I think the answer lies in a combination of several factors. First, Scout and Jem have experienced a number of life-changing events during the course of the novel. Scout has met Dill and fallen in love with him. After originally fearing Boo Radley, she has come to fantasize about meeting him, and by the final chapters he has become her hero, coming to her rescue and saving her life to boot. She has seen a Maycomb jury convict an innocent man defended by her father, a man who is later killed trying to escape from prison. Her relationship with Jem has changed drastically, Aunt Alexandra has come to live with them, and she has had to worry for the safety of her father. These events have happened in just a few short years, but when Scout looks out upon her neighborhood from Boo's front porch, things look altogether different to her. The seasons pass by in seconds as she reflects upon all the things that Boo must have seen from his window. Just as Jem is growing older, Scout is also maturing. She has survived the missionary circle tea, where she decided that "... if Aunty could be a lady at a time like this, so could I." She has escorted Boo, arm in arm, back to his house. She has lived to tell about the murderous intent of Bob Ewell. Just as time seems to pass more quickly when a person is older, so is time passing for Scout. She is growing up, and suddenly,

I felt very old... I thought Jem and I would get grwon but there wasn't much else left to learn, except possibly algebra.  (Chapter 31)