The over-arching change Arnold makes over the course of the book is his move from identifying as an outsider in many ways to seeing himself as an insider, or as part of many different tribes. Arnold knows he doesn't fit in in the tribe. People mock him and beat him up due to his disability and character quirks. He also doesn't fit in at Reardon, as demonstrated by the racism he's subjected to there. He struggles to fit in in both worlds throughout the novel, and it takes some time before he comes to the realization that it's okay to have many different aspects of his personality. He realizes that,
"sure, I was a Spokane Indian. I belonged to that tribe. But I also belonged to the tribe of American immigrants. And to the tribe of basketball players. And to the tribe of bookworms.
And to the tribe of cartoonists.
And the tribe of funeral goers.
And the tribe of beloved sons.
And the tribe of boys who really missed their best friends.
It was a huge realization.
And that's when I knew that I was going to be okay" (pg 190)
Though this change from exclusion to inclusion is the biggest that Arnold experiences, it isn't the only one. Another change he makes is from a lack of opportunities to having opportunities. Arnold knows that the rez is not a place where dreams come true. He talks about the dreams his parents and sister had, and who they would be if they weren't Indians living on a reservation, if they had opportunities. This situation is hit home to him when he gets his geometry textbook and sees that it's the same one his mother used when she was a student:
"And let me tell you, that old, old, old decrepit geometry book hit my heart with the force of a nuclear bomb. My hopes and dreams floated up in a mushroom cloud" (pg 34).
This event sparks Arnold's choice to go to Reardon High and sets him on a course to expand his opportunities in life. He sets himself up to graduate from a more prestigious high school, he makes the basketball team, he meets people from different walks of life. This is a personal growth that will continue to benefit Arnold.
One final way Arnold grows is in his social-emotional intelligence. As a frequent victim of bullying, Arnold has seen the worst side of people. During the course of the novel, however, he comes to discover that most people have both good and bad, including himself. When he thinks about Penelope, he is way too caught up in her looks and her ideal white-ness, rather than how much they have in common. As both Rowdy and Gordy point out, this is superficial of him, and rather sexist. Still, in his speculations on Roger after Roger secretly gives him some cash to pay for dinner and a ride home is that Roger is "of kind heart and generous pocket and a little bit racist" (pg 119). Clearly, Arnold realizes that people can be more nuanced than he previously thought.