Explain Jem and Scout's interpretation of the Dewey Decimal teaching system that Miss Caroline uses.

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Jem and Scout got to talk about the Dewy Decimal System in chapter two. Scout had just started school and Jem wanted to know how she was doing when they spoke during recess. Scout was upset about the remark her teacher, Miss Caroline Fisher, had made about Atticus and Jem tried to comfort her. He told her that Miss Fisher was using a new teaching method:

“Our teacher says Miss Caroline’s introducing a new way of teaching. She learned about it in college. It’ll be in all the grades soon. You don’t have to learn much out of books that way—it’s like if you wanta learn about cows, you go milk one, see?”

It's clear that Jem believed that the new system was a practical, hands-on approach that did not focus much on theory which is learnt from books. His assurance did not, however, please Scout all that much so he he continued trying to reassure her:

“I’m just trying to tell you the new way they’re teachin‘ the first grade, stubborn. It’s the Dewey Decimal System.”

As far as Scout was concerned, the system consisted of Miss Caroline waving cards imprinted with simple, basic vocabulary at them. They were not expected to comment and had to quietly just take in what was revealed to them. Furthermore, it also seems as if Scout believed that the system did not allow any harsh or demanding threats, as she mentioned later, when it seemed as if Miss Caroline could not maintain discipline:

...the shadow of Miss Blount fell over them. Miss Blount, a native Maycombian as yet uninitiated in the mysteries of the Decimal System, appeared at the door hands on hips and announced: “If I hear another sound from this room I’ll burn up everybody in it. Miss Caroline, the sixth grade cannot concentrate on the pyramids for all this racket!”

In addition, Scout firmly believed that the system prohibited books for she comments in chapter four that:

no tutorial system devised by man could have stopped him from getting at books. 

She felt that the system was cheating her out of something, although she could not exactly put her finger to it.

The children's misunderstanding is quite humorous since the Dewey Decimal System is not a teaching methodology at all but is, instead, a classification system developed by Melvil Dewey for the general knowledge organization of books in the library. Their reference is quite ironic though, since Jem understood that they were not much needed and Scout was sure that the system prohibited the reading of books (or anything else for that matter) when it, in fact, had everything to do with them.

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This is a very innocent and funny part of the book. During this section, Scout and Jem are talking about Scout's new teacher, Miss Caroline. Scout already started off on the wrong foot with Miss Caroline. One of the reasons for this was because Scout knew how to read and might have been resistant to learning Miss Caroline's way. 

Jem told Scout not to worry about his teacher and her new method of teaching. In fact, Jem stated that his teacher stated that Miss Caroline learned this method from college. 

As Jem and Scout continue to talk about Miss Caroline, this is where the mention of the Dewey Decimal System comes in. Scout insists that Miss Caroline's new method of teaching is called the Dewey Decimal System. According to Scout, Miss Caroline prints words on cards and wave them around.

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.

As one can see, the Jem and Scout have no idea what they are talking about. It is childhood. It is meant to be humorous. 

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