Cynthia Gunner is not easily daunted, but on an October afternoon in 2016, she was feeling especially discouraged. Gunner, 47, is a career educator who has worked for the Atlanta Public Schools for nearly 20 years, always in segregated neighborhood schools that primarily serve low-income students on the city’s predominantly black southwest side.

Gunner got her start at Peyton Forest Elementary, a K-5 school where she completed her student teaching in the late 1990s and later taught fourth and fifth grades through the mid-2000s. Stints at other schools followed — as a classroom teacher, a literacy specialist and an assistant principal. And as of that fall, she was back at Peyton Forest as a first-time principal, a promotion that felt like a homecoming.

In 2009 and 2010, the Atlanta school system endured a cheating scandal that involved more than 40 schools. That turbulent time had begun to feel thankfully distant. But the goal of increasing student achievement remained. High-poverty, segregated neighborhood schools like Peyton Forest have, on average, low reading and math scores. In 2015, it ranked in the bottom 10 percent of Georgia public schools, which were then being targeted for potential state takeover, and had earned an F on the state’s annual report card. As a result, Gunner and her teachers were under intense pressure to increase scores. That afternoon, Gunner was visiting teachers’ classrooms, as she did most days, and was struck by the dispiriting reality of how many of the school’s roughly three dozen teachers were struggling.

Although most of them had taught for three or more years, several of the veterans were new to the building. Over the summer, Gunner scrambled to fill multiple openings, especially in third through fifth grade, which were subject to state testing and particularly acute scrutiny. One new hire, for a fourth-grade class, was Bianca McNeal, who grew up in southwest Atlanta and graduated from college in Savannah, where she was still living just the previous December. Gunner conducted the interview by Skype, as principals often have to, and was concerned about McNeal’s inexperience — she was only 24 — but hoped, given her background, that she might have a rapport with students. “I’m going to take a chance on you,” she told the teacher.

Now Gunner, an imposing presence with a warm laugh, was turning from desk to desk in the back of McNeal’s classroom two months into the school year, kidding with students. She accused one of “throwing” her “under the bus” when he revealed her assistance on some work, prompting a rare laugh from McNeal, who with sober dutifulness was walking her students through a math problem. “So, the question,” McNeal said haltingly, “is how many students from each school will be inside the auditorium. We already have 140 and 110.”

Cynthia Gunner (left), principal of Peyton Forest, in her office with Mildred Toliver, a leadership specialist. Mark Peterson/Redux, for The New York Times

“Her voice used to put me to sleep,” Gunner said as she exited the room, referring to the start of school. But she wasn’t being unkind; she was noting McNeal’s improvement. She was speaking in less of a monotone, and her lesson was better than several others Gunner witnessed earlier in the day during the school’s two-hour “literacy block.” Gunner had been dismayed by the absence of books, reading or sustained engagement with texts of any kind in several classrooms, where teachers were devoting inordinate amounts of time to isolated skills, such as a nearly half-hour lecture in one class on the prefix “re.” “Our children can’t read, but hardly any reading is happening,” she groaned.

In the hallways between classes, she’d put a hand against a wall to brace herself, to pantomime her suffering at what she was witnessing, or give an exaggerated squint, to indicate her bafflement or incredulity. Such humor, often self-deprecating, was how she kept her spirits up and cheered those around her. But her agony for students was real. Gunner was particularly discouraged after sitting in on one class where the teacher had gathered students around a blue PowerPoint with dense definitions of “subject” and “predicate,” apparently lifted from a teacher’s manual or curriculum guide, which she was trying to impose on first graders still struggling with deciphering words like “that” and “hat.”

There were other challenges. One third-grade class still had a permanent substitute, and two other teachers, Gunner believed, were on the verge of quitting. Most of all, Gunner worried about her students, most of whom lived in four low-income apartment complexes, which saw a lot of transiency. Thirty-seven percent of the school’s students arrived or left midyear. The day before, a family showed up looking to enroll and was so poor that both the adults and children were barefoot and hoping for a free school lunch as much as classroom seats. When a school-board member asked Gunner at a district event early in the year what she needed as a new principal, Gunner immediately said a washer and dryer, so she could wash the clothes that many students wore day after day. Many students had experienced trauma — the violent death of a loved one or homelessness or physical, sexual or verbal abuse — and arrived in the mornings in emotional distress, easily dissolving into tears or erupting in fury. Over long weekends, students sometimes went untended or had little to eat, which made returning to school both welcome and difficult. Yet the school had only one full-time social worker and a counselor for more than 450 children.

