TRAINING SMA SEL UNAUTH XING OF AN ACTIVE RWY DURING TAXI FOR TKOF.

Narrative

AFTER ENG START; WE (MY STUDENT AND I) RECEIVED CLRNC TO TAXI FROM FBO TO RWY 9R VIA TXWY CHARLIE AND DO OUR RUN- UP ON CHARLIE PRIOR TO TXWY ALPHA. IN AN EFFORT TO SAVE TIME FOR THE LONG TAXI; I ASSUMED TAXI RESPONSIBILITY WHILE I INSTRUCTED STUDENT PLT (WITH LESS THAN 8 HRS) TO FOLLOW THE CHKLIST. WHEN OUR TAXI CLRNC WAS ISSUED; RWY 4 WAS NOT ACTIVE. THE STUDENT INADVERTENTLY SWITCHED TO TWR FREQ WHILE DOING THE CHKLIST. BECAUSE I WAS FOCUSED ON THE TAXI; I FAILED TO REALIZE THE CHANGE IN FREQ. AT THIS TIME WE HAD CROSSED RWY 4. I IMMEDIATELY SWITCHED TO GND AND DISCOVERED THEY HAD TRIED TO CONTACT ME TO HOLD SHORT RWY 4. WE MISSED GND CTL'S VERBAL AND LIGHT GUN SIGNALS TO STOP. AFTER A STERN REQUEST FROM GND CTL TO 'LISTEN UP;' I APOLOGIZED AND VERIFIED IF DAMAGE WAS DONE? THIS PROB COULD HAVE BEEN AVOIDED IF I HAD NOT BECOME SO ENGROSSED IN TAXIING TO SAVE TIME. I DIDN'T MONITOR MY STUDENT BECAUSE HE AS (I ASSUMED) ALERT AND CAUTIOUS. THE MORAL BEING DON'T TAKE YOUR STUDENT FOR GRANTED. MONITOR THEIR PROCS AND CORRECT ERRORS. IN THIS CASE; NO OUTRIGHT DAMAGE WAS DONE; HOWEVER; BY TRYING TO SAVE TIME; GREATER DAMAGE COULD RESULT. THEREFORE NO SHORT-CUTS. ALSO UPON XING RWY 4; I VISUALLY CLRED THE RWY; EVEN THOUGH FINAL WAS CLR IT WAS NONE-THE-LESS AN ACTIVE RWY. AS AN INSTRUCTOR I'M RESPONSIBLE FOR MANY ACTS; BY WORKING OUTSIDE THE STANDARD PROCS AN ERROR WAS MADE. THEREFORE MY RECOMMENDATION: BE VIGILANT AND AWARE OF THE SURROUNDING AND FOLLOW PROCS.