PA28 INSTRUCTOR AND STUDENT PLT HAD AN NMAC WITH A C172 AFTER THE STUDENT PLT TURNED THE ACFT TO CIRCLE TO RWY 32. THEY WERE CLRED TO CIRCLE TO RWY 14R.

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ON A HDG OF 166 DEGS; MY STUDENT ARRIVED AT THE MDA FOR THE VOR-A. WE WERE INSTRUCTED BY TWR TO CIRCLE R FOR A R DOWNWIND FOR RWY 14R. THE VOR-A TAKES US OVER THE THRESHOLD OF RWY 14R. MOMENTS BEFORE WE ARRIVED OVER THE THRESHOLD; TWR CLRED A C172 FOR DEP ON RWY 14R. MY STUDENT; ALREADY INST RATED AND CURRENT; HAD REMOVED THE VIEW LIMITING DEVICE PRIOR TO THIS AND WAS CTLING THE ACFT WITH VISUAL REFS. UPON XING THE THRESHOLD OF RWY 14R; HE BEGAN TURNING SLIGHTLY TO THE L; ALIGNING THE ACFT WITH THE RWY CTRLINE. MY FIRST THOUGHT WAS THAT HE WAS POSITIONING US FOR A WIDER CIRCLING APCH. HE THEN BEGAN ANOTHER TURN TOWARD THE E. AT THAT POINT; I CHALLENGED HIS ACTIONS; STATING THAT HE SHOULD BEGIN A TURN R TO A WESTERLY HDG. HE WAS CONFUSED; BUT COMPLIED WITH MY REQUEST. THE TWR ASKED IF WE HAD THE DEPARTING TFC ON RWY 14R IN SIGHT. AT THAT PRECISE MOMENT; WE SAW THE C172 ABOVE US AND TO OUR L. WE ESSENTIALLY PASSED UNDERNEATH HIM GOING OPPOSITE DIRECTION. MY STUDENT WAS STILL CONFUSED AND AGAIN STARTED TURNING L TOWARDS THE E. I TOOK CTL OF THE PLANE AND TURNED BACK FOR A R DOWNWIND. WHEN I REITERATED THAT WE HAD BEEN CLRED FOR A R DOWNWIND FOR RWY 14R; HE CONFESSED THAT HE WAS THINKING RWY 32L THE ENTIRE TIME; WHICH EXPLAINS WHY HE WAS ATTEMPTING TO TURN EBOUND WHEN WE CROSSED THE THRESHOLD OF RWY 14R; RATHER THAN TURNING WBOUND. THE LNDG WAS UNEVENTFUL. SUPPLEMENTAL INFO FROM ACN 604175: AFTER FLYING 2 HRS UNDER THE HOOD; AND COMPLETING 5 APCHS AND HOLDING; I RETURNED TO MY HOME ARPT. I REQUESTED A VOR-A WITH A CIRCLE TO RWY 14. I WAS CLRED WITH A R DOWNWIND TO RWY 14R. THE HOOD WAS REMOVED ON SHORT FINAL. I SAW RWYS (PARALLELS) AND TURNED L FOR A R DOWNWIND; HOWEVER; I WAS DISORIENTED. I WAS ON R DOWNWIND FOR RWY 32. WHEN I REALIZED IT; I TURNED R ACROSS THE END OF RWY 32L&R AND TURNED TO R DOWNWIND FOR RWY 14R. A PLANE TAKING OFF FROM RWY 14R PASSED IN FRONT AND ABOVE ME. I SAW IT AND DIVERTED BELOW AND BEHIND. I COMPLETED THE APCH AND LANDED. I BELIEVE MY DISORIENTATION WAS CAUSED BY 2 HRS UNDER THE HOOD WITH 5 APCHS AND A HOLD IN QUICK SUCCESSION; IN A VERY BUSY CLASS B AIRSPACE. TOO MUCH ACTIVITY WITH NOT ENOUGH TIME TO PLAN. IN THE FUTURE; I WILL PLAN TO SPREAD MY RECURRENT TRAINING OVER SEVERAL FLTS.