Still, there were bright spots, as there were every day. One teacher had led a lively discussion on the differences between a folk tale and a fable before students read a story about a chipmunk that lost its stripes. And there was always the marvelous Ericka Fluellen, who had been teaching at the school for six years and who could keep several centers, where students were reading or writing independently, in motion in her third-grade class, while working effectively with a small group of students at her desk.

What Gunner really needed, she thought, was more Ms. Fluellens. But teachers like that were always in short supply and weren’t exactly beating down the door to work at Peyton Forest. So part of Gunner’s job was to help the teachers she already had to improve — and to do so without igniting a revolt.

The nation’s public schools employ 3.2 million full-time teachers, more than the number of lawyers, physicians and engineers in the United States combined. Because the job is demanding and pay is low compared with other professions requiring a college degree, finding effective teachers, retaining them and helping those who need to get better is a never-ending challenge.

Yet starting in 2002, the federal legislation known as No Child Left Behind established guidelines for holding schools accountable for student scores on state tests, closed schools deemed ineffective and expanded the nation’s charter-school sector. A largely untested series of assumptions about teaching and its ability to increase student achievement began to drive education policy: that the best way to advance student outcomes was to increase teacher effectiveness, and that the way to do that was to hold teachers individually responsible for student performance on state tests, which in turn would ensure teachers found the means and motivation to improve. And nowhere, perhaps, did this idea blast off more quickly, rise as far and fall as hard and as fast as it did in Atlanta.

District officials aggressively pushed this reform agenda. Educators who didn’t meet the law’s ever-rising bar were fired or pushed out. And then test scores soared. Low-performing schools suddenly saw double-digit gains year after year. One school’s math scores jumped over 60 percentage points between 2005 and 2006. Philanthropies like the Bill and Melinda Gates Foundation rushed to invest in Atlanta’s miracle.

As the city soon discovered and the country learned only belatedly, however, the belief that simply setting ambitious targets would catapult 100 percent of American students to rigorous, grade-level proficiency by 2014 — the original goal of No Child Left Behind — was always unfounded. Starting in 2008, the city’s schools came under scrutiny from The Atlanta Journal-Constitution, followed by a state probe assisted by the Georgia Bureau of Investigation. The inquiries determined that some teachers and administrators in the school system, their livelihoods on the line, coached students during the 2009 test or tampered with students’ answers in response to a toxic “culture of fear” and retaliation in the district. More than 150 people who worked in or oversaw Atlanta’s schools, including Peyton Forest, were eventually implicated in the cheating and lost their jobs or voluntarily left.

“It was ugly and horrible for everyone whether you were accused of cheating or not,” says Gayle Burnett, who worked in the district’s central office at the time and is now executive director of the district’s office of innovation. “You were hearing horror stories about people being intimidated. You were crushed by what people were admitting they had done.”

Yet many teachers had also been put in a terrible bind. While teacher effectiveness may be the most salient in-school factor contributing to student academic outcomes, it contributes a relatively small slice — no more than 14 percent, according to a recent RAND Corporation analysis of teacher effectiveness — to the overall picture. A far bigger wedge is influenced by out-of-school variables over which teachers have little control: family educational background, the effects of poverty or segregation on children, exposure to stress from gun violence or abuse and how often students change schools, owing to homelessness or other upheavals.

Students from Bianca McNeal’s class on the first day of school, Aug. 1. This year she is teaching fifth grade. Mark Peterson/Redux, for The New York Times

Under No Child Left Behind, new models for rapidly increasing student achievement at high-poverty, segregated neighborhood public schools like Peyton Forest were supposed to emerge, but few did. Success stories existed, but they almost invariably involved changing the population of students within those schools: either through greater integration in the case of traditional districts or by opening up charter schools that attracted an entirely new set of students through a lottery system. By contrast, turnarounds of traditional neighborhood schools were often considered so difficult that almost no charter groups were willing to take on the assignment, and among those that did nationally, very few succeeded in increasing scores.

Prosecutors in Atlanta indicted 35 people on racketeering, a federal charge usually associated with drug trafficking or organized crime. Most of the defendants pleaded guilty, but 12 people stood trial for the supposed conspiracy, and in April 2015, all but one of them were convicted. The sentences were jaw-dropping — 20 years, in some cases, with seven to serve — even though the recipients, all of them black in the city’s majority-black school system, were first-time offenders. Two weeks later, the judge, apparently recognizing that the terms were insupportable, reduced the most severe prison sentences to three years, punishments that were still uncommonly harsh.

