As adults, there are times when we try to get out of the rut vary our daily routine in some way in order to stay motivated to do our daily chores. If we were in a classroom learning a new language, we would probably feel bored if the teacher used the same teaching format in all the classes. However, when it comes to teaching children, establishing a routine is an essential tool to cultivate a safe and comfortable atmosphere inside the classroom, while also helping the teacher in the application of their lesson planning. In addition, an appropriate classroom routine is also a constructive tool for the child learner, as it allows them to develop their independence and autonomy, as well as stimulating their socialization with peers and teachers.

We don't normally talk about getting out of a rut. We usually talk about being stuck in a rut, not getting out of it.

In addition, you cannot talk about "the" rut (using a definite article) without first introducing us to the topic of "a" rut (using an indefinite article).

You didn't mention any particular "rut" so the reader is left perplexed as to what rut you can be talking about when you suddenly refer to "the" rut.

(Perhaps you talked about "a rut" earlier in the paper, in the introduction. If so, then it might be OK to talk about "the" rut here, as long as you have already introduced it earlier using an indefinite article. However, "to be stuck in a rut" is slang and feels too informal for the tone of an academic paper. I would advise you against using that expression in formal writing).

Is that right?

This looks quite good.  Just a couple of suggestions to consider. Good luck with your presentation, article, etc.

Is that right?