PLT ENTERS CLASS B AIRSPACE WITHOUT A CLRNC.

Narrative

I WORK AS A NEW CFI AT TAMIAMI (TMB) ARPT. IT WAS MY 3RD DAY OF WORK; WHEN I ASKED TO GO ALONG WITH A LCL PLT TO PICK UP A SECOND ACFT AT MERRIT ISLAND ARPT (COI). MY JOB WAS TO BRING THE FBO'S ACFT BACK TO BASE IN TMB; WHILE I LEFT THIS PLT AT COI WITH THE OTHER ACFT. WE TOOK OFF FROM TMB AT APPROX XA30 HDG NW. THE LCL PLT WAS PIC FLYING THE ACFT ON TKOF AND CLB (HE WAS ALSO SITTING IN THE L SEAT). HE USED RWY 31 FOR TKOF AND CONTINUED ON A CLB MAKING SMALL HDG CHANGES. BEING A LCL PLT; I TRUSTED THAT HE KNEW THE MIAMI CLASS B AIRSPACE WELL; AND THAT HE KNEW WHAT HE WAS DOING. AFTER A CLB THROUGH 3000 FT WITHOUT CHANGING FREQ FROM TMB TWR TO MIA APCH; I STARTED TO PAY MORE ATTN TO WHERE WE WERE BY LOOKING AT MY SECTIONAL CHART. A LITTLE AFTER; AT APPROX 4500 FT; THE L SEAT PLT FINALLY CONTACTED MIA APCH SAYING THAT HE WAS 20 MI W OF MIA (WHICH WOULD PLACE HIM ON THE W BORDER OF THE CLASS B AIRSPACE). MIA APCH SAID THAT HE WAS AT 18 W OF THE MIA ARPT AND THAT HE HAD ENTERED THE AIRSPACE WITHOUT A CLRNC. MIA APCH TOLD HIM THAT HE SHOULD BE 'MORE CAREFUL NEXT TIME.' THEY REPEATED THIS STATEMENT APPROX 2-3 TIMES. THE REST OF THE FLT WAS UNEVENTFUL.