An interim superintendent was appointed to clean house. “He fired everyone who was a director or above in the instructional end of the central office,” Burnett says, which also served to drain the district of institutional memory. “Nobody knew what we were doing or why,” she says of the years immediately following. Most teachers hadn’t cheated. “We had huge dips in performance after the state came in, but it didn’t fall all the way back — all of it wasn’t fake,” she says. “But no one believed anything good happened before.” For decades, would-be school reformers had argued that almost anything would be better than the status quo. But there was something worse than no reform, it turned out: unsuccessful reform, which made finding the will, resources and trust for better, future change that much harder.

This was the landscape Meria Carstarphen stepped into when she arrived in Atlanta in 2014 as the first permanent schools superintendent since 2011. She introduced a new “turnaround” strategy, partnering with organizations including two local charter operators that were willing to forgo a lottery to operate traditional neighborhood schools, and a small nonprofit based in upstate New York called the Rensselaerville Institute. Through its School Turnaround program, Rensselaerville specializes in providing leadership training to principals to help them become masters at recognizing and teaching good instruction in their schools.

Gunner was assigned a Rensselaerville specialist named Mildred Toliver, who would work with her over the next two years. At the heart of Rensselaerville’s approach, which is similar to other programs for beleaguered neighborhood schools in urban districts, was a belief that principals had to get out of their offices and into classrooms — not as a “compliance officer,” stringently holding teachers to account, but as someone who intervenes and works side by side with teachers to help them become the very best they could be.

Gunner grew up in Beaumont, Tex., in the 1970s, which she recalls as a lot like Atlanta today. “All the black schools were on one side of town,” she says, “and all the white on the other.” (Atlanta is the second-most-segregated city in the country, after Chicago, according to one 2015 analysis, and has the highest level of income inequality of any metropolitan region, according to another in 2016.) Gunner didn’t attend an integrated school until 1981, after a federal court order compelled Beaumont to desegregate. She was entering sixth grade and was bused to a white school across town.

“It was the first time I’d ever seen a white principal or a white counselor,” she says. Gunner had tested into the gifted class the previous year. But at her new school, she was told a reading test she took disqualified her from the gifted program. Her mother, who worked for the Beaumont Independent School District as a teacher for homebound students, questioned the decision. So Gunner took the reading test again and passed. She was the only black student in the gifted track for most of middle school. “My mother,” Gunner says, “was always in there having to fight.”

Gunner eventually ended up at Spelman College, the historically black women’s college in Atlanta. She loved the city and stayed after graduation. When she was a young teacher at Peyton Forest in the 2000s during the No Child Left Behind era, the job was becoming so stressful — the principal who hired her was replaced for not sufficiently raising scores, according to testimony in the state investigative report on the cheating scandal — that Gunner considering taking a job in Buckhead, the affluent white suburb north of town. But that would have made her life’s work just a job and not the commitment to her community she wanted it to be, so she accepted a position at another elementary school, where her new principal became a life-changing mentor, showing her the difference a strong leader could make for teachers. She hoped to have the same impact at Peyton Forest.

Gunner tended to see her teachers there as belonging to one of three categories. First were the already excellent teachers like Ericka Fluellen. Second were several teachers like Bianca McNeal, the novice, who might not be strong instructors yet but were willing to put in the effort to improve. Third were the teachers “who can but won’t,” in Gunner’s phrase; these teachers had the capacity to become more effective educators but appeared to have no interest in doing so. They were already set in their pedagogical ways or didn’t think change at the school was necessary or possible or didn’t want to put in more effort, or there was some other reason Gunner couldn’t yet divine.

She spent most of her time pinning her hopes on the second category and being exasperated by the teachers in the third, who not only weren’t serving the students but also made life more difficult for their peers like McNeal, who needed better teaching models — a team — but didn’t have that. Throughout the fall, McNeal exhausted herself during the week, planning lessons late into the night and collapsing on the weekend. By early 2017, she felt she’d finally gotten over the hump and could catch her breath. Although she was so attached to the kids that she often let them stay with her for hours after school as she graded papers or prepared for the next day, she felt lonely and out of place among the adults. The other fourth-grade teachers were much older, and she often felt they were giving her the side-eye for keeping such long hours at the school. “I know they have kids and families at home,” she told me that winter, which she didn’t begrudge. But she also didn’t want them making her feel bad — asking her, for example, “Why would you do that?” — when she took several students to dinner or even once to Six Flags with her own money as a class reward. She did not feel comfortable turning to them for help and advice.

