Miss Caroline is Scout Finch's first-grade teacher in To Kill a Mockingbird, by Harper Lee. If being unaware is being insensitive, Miss Caroline is, indeed, insensitive to her students' needs.
This is Miss Caroline's first teaching assignment after graduating with her teaching degree, so she is very young--not even twenty-one years old. While she is certainly a trained teacher, Miss Caroline is not particularly able to adapt what she was taught with the students in her Maycomb County classroom.
One way Miss Caroline seems to be insensitive to her students' needs is telling Scout that she could not have learned to read properly because her father (whom Scout says helped her learn how to read) "does not know how to teach." Miss Caroline punishes Scout for knowing something which she should be applauding her for being able to do.
Miss Caroline does not know her students. She reads her class a story about some cats which are silly and human-like; while the children are respectful as she reads, they are clearly not interested.
Miss Caroline seemed unaware that the ragged, denim-shirted and floursack-skirted first grade, most of whom had chopped cotton and fed hogs from the time they were able to walk, were immune to imaginative literature.
Miss Caroline is doing what she was taught, but she is not adapting her plans to the students in her classroom. When she tries to teach them the alphabet, the class is bored because most of them are repeating first grade--some of them more than once. Later she tries to teach them what Scout calls the Dewey Decimal system.
The Dewey Decimal System consisted, in part, of Miss Caroline waving cards at us on which were printed “the,” “cat,” “rat,” “man,” and “you.” No comment seemed to be expected of us, and the class received these impressionistic revelations in silence. I was bored, so I began a letter to Dill. Miss Caroline caught me writing and told me to tell my father to stop teaching me. “Besides,” she said. “We don’t write in the first grade, we print. You won’t learn to write until you’re in the third grade.”
Again Miss Caroline seems more intent on teaching what she thinks she is supposed to teach than paying any attention to what her students' needs are.
Miss Caroline also does not understand the social and economic needs of her students any better than she does their academic needs. (Of course, the students know that is because she is from Winston County in Northern Alabama, and everyone knew that "North Alabama was full of Liquor Interests, Big Mules, steel companies, Republicans, professors, and other persons of no background.") When she blithely offers Walter Cunningham a quarter to buy lunch and says he can just pay her back, she has no understanding about the level of poverty in which some of her students live.
In short, Miss Caroline is not deliberately mean or hateful toward her students; she is, however, so focused on doing what she has been taught (and has no doubt laboriously prepared) to do, that she is unable to meet--or even recognize--the needs of her students. On a positive note, this is only her first day of teaching and we know that Scout makes it to second grade, so Miss Caroline may have learned a little bit about adapting her teaching to the needs of her students.