INSTRUCTOR WITH SPI CROSSES ACTIVE RWY WITHOUT CLRNC.

Narrative

THE PROBLEM AROSE WHILE GIVING INSTRUCTION IN AN SMA DURING THE TAXIING PHASE. WHILE DRIVING TO THE ARPT I THOUGHT I SAW SEVERAL AIRPLANES TKOF ON RWY 19. WHILE IN THE AIRPLANE; I HAD ALLOWED MYSELF TO BECOME TOO ENGROSSED WITH TEACHING THE STUDENT HOW TO TAXI THE AIRPLANE. I HEARD THE CTLR'S TAXI CLRNC WHICH TOLD ME TO TAXI TO RWY 32. HOWEVER; I UNCONSCIOUSLY FOLLOWED THE TAXIWAYS WHICH LED TO RWY 19. THIS HAD ME XING THE ACTIVE RWY (19) WHILE TFC (ANOTHER SINGLE ENG LOW WING ACFT) WAS TAKING OFF. I HAD DISCOVERED THE PROBLEM WHEN I SAW THE TFC TAKING OFF AND BECOMING AIRBORNE ABOUT 200-300 FT TO MY L; IT PASSED OVERHEAD BY APPROX 150 FT. WHEN I SAW THE ACFT; I TAXIED AS QUICKLY AS POSSIBLE ACROSS THE ACTIVE RWY. I DIDN'T PAY ATTN TO THE CTLR'S AUTHORIZATION/INSTRUCTIONS AND I LET MYSELF CONCENTRATE TOO MUCH ON THE STUDENT'S PERFORMANCE. I ALLOWED MYSELF TO AUTOMATICALLY RESPOND TO MY BELIEF OF WHAT I THOUGHT WAS THE ACTIVE RWY. BEING FAMILIAR WITH THE ARPT I BECAME COMPLACENT AND DID NOT GIVE THE SITUATION THE RESPECT OR ATTN IT DESERVED. I COULD HAVE AVOIDED THIS SITUATION BY BEING MORE ALERT AND BY SIMPLY WRITING DOWN THE CLRNC OR TAXI INSTRUCTIONS ON A NOTE PAD.