McNeal did what she did because her students’ hardships reminded her of some of her own. She grew up with her mother and an older brother in the Bowen Homes, a segregated public-housing project in northwest Atlanta. (Her parents weren’t together, but her father remained involved in her life.) The project was notorious for “warehousing families in concentrated poverty,” in the words of one Atlanta Housing Authority official, and was razed in 2009. “There was a lot of violence and drugs that a child shouldn’t have to see,” McNeal recalls.

Bianca McNeal and her fourth-grade class in May 2017. That month, Cynthia Gunner received raw results from the state’s tests: The school’s reading and math scores had both improved. Mark Peterson/Redux, for The New York Times

Her mother worked for a time as a cafeteria worker, cleaning homes on the side. “There was never enough money,” McNeal says. She attended Frederick Douglass High School, most of whose students were low-income. Her teachers encouraged her to stay in school, take A.P. classes and join the debate team. When she couldn’t afford a dress for the prom, a teacher bought her one. McNeal’s mother was one of 17 brothers and sisters, and McNeal had scores of aunts, uncles and cousins on that side, but she was the first among them to attend college; she graduated ninth in her high school class and won a full scholarship to the University of West Georgia outside Atlanta, where she decided to enter the pre-med program.

But for all her hard work and her teachers’ generosity, she hadn’t received the academic preparation she needed. She did well in her English classes, but despite studying around the clock, she barely got through college chemistry and failed a required math class, causing the university to rescind a portion of her scholarship, which threatened her ability to continue. She learned about a teacher-preparation program at Armstrong Atlantic State University in Savannah, now part of Georgia Southern University, applied and received enough new financial aid to graduate. Eight months later she was at Peyton Forest, having sought out a majority-black low-income school because she wanted to be the “second family,” she says, to her students that her teachers had been to her.

Gunner or a vice principal or one of the school’s literacy or math specialists was a regular presence in McNeal’s classroom. Gunner had been encouraged by Rensselaerville and her coach, Mildred Toliver, to give daily, concrete feedback that teachers could readily incorporate into their teaching instead of relying on a formal evaluation. At first, this made McNeal self-conscious, but after a while, she got used to it and welcomed the comments. But not every teacher felt the same way. One of them filed a complaint against Gunner, and a district “escalation” expert named David York, a former principal and teacher in his 60s, came to investigate and share his findings with Gunner.

The teacher felt as if she were “being targeted” with excessive expectations, York said, declining to identify the teacher. He told Gunner the teacher “was stressed” and had “a lot going on at home.” She had also heard from another teacher that Gunner had called her a slacker. “I’m not a slacker,” the teacher had tearily protested, according to York. “I thought I was doing what she wanted,” she said, and “I can’t work under these conditions.”

Gunner acknowledged that the teacher might feel under pressure. “We go into every room every day, sometimes twice a day, and that’s a paradigm shift for this entire school,” Gunner said. “I do think she’s sincere,” Gunner added, but, thinking about her teacher categories, she added, “What makes cases like this so hard is it gets to be where it’s will you — or can you?”

“I can’t say the efforts she’s putting forth are paying off,” York conceded, allowing that Gunner was “appropriately impatient.”

Gunner seized on the phrase. “Appropriately impatient! I like that!”

York encouraged Gunner to do more to recognize the teacher’s feelings. “You can’t tell someone how to feel,” York said, and noted that during his interview with the teacher, several former students visited the teacher’s classroom to get hugs, evidence that she was “having some kind of positive impact on kids.”

He also left Gunner with this warning. “She may quit,” he said, “and you might think, ‘Oh, goody!’ ” But Gunner, York noted, wasn’t likely to find a better teacher midyear and would very likely end up with another permanent substitute. “And then you’re going to have to figure out how to support her,” he said.

