CTLR TRAINING IN PROGRESS. ACR Y TCASII RA HAD LTSS FROM SMT X. EVASIVE ACTION TAKEN. SYS ERROR.

Narrative

I WAS TRAINING A DEVELOPMENTAL CTLR ON DALLAS S POS AT DFW. MY TRAINEE HAD BEEN DOING WELL AND WAS CLOSE TO CHKING OUT ON THE 3 E SATELLITE POS. HOWEVER; MOST OF HIS EXPERIENCE WAS IN A S FLOW AND DFW WAS IN A N FLOW. WE HAD STEADY ARRS OF TURBOPROP AND TURBOJET ACFT FOR RWY 31R. HE TOOK A HDOF ON A VFR SMT X AT 3500 FT FROM OVER DFW; EBOUND. THIS RTE OF FLT WAS OPPOSITE DIRECTION WITH THE RWY 31R ARRS. HOWEVER; IT IS A COMMON OCCURRENCE. I HAD INCORRECTLY ASSUMED THAT MY TRAINEE WOULD HANDLE THE SIT CORRECTLY SINCE IT APPEARED THAT HE KNEW WHAT HE WAS DOING. SMT X WAS NOT PUT ON A GOOD HDG AND I GOT DISTRACTED WITH THE RWY 31R FINAL. ACR Y GOT A LATE DSCNT ON FINAL AND SMT X PASSED OFF OF HIS L WITHOUT TFC BEING ISSUED. WE HAD DIVERGING COURSES BUT IT WAS A SLOPPY OP. ACR Y INITIATED HIS OWN CLB (TCASII EQUIPPED) BECAUSE OF AN RA. WHAT CAUSED THE PROB: 1) TRAINEE UNFAMILIAR WITH N FLOW AIRSPACE AND PROCS BECAUSE THERE WAS SO LITTLE N FLOW DURING THE SUMMER. 2) THE TRAINER (MYSELF) THOUGHT THAT THE TRAINEE WAS SMARTER THAN HE ACTUALLY IS. 3) I THINK THAT THE TRAINEE HAD A BAD WKEND. 4) I LET THE TRAINEE GO TOO FAR BECAUSE I DIDN'T WANT TO HURT HIS FEELINGS (TELL HIM WHAT TO DO).