NMAC BTWN A CESSNA 172 TRAINING FLT DSNDING FROM 7500 FT AND A TWIN ENG ACFT IN LEVEL FLT.

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MY STUDENT AND I WERE DSNDING FROM 7500 FT TO 6500 FT. DURING THE DSCNT WE WERE DOING 'S' TURN MANEUVERS TO CLR FOR TFC. OUR DSCNT RATE WAS APPROX 500 FPM. I WAS SCANNING MOSTLY OUT THE FRONT AND R SIDE OF THE PLANE FOR TFC WHILE MY STUDENT WAS LOOKING MOSTLY OUT THE FRONT L SIDE OF THE PLANE. WHILE I WAS LOOKING OUT ACROSS THE FRONT WINDSHIELD I SAW THE OTHER PLANE OUT THE CORNER OF MY EYE IN THE BOTTOM L CORNER OF THE WINDSHIELD. I THEN PULLED BACK ON THE CTLS ABRUPTLY TO AVOID THE OTHER AIRPLANE. THE OTHER ACFT APPEARED TO MAKE NO DEV. WHEN I GOT BACK ON THE GND A CO-WORKER TOLD ME THAT HE HEARD THE OTHER AIRPLANE RECEIVING TA'S WITH KALAMAZOO (AZO) APCH. HOWEVER; THE CTLR DID NOT TELL THE PLT OF THE OTHER AIRPLANE ABOUT MY ACFT ACCORDING TO MY WITNESS. THIS IS INCONSEQUENTIAL; HOWEVER; as IT IS STILL THE PLT'S JOB TO SEE AND AVOID OTHER TFC. I THINK THAT WHAT CAN BE DONE TO PREVENT ANOTHER SIT LIKE THIS WOULD BE TO SCAN MORE FOR TFC COMING FROM CONVERGING AND OVERTAKING ANGLES. ALSO; IF MY STUDENT IS LOOKING OUT THE FRONT OF THE PLANE; IT MAY BE MORE BENEFICIAL FOR ME TO LOOK MORE TO THE SIDES AND BEHIND; BENEATH; AND ABOVE THE PLANE.