That teacher did eventually quit, and by early 2017, so had another. Managing these sudden departures was hard on students. Fluellen, the third-grade teacher, told me that students who had experienced other traumatic losses and felt as if school was “their safe zone” would often act out when their teachers left. And in fact, days after Gunner replaced the second of these teachers, who taught fifth grade, with an emergency substitute, she received an urgent call in her office over a school walkie-talkie. A child in the class was “being disrespectful” to the new sub — not following directions and directing curse words at other students, though not at the teacher. Upset, the teacher was threatening to quit, too. Gunner thought that in the annals of fifth-grade antics, this was a situation a competent teacher should be able to handle. But she also couldn’t afford to have the parade of teachers continue, and she placed the offending child in a different class for the day. The sub quit anyway after just two weeks; only with the third teacher did the school finally find a consistent and capable instructor.

Gunner had a natural, take-charge assurance and almost frenetic energy that sometimes belied her own learning curve as a first-year principal. Straightforward with staff and expecting the same in return, she had little patience for what she liked to call “shenanigans” — excuses for repeatedly showing up late, for instance, or without a lesson prepared. But in her eagerness to see rapid improvement in the school’s instructional practices, she could sometimes overwhelm her staff with critical feedback and had trouble delegating authority — for example, giving such precise details of a message she wanted her assistant principal to convey to staff that the assistant principal finally blurted out, “What I hear you saying is you want to do this.”

It was Toliver’s job to help rein in some of these impulses. Toliver, who is 64 and has an instinct for what motivates people and an unflappable, seen-it-all-before manner, worked with Gunner at Rensselaerville’s multiday workshops, mapping out matters involving staffing and student data. Toliver visited Peyton Forest one or more days each month, and she and Gunner would tour classes. They would discuss what they’d seen or what they hadn’t and wished to — and how to address both.

Cynthia Gunner visiting Bianca McNeal’s classroom on the second day of classes this year. “We go into every room every day, sometimes twice a day, and that’s a paradigm shift for this entire school,” Gunner said. Mark Peterson/Redux, for The New York Times

When, early in the year, Gunner and Toliver watched the teacher use the PowerPoint with first graders, Gunner was so frustrated by the lesson on top of the others she’d seen that she went on a tear once she and Toliver were back in Gunner’s office. If a teacher didn’t know this was inappropriate for 6-year-olds, “how do you teach someone common sense?” She resolved to deliver a long list of “nonnegotiables” to her teachers that afternoon; one of the items on the list was going to be “no PowerPoints in grades K-2!”

Toliver agreed that the lesson was “ridiculous.” But she gently steered Gunner in a different direction, encouraging her to let her assistant principal, who would be less intimidating to teachers, lead the meeting and let them brainstorm about “instructional norms” they could embrace as a group, instead of Gunner’s just delivering dictates from on high. And she encouraged Gunner not to deluge her teachers with too many things to change, or they would just end up shutting down. Gunner had to pick and choose wisely.

The approach was something David Jernigan, the deputy superintendent of the Atlanta Public Schools and the founding executive director of Atlanta’s KIPP network of charter schools, thinks is critical. “As someone who’s been a principal as well — you can’t give a teacher a ton of feedback,” he said. “You have to be very focused, very targeted, make it actionable at that moment.” Figuring out what sorts of critiques were helpful for particular teachers was knowledge built over time, but that could be learned faster if you had a more experienced coach “walking around with you to test what it is that you’re seeing.” But for a coach to be able to give “tough feedback in a way that principals can hear,” Jernigan acknowledged, there had to be a trusting relationship first.

To Gunner, Toliver was “calmer, more mature and had a level of experience I just didn’t have,” but just as important, Toliver was someone Gunner could relate to. Toliver was also from the black side of a segregated Southern town, in her case Shreveport, La., but was a generation older. She was a first-year teacher in the early days of integration in Louisiana at a school with only a small number of black students. Her first class consisted of 23 students, all of them black, with third through sixth graders in a single class. It was like a one-room schoolhouse inside an otherwise affluent white school.

She taught seven more years and became a principal in Shreveport and later in Fort Worth, which contracted with Rensselaerville in 2002. Toliver was coached by Gillian Williams, a former teacher and principal who founded Rensselaerville’s School Turnaround program. (I knew Williams when we taught at the same school in New York in 1990.) Toliver liked how the program taught her to think about what it meant to be a leader, something she had never really considered, and also its relentless focus on the classroom, where the work of schools is actually done. When she left the school district, Williams hired her as a specialist. (Rensselaerville hires only specialists who have had successful leadership experience in low-performing schools, and more than half of them are men and women of color.) “It was the first time someone had come in from the outside,” Gunner acknowledged, “that I actually listened to.”

