Rotenberg says Peg isn't like "the two-dimensional female characters we often see in children's television."
Instead, "Peg is a complex character who real kids can identify with. Like any preschooler, she gets frustrated, has moments of totally freaking out, and then figures out a way to deal with problems and work with others to solve them."
She credits a lot of the success of that in the show from the young Connecticut actress.
"Peg's three-dimensional personality comes to life through the amazing voice behind the character," Rotenberg says.
Aronson says the show was originally aimed at a 3- to 5-year-old audience, "but we found that, as we tested math and watched the kids respond, that there's a wide range of what kids can do at different ages. Some kids at 3 are brilliant at math and some at the older ages are not so good and still have a hard time with it."
As a result, they never reveal Peg's actual age on the show, "because we want every kid to identify with her as much as possible." But privately, Aronson says, "we think of her as like 5, maybe 6 — kind of in the older range of our demographic."
"I'm not the same age as Peg," Hayley says, "but I feel like we have a lot in common. Like we both have a best friend that's always at our side and that if there's a problem, I always we can always solve it."
She also does a lot of things at home, like counting things in 5s, that she wouldn't ordinarily be doing. "Because I've been doing it so much [on the show], I feel like I can relate to her a lot," Hayley says.
Mostly, co-creator Jennifer Oxley says, "we try and make sure her voice is really relatable. She says things like, 'I'm totally freaking out!" and she uses words that I think kids would use. And, you know, Hayley is great with that because she keeps it real.
"Like, we'll be in the booth, and there will be lines of dialogue that are written for her, and she's like, 'That doesn't seem like something Peg would say,' or 'That word is kind of big. I don't even know what that means.' So it really helps us keep her very relatable. So Hayley's a huge help with that."
Aronson says they study Hayley to glean examples of kid authenticity. "There are certain things she says great," he says. "So we try to write them in as often as possible."
"Sometimes," Oxley says, "she says something in this really unique way that was totally unexpected, and we just make it part of her character.
"Hayley is just a joy to work with. She has like so much energy. I mean, I feel like she is Peg. Peg is energetic and so full of life, and so is Hayley. In between takes, she's doing cartwheels in the halls."
She also reports that Hayley draws "these amazing doodles" on her scripts in between takes. They are so striking they took one of them, scanned it in a computer and pasted it up on Peg's refrigerator in the show.
Though most of the questions at the press conference were for the grown-ups, Hayley says she enjoyed taking the trip to Los Angeles with her mother for the sessions, especially because of side trips to see the Hollywood sign and the homes of people like Kim Kardashian, Miley Cyrus and Justin Timberlake.
She's still going out on auditions for other acting jobs, with her ultimate dream landing a job on a kids' show on the Disney Channel or Nickelodeon.
But with PBS committed to making 40 initial episodes of "Peg + Cat," her voice will be heard for quite a few years on public television.
Back home, Hayley still has time for regular kid activities, mentioning "lacrosse and basketball and tennis and soccer."
"It amazes me that Hayley hasn't bragged to anyone about starring in the show," says her mother, Jara Negrin, a writer. Her husband Russell is a clothing manufacturer, and she has a 13-year-old brother, Sam. "She tells nobody and Russell and I tell everyone! She's extremely humble."
So far, Hayley says, nobody at school has gotten jealous of her new job.
"My friends are really supportive. They say, 'Have fun today!' They're nice. They say, 'I'm so proud of you!'"
Just the way Peg would say it.
"PEG + CAT" premieres on PBS Oct. 7, locally on CPTV, airing twice daily Monday through Friday, at 9 a.m. and 3 p.m.