The way Miss Caroline runs her classroom provides a window onto why these students might grow up to be as narrow minded as their parents. She is an outsider, to be sure, from "north Alabama, from Winston County," and uncertain in her place, she rules the classroom in a very authoritative and condescending way. She treats the children as if they know nothing at all rather than with respect and dignity, a mirror of the way whites view blacks in Maycomb and throughout the south. Just as whites regard blacks as no more than children that needed to be guided and punished, so she treats the class, slapping wrists to maintain order and reading them nonsensical books. She thinks she is being generous to Walter, but in fact she insults him, and that provides another analogy to the "Christian charity" of whites in regard to blacks. Miss Caroline is the complete opposite of Atticus, who raises his children with respect and a sense of democracy, and that is how Jem and Scout will understand others when they are adults.
Lee cleverly uses the character of Miss Caroline as an outsider's perspective to show readers a full picture of Maycomb, and through Maycomb, Southern culture. Seeing Miss Caroline interact with the kids is like looking through a television or at a picture. Her misunderstandings help Scout as narrator to better explain her world.
For example, Miss Caroline tries hard to discipline the Ewell boy and to bring him in as a part of the class. This allows Scout to explain that the Ewell's don't go to school and that the school accepts this. She also explains the nature of the Ewell family. Readers understand that part of the Southern culture includes both poverty and ignorance, people trapped into past behaviors who are unwilling to expand their horizons and change their ways. The situation with Walter Cunningham shows also demonstrates the past. Walter is a victim of poverty. Walter's father uses the barter system, which is accepted by the town members, in order to pay his bills. This situation also demonstrates Southern pride. Walter is proud and honest. He can not pay back the quarter Miss Caroline tries to lend him and so refuses to accept it.
Overall, Miss Caroline is pitied by the children because she doesn't understand the culture of Maycomb - which proves how important culture and tradition are in Southern communities.