A CFI AND HIS STUDENT FLY AN INCORRECT APCH INTO RWY 27L AT OAK; CA.

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WHILE ON A TRAINING FLT TO OAK; WE FLEW A 'MODIFIED' GPS APCH TO RWY 27L AT OAK INSTEAD OF THE ILS RWY 27R; SIDESTEP RWY 27L AS WE WERE CLRED FOR. THE REASON FOR THIS WAS THAT WE (THE STUDENT AND I) FORGOT TO SELECT 'NAV' ON THE #1 OBS INSTEAD OF 'GPS.' WE HAD ENTERED THE GPS 27L APCH IN THE GPS (KING KLN89B) BUT HAD PLANNED TO USE VOR/ILS NAV THROUGHOUT THIS LEG OF THE FLT. HOWEVER; ATC CLRED US DIRECT TO SABLO INTXN AT ONE POINT; SO WE ENTERED IT INTO THE GPS AND SELECTED 'GPS' FOR THE #1 OBS. LATER WE RECEIVED VECTORS FOR THE ILS. I SET THE GPS ON THE MISSED APCH POINT AND THE STUDENT SELECTED 276 DEGS ON THE OBS. BOTH OF US THINKING THE ILS WAS SELECTED; IT WAS IN THE #1 NAV RADIO AND WE IDENTED IT; BUT FORGOT TO SELECT 'NAV' ON THE OBS. WHEN WE RECEIVED OUR FINAL VECTOR FOR THE ILS; THE NEEDLE (CDI) STARTED COMING IN WHEN EXPECTED; ALBEIT A LITTLE SLOW. WE DIDN'T RECEIVE THE GS; WHICH SHOULD HAVE CLUED ME IN; BUT SINCE RWY 27R WAS CLOSED AND WE WERE TO SIDESTEP ANYWAY; I TOLD THE STUDENT TO DO THE LOC ONLY APCH USING DME. WHEN WE BROKE OUT AT ABOUT 900 FT MSL; WE WERE LINED UP FOR RWY 27L. THAT IS WHEN I NOTICED THE 'GPS' SELECTED. AFTER SWITCHING IT SHOWED US ALMOST FULL SCALE L OF COURSE AND BELOW GS. AN UNEVENTFUL LNDG WAS MADE. ALTHOUGH WE WERE ON THE GPS COURSE; IT WAS STILL IN 'ARM' MODE; NOT 'ACTIVE' SO OUR SENSITIVITY WAS NOT GOOD ENOUGH FOR THE GPS APCH (HENCE MY USE OF 'MODIFIED' EARLIER). FACTORS INVOLVED: I HAVE BEEN CONDUCTING AND TEACHING GPS APCHS FOR ABOUT 3-4 YRS AND I VERIFY THE GPS BUTTON IS SELECTED. HOWEVER; WHEN NOT FLYING A GPS APCH; I HAVE NOT TAUGHT STUDENTS TO VERIFY 'NAV' IS SELECTED. THAT WILL CHANGE NOW. THE SLOW INTERCEPT AND LACK OF GS SHOULD HAVE ALERTED ME TO SOMETHING BEING AMISS. A RECENT FLT TO 2 OTHER ARPTS HAD NAVAIDS QUIT ON US; SO I ASSUMED THE GS OUT INDICATION WAS THE NAVAID PROB TOO QUICKLY -- NOT THE PLT PROB. CORRECTIVE ACTION: FUTURE APCHS USING A NON DEDICATED OBS WILL BE CONFIRMED IN THE PROPER 'NAV' OR 'GPS' MODE TO COINCIDE WITH THE APCH BEING FLOWN.