When Baker was six, half a year after the family moved to Amherst, her parents sat her and her older brother down to make an announcement. The young Annie headed them off. “I’ll bet you’re getting divorced!” she blurted out.

“She paid a lot of attention to what was going on around her, and to how people were interacting with her and with one another—she was very tuned in to all of that,” her mother says. Custody was split; Baker’s father moved out and, a year later, took a job in New York, where he eventually raised a second family. Baker continued to live in Massachusetts, with her mother; every year, they would raise caterpillars into butterflies.

“It was intense to go back and forth, especially because my parents have very different personalities that required very different things from me and my brother,” Baker says. “I would train myself to be a very sassy, super-assertive person around my dad. Then I’d get back to my mother’s house, and she’d be like, ‘Why did you just speak to me that way?’ ”

“She thrives on confrontation,” says Baker’s older brother, Benjamin Nugent, who is also a writer. (His latest book is the novel “Good Kids.”) “I think our family was hard for her sometimes, because it wasn’t all that confrontational; my mother and I were quietly depressed in the years after the divorce, and I think her impulse was to try to hammer at our shells, to get us to be depressed more openly. I still see that shell-hammerer in Annie’s work.”

When Baker went away to college, at Tisch, N.Y.U.’s arts school, she enrolled as a dramatic-writing student. Today, she can’t recall why. “I was interested in writing,” she says. “And I was ‘interested’ in film and ‘interested’ in theatre. But I wasn’t like, ‘I’m going to be a playwright.’ ” She worked a string of odd jobs after graduation. She was an assistant residence-hall director for student ballerinas at the School of American Ballet. (It gave her a free apartment at Lincoln Center.) She was a contestant wrangler for “The Bachelor.” (“Awful.”) She took uncredited writing assignments for the extra cash. Her big break was with the quiz show “Who Wants to Be a Millionaire?,” which hired her to write “throws,” pre-commercial sendoffs: “Don’t touch that dial—we’ll be back with John in the hot seat.” Later, she became one of the show’s researchers. But her sense of vocation remained vague. At a doctor’s appointment when she was twenty-four, her physician, filling out her charts, asked what her job was. “I was like, ‘We-e-ell, you know, I write plays, but you can’t be a playwright, so I have a day job, and maybe I’ll end up teaching or something,’ ” she recalls. “And he was like, ‘One of my patients is a playwright! A very well-known playwright.’ And I was like, ‘Yeah, but you can’t make a living as a playwright. You can’t, like, be a playwright.’ ” Her doctor looked at her oddly. It was the first time that she realized this was an option.

By then, she was spending evenings deep in her imagined world. “Body Awareness,” one of the pieces that Baker was working on during this time, centered on a middle-aged academic lesbian couple, Joyce and Phyllis; Joyce’s twenty-one-year-old, etymology-obsessed son, Jared; and a visiting photographer at the nearby college, Frank. As the four of them struggle with the issues of power and identity—Phyllis thinks Frank’s photography of women is exploitative, Joyce thinks Phyllis is envious and controlling, and both think Jared might have Asperger’s syndrome—their intellectual and aesthetic certainties peel apart. It’s a play about the emotional stakes of intellectual dogmatism, strung against a jaunty portrait of college-town culture, and, appearing at a moment when theatrical taste ran toward small and tight domestic dramas, it brought Baker to national attention.

Neil Pepe, the artistic director of the Atlantic Theatre Company, who grew up in southern Vermont, was taken with her portrait of crunchy New England home life when he read the play, in 2007. “When you’re looking around trying to find interesting plays, the first thing you listen for is the truth of the author’s voice,” he says. Baker was by then living in Brooklyn, and when Pepe called to say that the play was going into production she fell down in the middle of Clinton Avenue.

One chilly afternoon in January, Baker went for a walk in Green-Wood Cemetery, a five-hundred-acre expanse south of Park Slope. She wanted some fresh air, and she took a southwest route over some hills, toward the ponds. After a few minutes, Baker wandered off the path to take a close look at a particular headstone:

LIFTCHILD Father Mother Frank A. Jean G. 1863-1952 1870-1954

She rummaged in her purse. Names like Liftchild are the sorts of thing that Baker takes down in her notebook. (The notebook is a Moleskine, which embarrasses her; she’s afraid, she says, of being mistaken for the kind of Brooklyn writer who takes notes in Moleskines.) She writes relatively little down—she goes through about one notebook a year—and sometimes can’t read her handwriting. But the record of thought proves useful as she tries to distill several months of reading into a few hours of unforced action.

The more intensely Baker has focussed on stripping conventional dramatic style out of her plays, the further she has wandered from her earlier work; today, she tries to distance herself from “Body Awareness” ’s straightforward style. “ ‘Body Awareness’ was written with very little thought about physical space and time and duration and design and all of the things that I think are integral to writing for the theatre—the first things I think about now when I sit down to write,” she said, working her way around a curve in the cemetery path. When the play was produced, her favorite parts had little to do with the dialogue. Instead, she loved the drama’s loose ends—details she’d put in on a whim, like a small wind instrument that Frank inexplicably carries in his pocket.

Trying to find a technique to help her draw out these moments, Baker went to graduate school in 2007, when she was twenty-six. She wanted to teach, and, even more, she wanted to work with Mac Wellman, a playwright, novelist, poet, and professor at Brooklyn College. A generation of young theatre writers passed through Wellman’s hands; his students included Young Jean Lee and Sarah Ruhl. Although he considers Baker among the three or four best dialogue writers he’s encountered, he also believes that playwrights fuelled by nothing but their talents tend to burn out. He made a point of providing her with varied intellectual silage—“Finnegans Wake,” Wittgenstein, narrative theory, all seen through the dramatist’s eye—so that she’d have some means of reinventing herself if exhaustion or shtick set in.

Today, most of Baker’s plays begin not with dialogue but with a conceptual constraint. In Wellman’s class, she’d read Mary Douglas’s book about circular plot structure, “Thinking in Circles,” and wanted to write a circular play, with the focal point in the middle (a plan she eventually abandoned). She had also been poring over transcripts of Fritz Perls’s Gestalt-therapy sessions, at the Esalen Institute, in the sixties. “Circle Mirror Transformation,” the play that arose from this study, follows a six-week small-town acting class whose members progress through a series of drama exercises—reciting one another’s biographies in the first person, improvising sentences one word at a time—and, in the process, reveal so much that their relationships start to strain and change.