Lewis D. Ferebee, left, the acting chancellor of D.C. Public Schools, visits Eastern High School last month in Northeast Washington, where he had a roundtable discussion with students. Sophomore Christian Johnson, 15, right, gave him a tour of the gymnasium. (Sarah L. Voisin/The Washington Post)

Lewis D. Ferebee has questions.

What method are you using to solve those algebra problems? Is this neighborhood still considered Capitol Hill? What improvements do you want to see in your school?

The mayor’s nominee to lead D.C. Public Schools — who has been serving as acting chancellor for nearly a month — is trying to deftly navigate the city’s bumpy education terrain as he prepares for the D.C. Council to decide his fate. A pivotal moment arrives Tuesday, when Ferebee is expected to be questioned by the council during the third and final public hearing on his nomination.

Since January, he has led a school system of about 49,000 students while trying to gain public support for his nomination, striving to show residents he is the right educator for the job.

For Ferebee, who never worked for the D.C. school system before becoming the most powerful man in it, that means guarding any agenda he may — or may not — have.

So he’s posing questions to teachers and students on school visits. To education leaders and activists at evening community meetings. To families at neighborhood meet-and-greets.

The marching band at Eastern High School visits with Ferebee last month during a school tour. (Sarah L. Voisin/The Washington Post)

And then, he says, he’s listening.

“It would be a misstep to talk a lot about Lewis’s strategy — what I believe we should do in a way where it sounds concrete and final without elevating voices from families and communities,” Ferebee said in an interview at D.C. school headquarters, wearing his trademark fitted suit and dark, oversized tortoiseshell eyeglasses.

Mayor Muriel E. Bowser (D) announced Dec. 3 that Ferebee, then superintendent of Indianapolis Public Schools, was her pick to lead the D.C. school system. The 44-year-old education leader cultivated a national reputation for working with charter schools and disrupting the status quo as he tried to boost the struggling, cash-strapped school system.

But some D.C. residents have raised concerns about Ferebee’s work in the Midwest, questioning whether he is the best person to bolster D.C.’s traditional school system, which faces competition from a charter sector that educates nearly half of the city’s children.

In Indianapolis, Ferebee dismantled neighborhood high schools and turned over many of the city’s lowest-performing elementary schools to charter operators even as those schools remained part of the traditional system — a move that weakened the teachers union. He continues to encounter backlash for his handling of a 2016 sexual abuse case involving a teacher and a student and is the defendant in three civil suits stemming from that episode.

Taivian Scott, 12, a student at Johnson Middle School in Southeast Washington, asks acting D.C. Chancellor Lewis D. Ferebee, who is distinctly tall, if he plays basketball. Ferebee said he prefers football and eats a lot of green beans. (Astrid Riecken/For The Washington Post)

“Are we to believe that there was absolutely no one else who could possibly be a better fit for this job?” Chantal Fuller, a ­special-education teacher in the D.C. school system, said at a recent hearing about Ferebee’s nomination.

Ferebee, who is slated to earn $280,000 a year, insists he would be a champion for neighborhood schools in the city and that he has no intention of replicating in the District what he did in Indianapolis.

Sure, he said, he has thoughts and observations about the District. It’s just that he’s not ready to say how they will translate into concrete ideas.

He noticed that some schools have significant enrollment of special-education students, while others have few. He thinks there could be a policy solution to remedy inequities this may cause.

He knows he needs to address aging technology in schools and wants to think about effectively integrating it into classrooms.

He has sensed from teachers and principals that a culture of fear exists — fear that with one misstep, they could lose their jobs.

So he wants to reevaluate the practice of awarding principals one-year contracts, and he plans to examine the city’s IMPACT evaluation system for educators — one of the first in the country to tie teacher bonuses and job security to annual evaluation scores.

But Ferebee is cautious to stop short of saying exactly what he thinks about IMPACT. When pressed by a teacher at a recent community meeting, he said he is “committed to an evaluation process that is fair.”

“It could be a scenario where IMPACT is not broken, it’s just how it’s being implemented,” he later said in an interview. “And I think that is still to be determined.”

So instead of offering concrete policy ideas, Ferebee said he is first trying to build trust in a school system that’s lacking in it.

“You can only move at the rate of trust,” he said.

Repairing trust, though, may be a lofty goal for someone who just showed up, entering a school system battered by a year of scandals and leadership instability.

“I’m not saying that Ferebee will not be accepted, but it will be a whole lot easier if he were from here,” D.C. Council member Vincent C. Gray (D-Ward 7) said at a public hearing at which residents offered the council feedback on Ferebee ahead of its vote on his nomination.

So Ferebee is showing up, talking with people who line up to tell him about their schools, posting cheery messages on Twitter, snapping photos with whoever wants them — trying to win over D.C. residents and employees one by one.

That means taking tours of schools in blustery weather, shaking hands with teachers and administrators. Cheering on and listening to impromptu performances from Eastern High’s marching band. And asking questions of each teacher, parent and student he meets.

During a seventh-grade English class at Johnson Middle School, Ferebee squished his tall frame into a middle-school-size desk and joined the students in a discussion of the novel “The Rock and the River.”

At one point, he played teacher for a few minutes, standing up and leading the class in a discussion about historical fiction, which transitioned into a discussion about the civil rights movement.

As Ferebee was leaving the classroom, 12-year-old Taivian Scott quietly asked the educator, who is distinctly tall, if he played basketball. No, Ferebee replied, he’s a former football player.

The boy then earnestly wondered how the acting chancellor could be so tall.

Vegetables, Ferebee quipped.

He later sat down with high school students and told them he wanted them to be connected to careers in high school and to have access to jobs. He references his high-school-age son when he can, trying to show the students he’s more than just a chancellor. Teenagers at Eastern and Ballou high schools took him on tours of their neighborhoods, where Ferebee learned about the corner takeout joints.

“Where do you get your hair cut?” he asked Christian Johnson, a sophomore at Eastern, after they passed a shuttered barber shop in the neighborhood.

The D.C. Council has vowed to conduct a rigorous confirmation process ahead of its vote, which has not been scheduled. If the council does not vote by April 9, Ferebee will automatically be confirmed.

Until then, Ferebee will be at schools and coffee shops, meeting residents, trying to prove he is not just an outsider attempting to make big changes in a city he does not know.

“If we’re going to truly improve outcomes in the District of Columbia,” Ferebee said, “I can tell you that, one, it’s going to be hard; and, two, it’s not going to happen unless we do it together.”