One of Toliver’s main messages is that to be helpful to teachers, you can’t just tell them what they’re doing wrong; teachers have to actually see what good teaching looks like, and they need to see how to do it with the children they are actually teaching. Fluellen told me that so much of instruction for teachers is generic and not relevant to schools like Peyton Forest. “Sometimes people will say, ‘Here’s a video of best instructional practices,’ and teachers are like, ‘Well, that’s not my kids — our kids can’t do that.’ ” To address this, Rensselaerville advises principals to set up a “model classroom” as an on-site resource and inspiration for teachers. Gunner made Fluellen’s third-grade class one of the school’s model rooms.

One afternoon in March 2017, shortly before dismissal, when the nerves in many classrooms are beginning to fray, Fluellen remained unruffled. She didn’t engage as students got annoyed by classmates’ making objectionable faces to their peers. When one’s boy anger at a girl seemed in danger of escalating, Fluellen wordlessly tossed him the class’s stress ball, which he began to squeeze, calming him for a time. Students then broke up into groups, as orchestral music softly played, to either rewrite a story about a girl on a soccer team from a first-person point of view or to interview classmates about their sports preferences for a math exercise on graphing data. At her desk, Fluellen had a third group and was playing a game with flashcards and giving high-fives to those who won.

Another way to teach teachers is for principals to go into classrooms themselves, a message Gunner took to heart. That same March, she helped McNeal, the fourth-grade teacher, grade essays that her students had written about Amelia Earhart and Charles Lindbergh. In the process, McNeal realized she had missed a key element of the assignment: comparing and contrasting the two figures, not just writing about each in turn.

A few days later, McNeal retaught the lesson with Gunner looking on. This time, McNeal explained that students were to write “all the similarities” in one paragraph and “all the differences” in another, bookended by an introduction and conclusion, two elements most of her fourth graders omitted entirely. Yet as McNeal got started, it was clear that most students still had no idea what an introduction entailed. As McNeal began to address this, she didn’t provide a preamble to pique students’ interest or draw them in, something she’d struggled to do all year.

Gunner jumped in to model a different approach. She dropped her loud teacher voice several registers, as if to invite students into a delicious conspiracy. “What if this was the very first day of school,” she all but whispered. “And you came and sat here. And you’d never seen your teacher before, right? And I walk in and said” — Gunner now strutted dramatically into the class, raising her voice back to thunder level — “ ‘Turn to Page 12, we’re going to be doing Problems 1 through 10!’ ” Several students giggled. She asked them what they would think. Tentative at first, a boy finally ventured he’d wonder who she was.

“You’d be confused, right?” Gunner signaled that his answer was correct. “But what if I came in and said” — her voice sweet and low again — “ ‘Good morning, my name is Ms. Gunner. I’m your new fourth-grade teacher, and today we’re going to be studying math.’ ”

Not only, she pointed out, would they know who she was and what was going on, they’d know the direction the class was going in — the same way a good writer helps a reader by hinting at the direction of an essay in the beginning. For the next 10 minutes, Gunner teased out with students how this literal introduction applied to introductions in their writing. By the lesson’s end, students were calling out when a classmate’s proposed opener was “effective” or when it was just “turn to Page 12 and do Problems 1 through 10,” a phrase students were now using as shorthand for bad writing.

But not every class was progressing. One day late in spring 2017, Gunner and Toliver were on their usual rounds. They looked in the window of a fifth-grade classroom. The students were horsing around, without any apparent work to do. The teacher was sitting at her desk, engrossed by her phone as she rapidly tapped the screen. She continued to tap without looking up. Gunner would get exasperated with teachers who didn’t circulate among students but sat at their desks for an entire lesson. But as soon as she opened the door, the teacher would usually get up and begin looking over students’ shoulders.

Now when Gunner swung the door open to enter, the teacher kept tapping, apparently unaware that her supervisors had just arrived in her classroom. The students looked at them and back at the teacher, wide-eyed, waiting for something to happen, as Gunner and Toliver continued to observe. Finally, one of the students alerted the teacher to their presence. But the teacher didn’t stand up. She simply put down the phone and gave Gunner an expressionless look. When they left, it was Toliver who was momentarily agitated, telling Gunner, “I’d write the teacher up,” meaning putting a formal complaint in her file, a move that principals typically take when trying to create a paper trail before deciding to fire someone. It would not prove necessary; the teacher left at the end of the year.

