The Finch children grow both physically and emotionally during the course of the novel. Jem is approaching puberty during the second half of the novel, and his time spent with Scout lessens, much to her dismay.
Jem was twelve. He was difficult to live with, inconsistent, moody. Atticus said... Jem was growing. I must be patient with him. (Chapter 12)
Calpurnia recognizes that Jem is approaching his teen years, and she begins calling him "Mister Jem." Later, Jem tells of his plans to go out for the football team and proudly displays his newly-grown body hair to his sister.
He unbuttoned his shirt, grinning shyly.
"Well can't you see it?"
"Well it's hair."
"There. Right there."
... I said it looked lovely, but I didn't see anything...
"Under my arms, too..." (Chapter 23)
As for Scout, she fights tooth and nail every attempt to make her a lady in the first part of the novel. But Scout takes giant steps at becoming a lady in the final chapters. At the Missionary Circle tea, she follows her aunt's lead when Alexandra and Miss Maudie return to serving refreshments as if nothing had happened after learning about Tom Robinson's death.
After all, if Aunty could be a lady at a time like this, so could I. (Chapter 24)
And at the end of the story, her fantasy comes true: She meets Boo Radley face to face and escorts him home.
... if Miss Stephanie Crawford was watching from her upstairs window, she would see Arthur Radley escorting me down the sidewalk, as any gentleman would. (Chapter 31)