C172 PLT INSTRUCTOR; WITH STUDENT FLYING; ON A XCOUNTRY; DSNDED IN TO TFC PATTERN AT MCI BEFORE INSTRUCTED TO DO SO BY TWR IN CLASS B AIRSPACE.

Narrative

I WAS ON A VFR XCOUNTRY TRAINING FLT FROM 9K4 TO MCI AT XA3O. BEFORE ENTERING KANSAS CITY'S CLASS B AIRSPACE; I HAD MY STUDENT CALL KANSAS CITY APCH TO GET CLRNC INTO CLASS B. KANSAS CITY APCH RESPONDED; 'CLRED INTO CLASS B AT 4500 FT' AND GAVE A SQUAWK CODE. ABOUT 5 OR 10 MINS LATER; THE APCH CTLR CAME OVER FREQ AND TOLD US; 'EXPECT TO CROSS MID FIELD; ENTER A R DOWNWIND LNDG RWY 19R.' WE RESPONDED BY READING BACK THE CLRNC. ABOUT 5 MINS LATER THE APCH CTLR ASKED US IF WE HAD THE FIELD IN SIGHT. AFTER RESPONDING WE HAD THE ARPT IN SIGHT; THE APCH CTLR CAME BACK AND SAID; 'RESUME YOUR OWN NAV AND CONTACT THE TWR.' WE RESPONDED WITH OUR READBACK AND SWITCHED TO TWR. WE THEN BEGAN OUR DSCNT DOWN TO TFC PATTERN ALT. I INTERPED THE CLRNC 'RESUME YOUR OWN NAV' AS ME BEING RESPONSIBLE TO CROSS MID FIELD AND ENTER THE R DOWNWIND AT TFC PATTERN ALT. UPON REACHING TFC PATTERN ALT; THE TWR CTLR CAME OVER FREQ AND ASKED; 'SAY ALT?' WE RESPONDED BY SAYING WE WERE AT TFC PATTERN ALT. THE CTLR THEN RESPONDED THAT HE THOUGHT WE WERE AT A HIGHER ALT. THERE WAS NO TFC CONFLICT OR ANY OTHER DANGER BROUGHT ABOUT BY OUR DSCNT. IT WAS SIMPLY A MISUNDERSTANDING OF WHAT THE TERM 'RESUME YOUR OWN NAV' MEANT. I UNDERSTOOD THE PHRASE AS BEING RESPONSIBLE FOR LATERAL NAV AND ALSO VERT NAV TO PUT MY PLANE IN A POS TO ENTER A R DOWNWIND AT THE TFC PATTERN ALT. IN ORDER TO CORRECT THE PROB; I THINK THERE COULD HAVE BEEN MORE CLARITY WITHIN THE CLRNC AS TO WHETHER OR NOT TO MAINTAIN ALT. I ALSO SHOULD HAVE QUERIED THE CTLR AS TO WHETHER OR NOT A DSCNT COULD BE STARTED. THANKFULLY; HOWEVER; OUR DSCNT TO TFC PATTERN ALT DID NOT CAUSE ANY PROBS.