Jem and Scout are two siblings who live in Maycomb, Alabama. During this time period, we learn that there still is a lot of tension between black and white people in the area. However, at the beginning of the book, this does not significantly affect the children. Moreover, they do not feel the weight of the town's prejudices. Throughout Part I, however, this begins to change.
In the case of Scout, one of the main changes she goes through is trying to spend time with other children when she begins school. Scout can be stubborn and impulsive, and this causes her to have problems with her classmates and her teacher. This motivates her to be a little more patient, and a little kinder.
In the case of Jem, one of the main changes he goes through involves Dill and Boo Radley. Jem struggles throughout Part I between respecting what Atticus has taught him, and following his own path and his own adventures. Jem continues fighting these feelings of maturity and independence throughout the book. However, in Part I, he leans towards the side of impulsiveness in order to better fit in with the character of Dill.