In the first school Cathleen P. Black visited, students in a fifth-grade classroom had one laptop apiece, from which they received individualized lessons. In the second school, for teenagers who had been on the verge of dropping out, counselors routinely show up at the homes of students if they are absent three days in a row. The third was one of four schools in a building that once housed one; students had violin and dance classes, aside from traditional subjects like history, English and math.

Ms. Black, who officially began her job as New York City schools chancellor on Monday, has been visiting schools for weeks. But the tour on Monday, more than an introduction to the system, was a tightly choreographed showcasing of the Department of Education’s