Many of the education department’s signature policies, like expanded pre-K, fall under the umbrella of what the city calls its Equity and Excellence for All agenda, which aims to improve every school for every child, adding computer science and Advanced Placement classes to schools, for example.

But the divides remain yawning, and the administration has attracted significant criticism for what has been called a halting and incremental approach to tackling the system’s enormous racial and socioeconomic segregation. While declaring diversity a top priority last year, Ms. Fariña said she wanted to see plans to desegregate the schools bubble up “organically” rather than be mandated from above.

Amy Stuart Wells, a professor at Columbia University’s Teachers College who studies segregation and is a member of the city’s school diversity advisory group, said Ms. Fariña’s department has paid more attention to the issue than past administrations, but that the work is just beginning.

“The release of a report and the creation of a task force is symbolically extremely important to say, ‘This is a priority,’” she said. “But where we go with it, and how deeply we address the issues of what happens inside of schools when kids get there, that will be the challenge for the next chancellor.”

To some, Ms. Fariña’s skepticism of data, and in particular her push to de-emphasize the role of test scores, has been refreshing. Aaron Pallas, a professor of sociology and education at Teachers College, said that under Mr. Bloomberg and his schools chancellor, Joel I. Klein, there was often “an active dismissal of the notion that teachers had the skills to do what they needed to do.”

“She does believe a lot in the wisdom of practice, the idea that experience imparts knowledge about how to do this kind of work of educating children that one really can’t get other ways,” Mr. Pallas said of Ms. Fariña.

While the Bloomberg administration in its final years went to war with the teacher’s union over issues like school closures, teacher evaluations, seniority rules and the status of so-called reserve teachers who had lost their positions, Mr. de Blasio and Ms. Fariña have pursued an amicable and cooperative relationship with the union. Observers say that has had benefits in terms of raising morale among teachers and reducing the level of open strife, which tends to diminish the public’s confidence in the school system, but that it has also had a price.