As an outsider to Maycomb (she comes from the strange and far-off land of northern Alabama), Miss Caroline gets as many lessons from her students as she gives to them. As a main booster for the school's new educational system (what Jem calls the "Dewey Decimal System" [2.25]), she represents the outside world and reinforces the idea that Maycomb is its own little world.
Here's the thing about the Dewey Decimal System: it's all about rules and categories. And Miss Caroline is utterly unable to cope when Scout's reading and writing exceed first grade standards: "We don't write in the first grade, we print. You won't learn to write until you're in the third grade" (2.26). This is obviously absurd, but is it any different from the rigidly categorized social hierarchy in Maycomb? Maybe not.
Scout's encounters with Miss Caroline suggest that maybe the smarter approach is to adapt the rules when necessary. On the other hand, in facing off with her Scout learns that sometimes when stupid rules won't bend you just have to make a show of following them to get by.