C152 FLT CREW LANDS WITHOUT LNDG CLRNC AT BTR.

Narrative

I WAS PROVIDING XCOUNTRY TRAINING TO MY STUDENT PLT. UPON ARR AT BTR; THERE WERE APPROX 4 ACFT IN THE TFC PATTERN TO RWY 4R AND SEVERAL AIRLINERS INBOUND FOR RWY 4L. THE CTLR HAD US ENTER A R BASE FOR RWY 4R BTWN 2 ACFT; ONE ON FINAL AND ONE ON DOWNWIND. WE WERE APPROX 1 MI BEHIND THE LNDG ACFT WHILE THE ACFT BEHIND US HAD TO MAKE A SIDE STEP MANEUVER FOR SPACING. WE REQUESTED A TOUCH AND GO AND WERE CLRED #2 BEHIND THE LNDG ACFT. THE LNDG ACFT MADE A SLOW APCH AND THEN DELAYED EXITING THE RWY. WE CROSSED THE THRESHOLD AT ABOUT 150 FT AGL AND THE ACFT HAD NOT CLRED THE RWY. THE TWR HAD NOT CALLED FOR A GAR. I ESTIMATED WE HAD AT LEAST 3000 FT FROM THE ACFT IN FRONT OF US. WHILE PREPARING TO GO AROUND; THE ACFT CLRED THE RWY. WE EXECUTED AN UNEVENTFUL TOUCH AND GO. AFTER CLBOUT I ASKED THE STUDENT IF HE REMEMBERED THE TWR EVER SAYING 'CLRED FOR TOUCH AND GO.' THE STUDENT REPLIED 'NO.' I DID NOT REMEMBER EITHER. THE CTLR WAS EXTREMELY BUSY. WE WERE BUSY TRYING TO MANAGE OUR SPACING. THE RADIO WAS VERY CONGESTED BUT WE STILL SHOULD HAVE CALLED TWR TO CONFIRM OUR LNDG CLRNC.