C172SP INSTRUCTOR HAS AN NMAC VICINITY OF BJC.

Narrative

WHILE INBOUND FROM THE N TO JEFFERSON COUNTY ARPT; MYSELF AND MY STUDENT (A STUDENT PLT) WERE COMING BACK IN FROM THE PRACTICE AREA FOR A FULL STOP LNDG IN A CESSNA SKYHAWK 172SP; WITH A G-1000 AVIONICS PACKAGE; INCLUDING A TIS SYS. WE ENCOUNTERED AN NMAC HEAD-ON WITH A LOW WING SINGLE ENG AIRPLANE APPROX 3 MI NW OF BJC. WHILE INBOUND WE CONTACTED TWR APPROX 11 MI OUT. TWR TOLD US TO ENTER A R DOWNWIND FOR RWY 29R AND TO RPT ON THE MIDFIELD DOWNWIND. WE READ BACK THE CLRNC. APPROX 2 MINS LATER TWR CAME ON AGAIN AND TOLD US THE WINDS HAD CHANGED; AND THEY WERE IN THE PROCESS OF A RWY CHANGE; AND TO ENTER A L BASE FOR RWY 11L. WE CHANGED COURSE AND BEGAN TO SET OURSELVES UP FOR A BASE TO RWY 11R. WHILE THIS WAS HAPPENING; TWR WAS TRYING TO REACH THE LOW WING ACFT THAT HAD JUST DEPARTED RWY 29. I BELIEVE THEY ATTEMPTED ABOUT 4 SEPARATE TIMES TO ESTABLISH RADIO CONTACT WITH THIS ACFT. THERE WAS NO RESPONSE BACK FROM THE ACFT TO TWR. I TOLD MY STUDENT THAT THIS IS WHY YOU MUST ALWAYS LISTEN WHILE IN THE CLOSE VICINITY OF AN ARPT. WHILE ON ABOUT A 3 MI L BASE FOR RWY 11L OVER THE GND RPTING POINT 'STORAGE TECH;' WE WERE ABOUT TO RPT THAT WE WERE ON THE 3 MI L BASE; WHEN TWR CAME ON AND SAID 'TFC ALERT; 12 O'CLOCK POS SAME ALT OPPOSITE DIRECTION!' AT THAT EXACT MOMENT OUR TFC ALERT SYS ANNOUNCED; 'TFC.' WE WERE CURRENTLY RANGED OUT ON OUR MFD SCREEN AND COULD NOT DIFFERENTIATE ONE PLANE FROM THE OTHER ON THE TIS BESIDES FOR THE YELLOW COLORED ICON REPRESENTING THE HEAD-ON AIRPLANE. I TOOK CTL OF THE ACFT AND PULLED UP ON THE CTLS AND BEGAN A R TURN WHEN MY STUDENT SAID; 'THERE IT IS.' I LOOKED UNDER US AND SAW THE TAIL OF THE ACFT ZIP UNDER US. I RPTED 'TFC IN SIGHT; IT JUST PASSED UNDER US.' THE TIS SYS RPTED THAT THE ACFT WAS AT 00 FT ALT DIFFERENCE FROM OUR AIRPLANE. I WOULD GUESS THAT THE ACFT PASSED UNDER US APPROX 50-75 FT. TWR TRIED ONE MORE TIME TO GET A HOLD OF THE LOW WING AIRPLANE; AND HE FINALLY RESPONDED WITH HIS TAIL NUMBER. TWR THEN HARSHLY TOLD THE OTHER PLT THAT HE (TWR) HAD TRIED TO CONTACT HIM SEVERAL TIMES; AND HAD NEVER GIVEN HIM CLRNC TO TURN N; AND THAT HE NEEDED TO PAY MUCH CLOSER ATTN WHILE IN CLASS D AIRSPACE.