As I understand, after Prof. Dippet retired it was the transfiguaration teacher Prof. Dumbledore who became Headmaster of Hogwarts. During the course of the Harry Potter books we see that Prof. McGonagall is the deputy headmistress and the transfiguration teacher. This would mean that Prof. Dumbledore now doesn't hold that teaching position anymore.  So what exactly does a Hogwarts Headmaster/Headmistress do?  Naturally they would appoint teachers and have some amount of administration work including the sending out of letters of acceptance to Hogwarts but what (if anything) else? Don't they have to teach?  EDIT : I get that Dumbledore had many duties being chief Warlock of the Wizemgamot etc., but is there any evidence that all previous Heads had similar duties? I was asking about a Head of Hogwarts in general, not just Dumbledore.
When he was just a professor, Dumbledore taught Transfiguration. As Headmaster what was he doing all day? In the 6th movie he was diligently looking for Horcruxes, but what about the other times?  When Fred and George pass the Maurader's Map to Harry they note that Dumbledore is pacing in his office. "He does that a lot" one of them says. Did Dumbledore just endless pace in his office as Headmaster, afraid to leave it for fear someone would know that he produced no work?   Sure, every year he had to go find a new DADA teacher, but most of those it seemed he did through correspondence. Horace Slughorn was the only one that seemed to resist. Dumbledore's 6th year may have been the only one where he earned his paycheck.
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