Harper Lee’s descriptions of the school give readers a glimpse into the complexities of Southern culture. In particular, Lee highlights the diversity in socioeconomic class by focusing on the differences between the students and their teacher, Miss Caroline. Miss Caroline comes to Maycomb with expectations for all the children that do not take into account their context.

For instance, consider how Miss Caroline feels as if she must teach Burris Ewell about proper hygiene practices on the one day he is in school. Scout explains to her that the Ewells are extremely poor, and it is simply accepted that they don’t go to school. Scout feels that she must educate Miss Caroline about how things are done in Maycomb, which tells the reader that people in the South take pride in maintaining their way of life.

As Miss Caroline learns about the students, so does the reader, and we begin to learn how people’s socioeconomic status plays a role in the the way they act in the South. For instance, consider how Walter Cunningham refuses to accept the quarter Miss Caroline tries to give him because he knows he cannot pay it back. Walter is a child, and thus his pride in this moment must be a reflection of his father’s attitude. This tells the reader that legacy and familial ties are important in the South. Walter’s refusal also underscores that people in the South pride themselves on self-sufficiency. Consider how Scout explains Walter's actions here:

You're shamin' him, Miss Caroline. Walter hasn't got a quarter at home to bring you, and you can't use any stovewood (Lee, 15).

Because Miss Caroline is new to the area, she does not understand that urging Walter to accept the money actually brings him embarrassment and shame. In this quote, Scout tries to get her to understand that in this culture, it is better to respect a person's refusal of help than pressure them into accepting it.

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.

The school is a great place for the entire spectrum of Southern culture to be revealed, because children from all walks of life, from every demographic and socio-economic category all go to the school.  So, each type of person and every quirk of the culture can be represented through the children in one small classroom.  Even better is if the teacher is new to the area, and so must be "initiated" into the culture, either through direct instruction (as Scout attempts to do), or through personal experience (as happens when Miss Caroline tries to instruct Burris on his hygeine).

In the classroom, we get to see the rather infamous Ewell children first-hand, along with unsavory details about their appearance and dress.  We learn that they only attend the first day of school, so as to avoid the authorities and their meddling, and that education is of little value to the entire family; we also learn that their father is a no-good drunk.  We also learn all about Chuck Little, who was also poor, but "was a born gentleman."  Then there is Walter Cunningham, also poor, but with a proud father who refuses governmental help.  All of these different categories of people have their own way of living in the south.  Scout herself tries to inform the naive and uninformed Miss Caroline about the intricate ins and outs of Maycomb culture, but she doesn't receive it too well.

The classroom provides first-hand witness to some of the different social classes that exist in the town, and it does so in an amusing and harmless way, as a sort of precursor to the more intense and serious action that is to happen later on in the book.  Later, we see these same families behaving in rather unfortunate ways, and it helps to have a bit of background, through the school, before those events occur.  I hope that helps; good luck!