Symbolism, Imagery, Allegory
Natalie's button box is her prized possession, and she sits for hours, counting and re-arranging its contents: "[S]he knows more about those buttons than it seems possible to know. If I hide one behind my back, she can take one look at her box and name the exact button I have" (1.8). This quote does two things that really matter: It clues us into the fact that Natalie is different, and it also lets us know that she's really good at something—her memory and observation skills are pretty freaking keen, at least when it comes to her buttons.
Why is this such a big deal? Throughout the book, Natalie is treated like a problem to be solved—particularly by her mom. Life as Natalie knows it simply isn't acceptable long term to Mrs. Flanagan. But in the first clue we're given that something's different about Natalie, it's presented as a strength or skill, not a weakness. And in the end, things start truly looking up for Natalie because Moose is able to get their mom to see that Natalie isn't broken; she just is who she is.
Throughout the story, whether it's healthy for Natalie to play with her buttons is a big question. At the urging of Natalie's (latest) doctor, Mrs. Flanagan tries to take them away a few times, though this only results in mayhem. Underlying this is an even bigger question: Is the best way to help Natalie to change her routine, or let her continue her habits as she's created them? At its heart, this is a question about authority, and whether Natalie should run her own show or follow the path others lay out for her.
Since Natalie throws epic fits when she doesn't get what she wants, it's always been easier for the Flanagans to just let her do her thing. As Moose explains, "Sometimes Natalie's tantrums go on and on for days and nothing makes them stop" (2.36). Yup, we'd probably let her keep her buttons, too.
The trouble, though, is that Natalie's relationship to her habits—like playing with her buttons—is a barrier to her ability to integrate into the bigger world. In fact, the button box ends up being the reason she has to leave the Esther P. Marinoff School; she throws a huge tantrum when they take it away from her. When Moose and his mom go to pick Natalie up, the administrator they meet with says, "I'm afraid she… there was a bit of a skirmish over a box of buttons and some unfortunate behavior" (11.39). Instead of trying to work through this with Natalie, the school just asks her to leave. Ouch.
The Marinoff School aren't the only folks insisting Natalie change; when she meets her new therapist, Dr. Kelly, she is not a fan of the buttons either. Moose's mom tells him: "'She says we need to do a clean sweep. Throw away Nat's button box. They'll be no more counting for her. No more obsessions'" (13.15). Again, then, we see authoritative professionals insisting Natalie change her ways, instead of trying to figure out how to help her get by in the world and be herself.
Moose is skeptical of this whole no-more-buttons idea, to say the least. And whenever he's in control, Natalie gets her buttons. And the thing is, we never really get a clear idea of who has the right idea—though they're treated as deal breakers, we never see the buttons really make or break a situation. Instead, more than anything, the buttons highlight Natalie's difficult behavior and habits, the difficulty everyone has trying to help her, and the resistance the world has to someone with autism. Buttons or not, Natalie is autistic, and nothing is going to change this.