NMAC BTWN 2 C172'S IN THE TFC PATTERN AT HYR; WI.

Narrative

I WAS ON A DUAL XCOUNTRY FLT WITH A STUDENT PLT APCHING FOR LNDG AT HYR. WE WERE APCHING FROM THE S AND THE WIND WAS OUT OF THE ENE FAVORING RWY 2. THE STUDENT ELECTED TO ENTER THE TFC PATTERN ON THE UPWIND LEG RATHER THAN FLY A STRAIGHT-IN APCH. THE STUDENT RPTED EACH LEG OF THE PATTERN OVER THE CTAF. WHILE ON XWIND FOR RWY 2; WE HEARD A PIREP CIRCLING AT 2200 FT (TFC PATTERN ALT) SLIGHTLY E OF THE CITY OF HAYWARD. THE STUDENT AND I STARTED LOOKING FOR THE CONFLICTING TFC. WE SPOTTED THE OTHER ACFT AFTER TURNING ONTO DOWNWIND; HE WAS CIRCLING AROUND A SMALL BRUSH FIRE AT PATTERN ALT NEAR THE POINT WHERE ONE WOULD NORMALLY TURN FROM DOWNWIND TO BASE. THE STUDENT STARTED A DSCNT BELOW PATTERN ALT. I DID NOT PERCEIVE OUR DSCNT GOING FAST ENOUGH; SO I MADE AN ADDITIONAL PWR REDUCTION AND APPLIED MORE FORWARD PRESSURE ON THE YOKE TO SPD UP OUR DSCNT. WE PASSED BENEATH THE CIRCLING ACFT BY ABOUT 250 FT. HAD I NOT BEEN PREOCCUPIED WITH ENSURING THAT WE AVOIDED A MIDAIR; I WOULD HAVE TALKED TO THE OTHER PLT ABOUT HIS CHOICE OF ALT (POOR JUDGEMENT ON HIS PART). THIS IS A CASE WHERE FLYING A STRAIGHT-IN APCH TO RWY 2 WOULD LIKELY HAVE AVOIDED AN NMAC.