Because Chapter Two of Harper Lee's To Kill a Mockingbird deals with Scout's first experience with public school, some of the things we learn about Scout in here reveal the life she has led at home.
We discover that Scout has been wishing for a long time to go to school; her anticipation is seen as she watches the children in the school yard from a tree. Unfortunately, Scout runs into problems with Miss Caroline, her teacher, ironically because Scout can already read. It's not just that she can read a storybook, but she can read a newspaper: even the financial section. We discover that Atticus has been teaching to read at home and she has excelled. Jem says she just sort of started reading on her own, almost born to it. She is scolded by her teacher. (Later Atticus agrees that what they read at home will be done in secret.)
Scout also has learned to write from Calpurnia, and not just printing, but writing, as she copies scripture from the Bible. Her education has come to her through non-traditional ways, in the teacher's opinion, though for many years, children would be schooled in things at home.
We discover, too, that Scout is a part of the community as a whole in the classroom. She and the other children are well aware that the Cunninghams have no money. The children must have some respect for Scout's ability to speak with adults as they suggest that she try to explain "about the Cunninghams" to Miss Caroline, which does her more harm than good.
Scout is a very mature little girl, who—in this case—is punished or censured for knowing too much. Her abilities and attempts to assist the teacher are not appreciated at all. She has learned many more things at home that most children of her age, and is more mature than one might expect.
As is so typical of children, what transpires at home is considered the norm for everyone else. Therefore, when Scout volunteers information to Miss Caroline, she does not understand why her teacher becomes upset with her since the equal exchange of ideas is an everyday thing. Also, Scout does not realize that she is precocious, thinking that there is nothing out of the ordinary about reading proficiently at such an early age. In addition, having been exposed to many situations involving her father and his clients such as Mr. Cunningham, Scout is dumbfounded when Miss Caroline grabs her and shakes her after having told her teacher that she is "shaming" Walter Cunningham. For, Scout believes that Miss Caroline will appreciate her explanations.
Because Scout has an attorney for a father, who raises his children in a liberal setting in a very conservative area, she does not understand that she is virtually an anomaly in her environment. When Miss Caroline "caught [her] writing," and tells her to instruct her father to stop teaching her, Scout is amazed,
Calpurnia was to blame for this. It kept me from driving her crazy on rainy days, I guess.
Certainly, Scout has always been treated like an adult by her father; therefore, when she is criticized for acting like one, she is dumbfounded and hurt.