A RPTING HIGH WING ACFT HAD AN NMAC WITH A NON RPTING LOW WING PIPER THAT APPARENTLY WAS FLYING TO THE WRONG RWY AT DPA.

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WE WERE INBOUND ON THE ILS 1L APCH AND WERE JUST HANDED OFF TO TWR. NUMEROUS ACFT WERE IN THE VICINITY OF THE ARPT. TWR SEEMED TO BE KEEPING ACFT THAT WERE DOING TOUCH-AND-GOES ON RWY 10 WHILE INBOUND ACFT WERE UTILIZING RWY 1L AND RWY 1R. WE HAD JUST PASSED THE OM INBOUND AND HAD CONTACTED TWR WHEN WE WERE CLRED TO LAND ON RWY 1L. TWR ALSO CLRED AN ACFT TO LAND ON RWY 1R. MY ATTN WAS INSIDE THE COCKPIT AS I WAS EXPLAINING HOW TO FLY THE ILS TO A STUDENT. AS A RESULT; I DID NOT PERFORM MY DUTY OF LOOKING OUTSIDE FOR TFC AS WELL AS I SHOULD HAVE. I LOOKED UP TO SEE A LOW WING PIPER SINGLE ENG PASSING JUST IN FRONT AND ABOVE THE R WING. HE HAD BEEN IN OUR BLIND SPOT DUE TO WING PLACEMENT AND I DID NOT SEE HIM UNTIL HE CAME INTO VIEW IN FRONT OF THE ACFT. THE TWR CHIEF CAME ON FREQ AND TOLD US TO BREAK OFF THE APCH AND LAND ON RWY 1R. EVIDENTLY THE OTHER PLT MISTOOK RWY 1L FOR RWY 1R. BETTER VIGILANCE ON THE OTHER PLT AND MYSELF COULD HAVE PREVENTED THIS INCIDENT. IN THE FUTURE; I WILL SPEND MORE TIME LOOKING OUTSIDE FOR TFC ON IFR FLTS IN VFR CONDITIONS AS NOTHING SUBSTITUTES FOR SEE AND AVOID.