Harper Lee expresses an opinion that the schools were very structured to the detriment of the student. Scout already knows how to read and write. Her teacher tells her to stop.
"We don't write in first grade, we print. You won't learn to write until you are in the third grade." (pg 18)
"Now, you tell your father not to teach you any more. It's best to begin reading with a fresh mind. You tell him I'll take over from here and try to undo the damage...." (pg 18)
Consequently, Scout wanted to quit school. How is a first grader suppose to forget how to read and write? How are her needs being met? Miss Caroline has just learned a new method of reading and that was suppose to fix all. They believed that the schools were the only source of education.
Later inthe book, when Miss Caroline introduces "democracy" she basically introduces the term. She touches on Hitler, but the children seem to be much more aware of hatred and prejudice. They take an active part in the discussion, but she moves on to arithmetic. It is ironic that she says,
Over here we don't believe in persecuting anybody. Persecution comes from people who are prejudiced." (pg 244).
She is saying this to a group of children who are in a society that is very prejudiced and just condemned and killed a black man who wasn't guilty of anything. In fact it is doubly ironic because one of the children asks about the Jews,
"...that ain't no cause to persecute them. They're white, ain't they?" ( pg 245)
Notice that there are no blacks in their school either. The schools also bent the rules when it was inconvenient for them to continue working with the children. The Ewell children only came to school one day a year, and even the truant officer had given up on them. They bent the rules for them.
As for what the children learned outside of school, one of the lessons that repeats throughout the book is to put yourself in another person's shoes before you make a judgement of them.
When Scout doesn't want to go to school, Atticus tells her
"...if you can learn a simple trick, Scout, you'll get along a lot better with all kinds of folks. You never really understand a person until you consider things from their point of view.......until you climb into his skin and walk around in it." (pg 30)
This piece of advice allowed Scout to accept Miss Caroline's decisions. Another example is when the mob attempted to get ahold of Tom Robinson and Scout talked Mr. Cunningham out of it. Atticus remarks,
"Hmp, maybe we need a police force of children...you children last night made Walter Cunningham stand in my shoes for a minute. That was enough." (pg 157)
Both Jem and Scout could see how it was important to do that. Finally, when Jem expresses a concern over Bob Ewell's threats to Atticus, Atticus tells him,
"Jem, see if you can stand in Bob Ewell's shoes a minute. I destroyed his last shred of credibility at that trial, if he had any to begin with. He had to have some kind of comeback, his kind always does." (pg 218)
This allowed Jem and Scout to come to terms with Bob Ewell's threats..
The page numbers I have given are for my edition of the book. They should be somewhere close. Check the chapters referenced below if you are having a hard time finding them.