To Kill A Mockingbird Question

Miss Caroline Fisher has been hired as a teacher. (Oh dear.) What are some of her (strongly-held) beliefs? Where and how do these clash with the kids she has in front of her? She does not seem to understand when Scout informs her that "Miss Caroline, he’s a Cunningham", referring to Walter who has not brought a lunch to school. The other kids turn to Scout to fill Miss Caroline in. This later gets Scout a caning. How does the other teacher referred to change the class’ behaviour with two sentences? And why does it work? Later, Scout hints that the whole idea behind school was that the State of Alabama meant for her to be tested with twelve years of uninterrupted boredom. What on earth is school for (in Maycomb County)? Does it work? And why would the grade sixes referred to by another teacher be studying the pyramids?