What does Scout think of current fashions in education? What do her opinions reveal about Scout's character in To Kill a Mockingbird?

Scout does not approve of the Dewey Method or collaborative learning, showing that she is intelligent and opinionated.

When Scout starts school, she already knows how to read.  She and the rest of the sixth grade find their teacher Miss Caroline’s methods truly baffling.  This includes reading the class a story about talking cats. 

By the time Mrs. Cat called the drugstore for an order of chocolate malted mice the class was wriggling like a bucketful of catawba worms. 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. (Ch. 2) 

Scout’s teacher has no idea what to do with her.  She was not expecting to have a student in her first grade class who could already read and write in cursive.  She was expecting to teach them all the alphabet.  She feels threatened by Scout, and Scout feels puzzled and irritated with her.  She does not want the teacher to take reading away from her, because she values it as much as breathing. 

Scout is bored and frustrated with her class.  She tells Jem, and he tells her it is a new kind of teaching method. 

“Yeah Jem, but I don’t wanta study cows, I-”

“Sure you do. You hafta know about cows, they’re a big part of life in Maycomb County.”

I contented myself with asking Jem if he’d lost his mind.

“I’m just trying to tell you the new way they’re teachin‘ the first grade, stubborn.

It’s the Dewey Decimal System.”  (Ch. 2) 

Jem is confusing the teaching philosophy of John Dewey with the method of arranging library books.  Either way, Scout is not impressed.  She feels that her teacher is completely out of touch with Maycomb’s ways and its children.  She is so bored that she writes a letter to Dill, because she can’t wait for summer to arrive. 

Despite the misguided methods of her school, Scout does not seem to hold it against them. 

The remainder of my schooldays were no more auspicious than the first. Indeed, they were an endless Project that slowly evolved into a Unit, in which miles of construction paper and wax crayon were expended by the State of Alabama in its well-meaning but fruitless efforts to teach me Group Dynamics. (Ch. 4) 

It seems clear, however, that Scout is not really learning anything in school.  She is extremely precocious, and no one in her school is prepared to deal with that.  I guess they didn’t have gifted programs in the 30’s in Alabama.  Although she complains, Scout learns to generally go with the flow.