STUDENT PLT FAILED TO LEVEL OFF AT INITIAL DEP ALT RESULTING IN PENETRATING CLASS C AIRSPACE.

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ON JAN/SAT/95; I WAS FLYING WITH A STUDENT AND WE INADVERTENTLY CLBED ABOVE A RESTR ALT IN CLASS C AIRSPACE. MY STUDENT AND I DEPARTED RDU ARPT FOR PERSON COUNTY ARPT. WE OBTAINED A VFR CLRNC FOR THE CLASS C AIRSPACE THAT INCLUDED A HDG TO TURN TO; AFTER TKOF; AND AN ALT RESTR OF 'AT OR BELOW 2000 FT.' IT IS IMPORTANT TO UNDERSTAND THAT THE STUDENT WAS ALMOST READY FOR HIS PVT PLT FLT TEST AND THAT TO MAKE SURE THAT HE WAS READY I WANTED TO SAY THE LEAST POSSIBLE. IN OTHER WORDS; I WANTED TO LET HIM MAKE HIS OWN MISTAKES WITHOUT ME HELPING HIM OUT. AFTER TKOF; TWR USUALLY HANDS US OFF TO DEP BEFORE WE REACH 2000 FT; BUT IN THIS CASE THEY DID NOT; AND WE APCHED 2000 FT. I WAS PAYING ATTN; BUT WANTED TO SEE IF MY STUDENT LEVELED OFF WITHOUT GOING ABOVE 2000 FT. HE STARTED TO DO SO; AND I WAS VERY PLEASED. I THEN SUGGESTED THAT HE COULD REQUEST FREQ CHANGE AS A WAY TO REMIND THE TWR THAT WE WERE STILL WITH THEM. HE DID SO. AT THAT POINT I GOT DISTRACTED WATCHING TFC; AND THEN IT HAPPENED. WHILE MY STUDENT GOT THE FREQ CHANGE; AND CHANGED TO DEP; HE LET HIS ALT INCREASE. WHEN HE SWITCHED TO DEP THEY WERE BUSY; SO HE DID NOT CALL RIGHT AWAY; AND THEY ACTUALLY CALLED HIM AND ASKED 'WHAT IS YOUR ALT?' BY THE TONE OF THE CTLR'S VOICE I REALIZED THAT SOMETHING WAS WRONG; AND AS I LOOKED AT THE ALTIMETER (FROM KEEPING AN EYE ON THE TFC); MY STUDENT REPLIED 2500 FT.