What does Miss caroline learn about several of her students on the first day of school?

Miss Caroline is a new and inexperienced teacher. It's the first day of the new term and she's completely out of her depth. Not only does she adhere to a rigid curriculum, she's also unfamiliar with her pupils, their personalities and educational needs. She's appalled to discover that Scout has been taught to read at home by Atticus. This may seem a rather strange attitude for a teacher to have, but it's a sign of insecurity and inexperience on her part. As far as she's concerned, Atticus is treading all over her professional prerogatives as a teacher.
It's not just Scout that Miss Caroline handles badly. She offers Walter Cunningham a quarter for his lunch as, of course, he doesn't have any money being as how his family is so dirt poor. The Cunninghams are indeed poor, but also intensely proud, and so won't accept charity from anyone. Scout knows this; the Cunninghams often provide payment in kind for the legal services rendered to them by Atticus. But when she tries to appraise Miss Caroline of the situation all she gets is a rap across the hand with a ruler for her trouble.
Burris Ewell has turned up for his annual day at school. As with the rest of his family, he's somewhat lacking in the personal hygiene department. His matted hair harbors a thriving colony of cooties, or hair-lice, one of which falls out on his desk. Miss Caroline tells Burris to take a bath before coming into school the next day. Once again, she displays total ignorance of the situation. Burris only comes to school once a year to fullfil the truant officer's obligations. This time, Miss Caroline appears genuinely interested when the children point this out to her. She then tells Burris to sit down, but there's no chance that's ever going to happen; Ewells don't take orders from anyone. He shouts right back at her, slouches to the door and then gives her some smack talk before leaving school behind for another year. A crying Miss Caroline now knows exactly what kind of pupil she's dealing with in Burris Ewell.