New Schools Chancellor Cathie Black called her role “a dream job” and the “chance to make a difference” as she visited a school in each borough on her first official day.

Black’s tour began at PS 262, a high-performing, high-poverty school in Bedford-Stuyvesant, Brooklyn — and concluded at the Staten Island special-education gem, The Hungerford School.

“For me, this is a dream,” Black said at her first stop. “It’s a dream job; it’s a dream opportunity — a chance to make a difference.”

Black heralded the gains in schools under former Chancellor Joel Klein but said her appointment could bring about welcome changes.

“A change in leadership, I believe, is a very good thing — whether it’s in the private sector or the public sector — because it represents an opportunity for a fresh set of eyes to look at a set of different problems,” she said.