What was Scout's first "crime" at school in To Kill a Mockingbird ?
Scout's first "crime" at school is knowing how to read.
After putting the alphabet on the board, Miss Caroline asks the class if anyone knows what the letters are. Because Scout is among those who raise their hands and she knows Scout's name, Miss Caroline calls on her. However, when Scout recites the alphabet with great familiarity, her teacher then has her read from the primary reader, My First Reader, as well as the stock-market quotations from The Mobile Register. As Scout does so, her teacher watches with apparent disapproval. When Scout finishes, Miss Caroline instructs Scout to inform her father that he should not teach her any more, as doing so will "interfere" with her reading.
"Teach me?" I said in surprise. "He hasn't taught me anything, Miss Caroline.
...Miss Caroline apparently thought I was lying...."Now 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--"
When Scout expresses wonder at this remark made by her teacher, Miss Caroline explains that Mr. Finch does not know how to teach reading. Scout mumbles her apology, and she sits down, "meditating upon [her] crime."
This scene about Scout's knowing how to read, but Miss Caroline's informing her that it is not the correct approach is Harper Lee's humorous way of satirizing some of John Dewey's theories of education, and the inflexibility of some teachers who insist that children learn through a certain process, and no other way.