C172 AND PA28 HAVE NMAC IN NON-TOWERED TRAFFIC PATTERN.

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I WAS AT ELKINS ARPT (EKN) WITH A PRIMARY STUDENT (POST SOLO) PRACTICING TOUCH-AND-GOES (L TFC RWY 32). I WAS ON ELKINS CTAF AND DEMONSTRATING PROPER UNCTLED FIELD RADIO TECHNIQUES. I WAS THE ONLY ACFT IN THE AREA (KNOWN; UNTIL THE EVENT). RWY 32 WAS IN USE; WINDS 330 DEGS AT 3 KTS; FEW CLOUDS AT 080. I WAS ON DOWNWIND; FROM A PREVIOUS TOUCH-AND-GO; AND MY STUDENT SAID 'LOOK; ANOTHER PLANE.' I LOOKED UP AND SLIGHTLY TO MY L; AND THERE WAS WHAT APPEARED TO BE A PIPER CHEROKEE APPROX 40 FT VERTICALLY ABOVE AND OVERTAKING ME. WE APPEARED TO BE A FEW SECONDS AWAY FROM A MIDAIR AS I WAS AT TPA AND HE APPEARED TO BE DSNDING TO TPA. AT THAT POINT IN TIME I TOOK THE FLT CTLS TO INPUT EVASIVE MANEUVERS. I PERFORMED A DSNDING L 360 DEG TURN. I DO NOT BELIEVE ACFT #2 SAW ME. ACFT #2 WAS NOT USING COMS; NOR DID IT APPEAR HE WAS MONITORING. AN AIM RECOMMENDED PATTERN ENTRY WAS NOT UTILIZED BY ACFT #2 NOR WAS FAA RIGHT-OF-WAY REGS. IT APPEARED TO ME ACFT #2 ENTERED THE TFC PATTERN DIRECTLY INTO DOWNWIND.