As spring advanced, anxiety about the state tests, which were in late April, after spring break, began to mount. Gunner worried students would be hungry and otherwise at loose ends over the vacation, making them ill prepared for days of tests upon their return. Gunner and other staff met individually with “bubble” students from each grade, whom she, Toliver and the school’s leadership team had identified as having the best chance of jumping from “developing” to “proficient” in reading, math or both.

Gunner couldn’t always hide her own anxiety, which sometimes permeated whatever space she was in. She would call out to students randomly in the hallway, “Only 21 days to the test!” or “Only 14 days to the test!” Over the last decade, pep rallies before state tests have become rites of passage in schools, as familiar as the prom. Peyton Forest had theirs.

The atmosphere became increasingly frantic, as Gunner began to encourage teachers to do extra lessons on reading and math, even if this meant neglecting other subjects. Gunner complained to Toliver about a teacher who conducted a science experiment involving dirt and water, which resulted in a lot of mud. Gunner didn’t relish the expenditure of time “so close to the test” on something other than reading or math. “We’re going to have to have a tough conversation about that,” Toliver told me, referring to what she saw as a counterproductive narrowing of the curriculum. To read well, students needed familiarity with a range of experiences and exposure to broad subject matter. The original intent of the standards movement had been to infuse schools with richer, more substantial content. But the nation had ended up with an “accountability” movement instead.

In May 2017, Gunner got the raw results from the state’s tests. The school’s scores had improved: In reading, the percentage of third-through-fifth-grade students who were scored “proficient” had moved to 15 percent from 12 percent. In math, the jump was greater: to 21 percent from 11. And when the state calculated the school’s College and Career Ready Performance Index (C.C.R.P.I.) score, which adjusts for factors like poverty, the school did sufficiently well to move from an F on the state report card to a D.

Still, given how hard everyone had worked, Gunner had hoped for an even bigger rise. Over that summer, 12 more teachers decided not to return to Peyton Forest. In the hunt for replacements, Gunner decided that it was better to be frank about the demands of the job and the needs of the students than to try to sugarcoat the challenges and then have a teacher be surprised and quit.

Even so, a fifth-grade teacher quit two weeks into the new school year, and in November, three more teachers abruptly left. Still, there were some positive signs. By fall 2017, enrollment at the school had grown by more than 15 percent, a sign to Gunner that word on the street about the school was good. No longer a first-year principal and having shown some small gains, Gunner felt the pressure ease. She opened a “lit lounge” in the school, a room that looked like a child’s fantasy clubhouse, with colorful rugs, beanbag chairs and donated games like air hockey and even an electronic bowling alley. Students could win lit lounge privileges by behaving in a way that demonstrated that month’s character word, such as “risk-taker” or “courageous.” There were pajama reading parties and Friday movie nights and money for field trips, under a district plan to give principals more control over their budgets.

By this spring, there was a palpable difference in the school. Reading classes included more actual reading, and from class to class, students were toting library books. Fluellen was now an instructional coach and had started a “new-teacher academy” to help develop and retain the school’s recent hires. Teachers were meeting weekly after school in grade and subject teams, discussing instructional problems they had in class and helping one another to resolve them. McNeal, no longer tentative, showed a group of her colleagues a new way to teach adding fractions.

Last month, the scores arrived for this past school year. The reading scores climbed to 21 percent “proficient.” Some of the biggest gains were in fourth grade, where McNeal taught the entire grade language arts. Math inched up another point to 22 percent. (The C.C.R.P.I. score and state report card grade won’t be calculated until later this year.)

But how much more a school like Peyton Forest can improve without addressing the more systemic challenges it faces is anyone’s guess, and past experience is not encouraging. In the years after No Child Left Behind was enacted, scores on the National Assessment of Educational Progress, widely considered the gold standard for measuring achievement over time in American schools, rose marginally in reading but more so in math, suggesting that an initial injection of energy and attention into districts may have goosed scores. But they have since stagnated, remaining flat for roughly a decade. Teaching does matter, and it can improve. But there is little evidence — at least to date — that it can counter the effects on children of attending neighborhood schools that remain racially and economically isolated.

On Gunner’s worst days, she told me once, “I don’t think people really think it’s possible,” referring to turning around neighborhood schools like Peyton Forest. On days that aren’t her worst, Gunner tries to focus on the job right in front of her. And it is a job, in fact, that she loves. The profession, as it is currently constituted, seems to require a bifocal vision: an ability to see the dispiriting big picture, but also an ability to see the child close at hand.