A C172 TRAINING FLT LANDS WITHOUT CLRNC WHEN ONLY CLRED FOR A LOW APCH AT ICT; KS.

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I WAS ON AN IFR XCOUNTRY WITH ONE OF MY INST STUDENTS. I AM A CFII WITH NEARLY 800 HRS. MY STUDENT IS A PVT PLT WITH LESS THAN 100 HRS. OUR ROUTING WAS FROM SLN-HUT-ICT-SLN DOING A PRACTICE APCH AT EACH ARPT. HUT WENT 'FIR' AND AFTER OUR DEP WE WERE GIVEN VECTORS TO INTERCEPT THE VOR/DME RWY 14 APCH INTO ICT. WE WERE THEN INSTRUCTED TO CIRCLE TO LAND ON RWY 19R; CLRED THE RWY 14 CIRCLING APCH AND CONTACT ICT TWR ON 118.2. UPON CONTACTING TWR WE WERE CLRED LOW APCH RWY 19R. I DID NOT HEAR THIS CLRNC; BUT MY STUDENT DID. MY STUDENT WAS UNSURE OF THE MEANING OF LOW APCH AND DID NOT ASK. BEFORE THE MISSED APCH POINT WE WERE INSTRUCTED TO MAKE SHORT APCH TO RWY 19R. I THEN ASKED IF I COULD GET TOUCH-AND-GO; TWR SAID 'UNABLE.' WE LANDED. I KNOW I SHOULD HAVE GOTTEN THE CLRNC THE FIRST TIME TO MAKE LOW APCH; BUT IN THE BUSY ENVIRONMENT OF ICT REPEATING IT WOULD HAVE BEEN VERY HELPFUL. SUPPLEMENTAL INFO FROM ACN 469579: BY BEING TOLD THIS I HAD BELIEVED THAT WE HAD BEEN CLRED TO LAND; BUT I WAS NOT 100% SURE. I BELIEVE THE CORRECTIVE ACTION TO MAKE SURE THAT THIS WILL NOT HAPPEN AGAIN IS TO ASK MY INSTRUCTOR IF I HAVE ANY QUESTIONS.