How does the grammar book help you to learn your mother language correctly?

It shows you the proper form of reading and writing.

It makes you a more fluent speaker

It makes you a more fluent reader

Certainly it gives you the correct form and function of the basics like nouns, pronouns, verbs.... Casual speech is different than propper grammar even for native speakers. I'm not too sure what you want for examples but here are three common mistakes.

There ain't no way to understand. (double negative)

We went camping finding a good spot. (verb tense)

I'm sure he could go. (sentence fragament)