ALBANY — Opponents of Cathleen P. Black’s appointment as New York City schools chancellor tried to convince a judge on Thursday that the state education commissioner misinterpreted the law when he approved her selection.

At a hearing in State Supreme Court here, their lawyers argued that state law did not permit Ms. Black, who has 40 years of experience in publishing, to assume the chancellor’s job, because she had no teaching experience and no degree beyond a bachelor’s.

But lawyers for the city and the state said that the education commissioner, David M. Steiner, had the discretion to waive the traditional requirements for the job.

Justice Gerald W. Connolly gave no indication of when he would rule on the suits. Ms. Black is due to start work on Jan. 3.

Ms. Black, who was appointed last month by Mayor Michael R. Bloomberg to succeed