-CLT UNEVENTFUL. SECOND LEG CLT-CRE; DEPARTED CLT AND SHORTLY AFTER REACHING OUR CRUISING ALT; 5000 FT; VACUUM PUMP FAILED. WE RPTED LOSS OF DIRECTIONAL GYROSCOPE AND ATTITUDE INDICATOR TO CLT APCH. REQUESTED DIVERSION BACK TO OUR HOME BASE AHN AND PICKED UP THE NEW CLRNC FROM FLO APCH: DIRECT GRD; DIRECT AHN; 4000 FT. THIS NEW HDG AND ALT PUT US IN A BROKEN LAYER OF CUMULUS CLOUDS. I CONSIDERED DSNDING TO VFR CONDITIONS BUT MY STUDENT WAS DOING A GREAT JOB USING THE MAGNETIC COMPASS AS THE ONLY DIRECTIONAL INST AND TURN COORDINATOR TO KEEP THE WINGS LEVEL. HE STARTED REALIZING WHY WE HAD DONE ALL THE PARTIAL PANEL TRAINING. MY OTHER STUDENT WAS IN THE L BACK SEAT AND THE FLYING STUDENT POINTED OUT HOW HE HAD CTL INPUTS TO THE R TO MAKE THE PLANE GO STRAIGHT. WE WERE HANDED OVER TO SHAW APCH AND SHORTLY AFTER THAT MY STUDENT STARTED A SHALLOW L TURN. WE WERE IMC AND NEITHER ONE OF US NOTICED THE TURN. SUDDENLY WE WERE HDG 120 DEGS INSTEAD OF 210 DEGS. THE SIMILAR NUMBERS CONTRIBUTED TO OUR CONFUSION. WE WERE TRACKING DIRECT GRD AND THE OBSERVER NEEDLE SHOWED US L OF COURSE. I NOTICED OUR HDG ERROR AND HAD MY STUDENT TURN BACK ON COURSE. JUST THEN THE SHAW APCH CTLR CALLED AND ASKED OUR INTENTIONS. I ANSWERED HONESTLY THAT BECAUSE OF OUR VACUUM FAILURE WE HAD BEEN TEMPORARILY CONFUSED BUT WERE TURNING BACK ON COURSE. CTLR SAID YOU ARE NOT TO TURN AROUND AS YOU WISH IN MY AIRSPACE. TURN TO HDG 240 DEGS IMMEDIATELY. AFTER A FEW MINS SHE RETURNED AND ASKED WHAT A VACUUM FAILURE IS WHICH I EXPLAINED. SHE NEVER SPECIFIED WHETHER 240 DEGS WAS RADAR VECTORS OR SUGGESTED HDG. WE WERE ABOUT TO PASS THROUGH OUR COURSE TO THE N WHEN I ASKED WHETHER SHE WANTED US DIRECT GRD OR RADAR VECTORS. SHE ANSWERED: 2....4....0.... HDG MA'AM SHOULD TAKE YOU DIRECT GRD! THERE I WAS WITH 2 STUDENTS THAT I TEACH THAT ATC IS THERE TO HELP YOU AND NEVER HESITATE TO ASK IF YOU ARE NOT SURE WHERE THEY WANT YOU; OR WHAT THEY WANT YOU TO DO. WE DECIDED TO TRACK DIRECT GRD WHICH WAS APPROX 215 DEGS. I REALIZE MY ERROR: LETTING MY STUDENT GO TOO FAR OFF COURSE AND WE ALL LEARNED A LOT FROM THE EVENT.