INSTRUCTOR GA SMA ON IFR CLRNC AND TRAINING MISUNDERSTOOD CLRNC FOR MANEUVER AS CLRNC FOR ALT CHANGE. DESCENT CAUSED LESS THAN STANDARD SEPARATION.

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I WAS GIVING A STUDENT AN INSTRUMENT FLT LESSON. WE ASKED AZO ATC FOR AN INSTRUMENT CLRNC FROM AZO TO KILBUR INTXN; THEN V100 TO ATHEN INTXN; THEN DIRECT TO LEROY INTXN. WE THEN INDICATED WE WOULD LIKE TO DO SOME INSTRUMENT MANEUVERS BEFORE BEING RADAR VECTORED TO AZO FOR A BACK COURSE 17 APCH AND FULL STOP LNDG AT AZO. AZO ATC GAVE US A TRANSPONDER CODE AND CLRED US AS REQUESTED; CLB AND MAINTAIN 4000' MSL. WE TOOK OFF; CLBED TO 4000' MSL; WENT TO KILBUR; ATHEN AND LEROY AS CLRED. ATC ASKED US IF WE WERE GOING TO BE DOING HOLDING PATTERNS. WE SAID; 'NO.' THEN WE ASKED AZO ATC FOR A 270 DEG HDG AND A CLRNC TO DO MANEUVERS. THEY SAID 270 DEG HDG AND MANEUVERS APPROVED. WE TURNED TO A HDG OF 270 DEGS; STILL AT 4000' MSL; AND STARTED A VERT S MANEUVER. WE BEGAN DSNDING TO 3000' IN VFR CONDITIONS. WHEN WE GOT TO 3300' MSL ATC TOLD US WE SHOULD BE AT 4000' MSL AND TO CLB TO 4000' MSL IMMEDIATELY AND TURN TO A HDG OF 180 DEGS. ATC TOLD US THERE WAS AN ACFT THAT DEPARTED BATTLE CREEK ARPT AND WE GOT TOO CLOSE. THEY INDICATED WE SHOULD HAVE BEEN HOLDING 4000' MSL; AND THAT WE WERE TOLD TO MAINTAIN 4000' MSL AT LEROY. IF HE TOLD US 4000' AT LEROY; MY STUDENT AND I BOTH MISSED IT. I ASSUMED BY BEING CLRED FOR MANEUVERS WE COULD CHANGE ALTS. AZO ATC OBVIOUSLY DID NOT. I CALLED THE TWR AFTER WE LANDED AND ATC SAID HE WOULD RPT THIS AS AN INCIDENT TO THE FAA. ATC TOOK MY NAME AND LICENSE #. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: RPTR COUNSELED AND DOES UNDERSTAND THAT WHEN ON IFR CLRNC THAT A CLRNC FOR MANEUVERS DOES NOT ALLOW ALT CHANGE UNLESS SPECIFICALLY REQUESTED AND GIVEN. MANEUVER DID RESULT IN LOSS OF STANDARD SEP TO BTWN 4-5 MI. INCIDENT WAS RPTED TO FSDO. THEY INVESTIGATED; BUT SAID NO ACTION; THE INCIDENT IS CLOSED.