SMA ACFT ON TRAINING FLT AND IN TFC PATTERN TURNED DOWNWIND AS CLRED BY THE TWR FOR CLOSED PATTERN. RPTR INSTRUCTOR HEARD A CESSNA TAKING OFF BEHIND HIS ACFT RECEIVE THE SAME CLRNC. CESSNA TURNED INSIDE RPTR ACFT AND WAS ON A COLLISION COURSE WHEN TWR INTERVENED TO ALERT OTHER PLT OF RPTR ACFT.

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MY STUDENT AND I WERE EXECUTING TOUCH-AND-GOES AT WHITEMAN ARPT. AFTER 1 SUCH TOUCH-AND-GO WE WERE CLBING OUT ON THE UPWIND LEG WHEN I HEARD THE CTL TWR CLR A CESSNA FOR TKOF WITH APPROVAL FOR A L CLOSED TFC PATTERN (SAME AS US). AFTER REACHING 500 FT ABOVE THE ARPT ALT; WE TURNED L FOR OUR XWIND LEG AND CONTINUED OUR CLB TO PATTERN ALT (2000 FT). BEFORE TURNING L AGAIN FOR OUR DOWNWIND LEG WE LOOKED TO OUR R FOR TFC; AND THEN L FOR TFC AND TO JUDGE OUR TURN IN REF TO THE RWY. AS MY STUDENT BEGAN HIS TURN L ONTO THE DOWNWIND; I KEPT LOOKING TOWARDS THE RWY IN ORDER TO JUDGE MY STUDENT'S PROPER ROLLOUT ONTO THE DOWNWIND; WHILE SIMULTANEOUSLY LEVELING THE AIRPLANE AT PATTERN ALT. THIS IS WHEN I COULD SEE SOME MOVEMENT OFF TO MY L COMING UP TOWARDS OUR ACFT. AS I FOCUSED ON THE OBJECT I COULD SEE IT WAS A CESSNA SINGLE ENG HIGH WING AIRPLANE. JUST BEFORE I COULD MAKE A CALL TO QUESTION THE TWR AND THE OTHER AIRPLANE; THE TWR ASKED THE CESSNA IF THEY HAD OUR ACFT IN SIGHT; WHICH REPLIED 'NEGATIVE; UH...OH; OH.' THE TWR THEN CALLED ME; MUTTERED SOMETHING; AND I IMMEDIATELY ASKED FOR A R 360 DEG TURN WHILE EXECUTING IT; AND LET THE CESSNA FLY PAST US. CONTRIBUTING FACTORS: IN MY OPINION; THE TWR SHOULD HAVE ASKED THE CESSNA IF IT HAD US IN SIGHT BEFORE CLRING IT FOR CLOSED TFC IMMEDIATELY FOLLOWING OUR TOUCH-AND-GO. ALSO; THE PLT OF THE CESSNA CUT THE TFC PATTERN; ON THE UPWIND; SHORT; WHICH HAD THE AIRPLANE COMING UP AT US ON ITS XWIND LEG. I SHOULD HAVE BEEN WATCHING FOR THE CESSNA AS SOON AS IT WAS CLRED FOR TKOF AND CLOSED TFC WITH US.