NMAC BTWN A STUDENT PLT ON 2ND SOLO IN A C172 TURNING L BASE LEG FOR LNDG AND A PRIVATELY OPERATED C182 TURNING A R BASE LEG FOR LNDG AT AN UNCTLED ARPT. THE C182 PLT MADE AN EVASIVE ACTION 360 DEG TURN TO AVOID THE STUDENT'S C172. THE STUDENT NEVER DID SEE THE C182 SINCE IT TURNED IN BEHIND HIM.

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MY STUDENT; IN C172; AND I HAD BEEN CONDUCTING TKOFS AND LNDGS AT 1G5 IN PREPARATION FOR HIS 2ND SOLO FLT. HE COMPLETED 3 LNDGS AND TKOFS FOR ME TO MY SATISFACTION AND I LEFT THE PLANE TO WATCH HIM SOLO. I STOOD ALONGSIDE RWY 27 (THE ACTIVE) WITH MY HAND HELD RADIO TO MONITOR HIM. PLT TOOK OFF AND COMPLETED 1 LNDG; SO I SENT HIM FOR HIS SECOND AND THIRD LNDGS (SOLO). ON HIS THIRD LNDG; HE WAS ON BASE LEG; JUST GETTING READY TO TURN FINAL; WHEN ANOTHER ACFT (C182) CAME INTO THE PATTERN ON A R BASE (NON STANDARD). THE SKYLANE TOOK EVASIVE ACTION BY COMPLETING A L HAND 360 DEG TURN ON FINAL; AND TO MY VIEW NARROWLY MISSING MY STUDENT (C172). BOTH ACFT LANDED AND I TOOK A PHOTO OF THE C182 AS IT LANDED. MY STUDENT TOLD ME HE NEVER SAW THE OTHER ACFT. I NEVER HEARD THE OTHER ACFT MAKE ANY RADIO ANNOUNCEMENTS AS TO POS; AS I WAS MONITORING ON HAND HELD RADIO. PREVENTION: ALL MUST BE ALERT IN TFC PATTERN FOR OTHER ACFT. NON STANDARD ENTRIES AND OP IN PATTERN ARE PROHIBITED OR AT LEAST DISCOURAGED. RADIO CALLS AS POS ANNOUNCEMENTS MANDATORY.