Springfield Arbors preschool consists of one long hallway on the ground floor of an assisted-living facility, with several classrooms strung along either side. The surrounding neighborhood, known as Six Corners, is home to a high school (the same one that Kelly attended), a community college and a steady beat of drug- and gang-related violence. Six Corners children live on the down side of what’s known in education circles as the achievement gap. According to analysis done by the Massachusetts-based nonprofit Strategies for Children, between 12 and 14 percent of third graders in some Six Corners schools read at or above grade level, compared with between 37 and 43 percent in nearby Forest Park, a neighborhood known for its well-preserved Victorian homes, and as the birthplace of Dr. Seuss, the city’s most famous native son.

Kelly came to preschool teaching about a decade ago, when the local caterer she was working for abruptly shut down. For a single mother with a high-school diploma, the options in Springfield were limited: Home health aides, retail salespeople and food-service workers all made about the same salary. Receptionists and secretaries made more, but those jobs required office experience, and the work itself sounded dull. Kelly wanted a job helping people. She had only ever worked in food service, but when she found a local preschool with an opening in the kitchen, she saw a chance to pivot.

She started by making herself known in the classroom, lingering to help out when she delivered lunches, introducing herself to parents in the hallway, befriending the teachers and asking them about their work. When an assistant-teacher spot opened up, she jumped on it. She considered it a promotion, even though the teacher’s salary ($9 an hour) was actually $1 an hour less than what she made as a school cook. For the first year, she split her time between the kitchen and the classroom while she earned her Child Development Associate certification, or C.D.A., which required her to complete a nine-month course that met for four hours every Saturday at the local Y.M.C.A.

At first she thought that credential would help her carve a path to some greater edification: a higher degree, maybe, and a higher wage along with it. But those dreams were quickly jettisoned. In 2011, just as she was completing her first class at the community college, an electrical fire tore through the three-family home that Kelly and her two children shared with her grandmother, mother, aunt and cousin. Her relatives’ apartments weren’t damaged much, but Kelly and her children lost nearly all their possessions. Worse, the fire seemed to usher in a newly dark chapter in her life. In 2012, her younger brother died in a horrific car accident; a year later, her cousin was shot and killed, and her aunt died. Her daughter’s boyfriend — the father of her newborn grandson — was also killed, in another shooting. Somewhere in the middle of those heartaches, the preschool she worked at closed, and Kelly moved on to Springfield Arbors.

The C.D.A. taught her the basics of lesson planning, class structure and family engagement, but her real training came through trial and error. Kelly’s classroom was often chaotic, but parents quickly learned that they could come to her with concerns, even after their children had aged out of her classroom. One mother asked her to step in as foster parent during a particularly tough time. Others hired her to babysit when they picked up night shifts at one job or another, so that Kelly might welcome a given child at 8 in the morning and not return him to his mother until well after 10 or 11 at night. The work was exhausting, but she found she had a knack for it — an instinct for what her students needed, an ability to relate to them and, when all else failed, a willingness to keep trying.

One early-spring afternoon, when a rainstorm kept the children indoors during what would normally be playtime, Kelly tried arranging a field trip to the basement hallway — the only substitute playground at Springfield Arbors. But when too many of them fell into tantrum mode at the same time, she changed tack and set up the portable chalkboard at the front of the room. It did not take long for one, then three, then a dozen of the children to notice her chalking letters and gather around. The letter of the week was “D,” and she had been teaching the students what words it was used in and showing them how to write and pronounce it. “Down, over, over,” she said in a long, slow drawl, as she drew first the spine and then the hump of the letter. She was speaking to one little boy specifically, and when she was done, she handed the chalk to him and held his hand as he repeated her movements. Then she removed her hand and nodded at him to try on his own.

At first, the class was enthralled by this demonstration. But then one little boy started screaming. Grandma, an elderly volunteer who sometimes came for an hour or two and mostly sat in back of the room on a small couch, grabbed the boy’s arm and yanked him to her side. “Cut it out,” she said. “Come sit!” The boy yanked his arm back, flopped onto the floor and wailed. Kelly kept her focus on the students at the blackboard. Eventually the screamer ran back over to the circle and forced another little boy off his seat, which made the other boy cry, which distracted the rest of the class and set half of them wandering off, before anyone had made a full D.