NMAC BTWN 2 SMAS IN DEV FROM STANDARD TFC PATTERN PROC.

Narrative

MY STUDENT AND I ENTERED A L XWIND FOR RWY 24 PAYSON WHICH UNICOM INFORMED US TO BE THE ACTIVE RWY. I HEARD A PLANE CALL 'READY FOR TKOF; STRAIGHT OUT DEP'. (I DID NOT HEAR HIS N NUMBER OR ACFT TYPE.) JUST AS WE TURNED TO DOWNWIND; WE WERE AT PATTERN ALT (6200 FT) JUST SHORT OF MIDFIELD WHEN MY STUDENT SUDDENLY JERKED THE PLANE UP AND TO THE R. HE TOLD ME HE WAS SORRY FOR DOING THAT BUT HE HAD JUST MISSED AN AIRPLANE COMING UP FROM IN FRONT AND TO THE L. I TURNED AROUND TO SEE WHAT APPEARED TO BE AN SMA Y FILLING THE BACK WIND SCREEN. I RPTED OVER 122.8 (CTAF) THAT WE HAD JUST HAD A NEAR MISS WITH AN SMA Y THAT I NEVER HEARD GIVE A POS RPT. A VOICE CAME OVER THE RADIO STATING 'I HAVE BEEN GIVING POS RPTS AND THAT YOU HAD BETTER WATCH OUT WHERE YOU'RE GOING'. I AM NOT SURE IF THIS WAS THE ACFT WHO CALLED STRAIGHT DEP AS WE TURNED DOWNWIND. WE CALLED DOWNWIND AS WE TURNED FROM XWIND TO DOWNWIND. WE WERE AT RECOMMENDED PATTERN ALT APPROX 3/4 MI FROM THE RWY. THE PLANE WAS ON MY BLIND SIDE. I HAD NO WAY OF SEEING IT. THANKFULLY MY STUDENT DID AND REACTED PROMPTLY AND CORRECTLY. I DO NOT KNOW WHAT HE WAS DOING FLYING THE OPPOSITE DOWNWIND OR DEPARTING TO THE L AT MIDFIELD INTO OPPOSING TFC. THE ONLY THING I COULD HAVE DONE (AND WILL DO FROM NOW ON) IS TO REALLY CHK MY BLIND SIDE MORE OFTEN AT ALL TIMES. I FEEL THAT WE ENTERED THE TFC PATTERN CORRECTLY AT THE PROPER ALTS AND DISTANCES AND MADE THE PROPER CALLS.