AN SMA FLYING FOR INST INSTRUCTION ASSUMES CLRNC TO DSND; AND DSNDS 500 FT BELOW ASSIGNED ALT. ZME WAS CTLING AT THE TIME.

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WHILE ACTING AS FLT INSTRUCTOR; OUR ACFT WAS EXECUTING A PRACTICE ILS RWY 29 APCH TO MSL; AL; ARPT. ZME CLRED ACFT TO INTERCEPT LOC. WE MISTAKENLY ASSUMED THAT WE WERE CLRED TO THE NEXT STEPDOWN ALT RATHER THAN MAINTAIN PREVIOUSLY ASSIGNED 3000 FT. CTLR QUESTIONED OUR MODE C READOUT AT WHICH TIME WE WERE APPROX 500 FT BELOW ASSIGNED ALT. WE WERE THEN CLRED FOR THE APCH. WX WAS CLR WITH APPROX 20 MI VISIBILITY. CTR SEEMED TO BE VERY RELAXED IN THEIR INSTRUCTIONS REGARDING OUR TRAINING REQUEST. SPECIFICALLY; GIVEN CLRNC TO ENTER HOLDING AT OAKLA 'LET US KNOW WHEN YOU GET READY TO DO SOMETHING ELSE.' IE; NO EFC TIME. ALSO; 'CLRED FOR VOR APCH.' WE EXECUTED THE VOR 29 APCH WHICH WAS CONSISTENT WITH OUR EARLIER REQUEST. CTR WAS UNDER THE IMPRESSION WE WERE EXECUTING THE RWY 11 APCH. SUPPLEMENTAL INFO FROM ACN 383080: WE INADVERTENTLY FELT WE WERE CLRED FOR APCH AND PROCEEDED TO NEXT STEPDOWN ALT RATHER THAN EARLIER ALT ASSIGNED OF 3000 FT. ZME QUESTIONED OUR MODE C DISPLAY AT WHICH TIME WE WERE AT 2500 FT OR 500 FT OFF ALT.