Three months into her tenure as chancellor of Schools, Cathie Black has a popularity problem: A NY1-Marist poll found she had a 17 percent approval rating, and around two-thirds of those polled said they disapproved of Mayor Bloomberg’s management of the school system. “It doesn’t paint a pretty picture,” said Lee M. Miringoff, the director of the Marist College Institute for Public Opinion. “It is a long way from 50 percent, where you can at least say the city is divided about her. There’s no real core support.” Black’s rating is down from a February poll in which 21 percent said they approved of her performance. Still, the poll reported that around 53 percent of public-school parents gave their local schools either excellent or good ratings. So good schools, bad chancellor?