In international school, there are many students who often don't listen to their teachers and behave badly.

Correct: In international schools, there are many students who don't often listen to their teachers and who misbehave.

Explanation: In negative sentences, verbs come first after adverbs. Choose appropriate words in your sentence. Use "misbehave" to make your sentence better.

I think these are why students don't listen to teachers well:

Correct: I think these are why students don't seem to be interested in class:

Explanation: What really happen is that students do not focus in class because they are not interested in their teacher. They listen but they do not pay attention.

First, teachers don't punish students in effective ways.

In local schools, reward and punishment are very vivid but in international school they just make them to have 15 minutes detentions at lunch time when they didn't bring textbooks and other materials they need for class.

Correct: In local schools, reward and punishment are very vivid but in international schools they just make them to have 15 minutes detentions during lunch time when they didn't bring textbooks and other materials they need in class.

All students do in detention time is just staying in classroom without talking.

Correct: What detained students do is just to stay long in the classroom without talking.

Explanation: Avoid redundancy. When you already used a word in your previous sentence, use a different word that conveys the same meaning to make your essay comprehensive.

So students are not afraid of having detentions.

Correct: So, students are not afraid of being punished.

Explanation: Avoid redundant words. try to rephrase or use synonymous words in your sentence.

Second, the pressure of parents and teachers about studying and test score isn't heavy.

Correct: Second is that the pressure on parents and teachers about the student's academic performance is not heavy.

Explanation: Use the right preposition in your sentence. Pressure comes with "on" when it pertains to putting weight on something. "Put pressure on" is an idiom.

Although they get low marks or do things that they shouldn't do in school, parents don't care much.

Correct: Although they get low grades or do things that they shouldn't do in school, parents don't care much.

Explanation: Use grade instead of mark when you are pertaining to a result of your performance in school. "Markings" are what teachers use designated to some measurement.

And teachers also don't care much unless the situation is really serious.

Finally, students of international schools have much freedom then local schools.

Correct: Finally, students in international schools are more free than those in public schools.

Explanation: Students are not owned by schools. We do not say "students of" but rather "students in". Be mindful of words when

comparing things. We use "than" to show that something has a different value with another.

They can bring phones to school and use them in break time.

It makes students to not behave like students.

Correct: It makes students to behave inappropriately.

Explanation: To avoid redundancy of the word "student", use a different phrase.

I think students and teachers both have responsibilities of behavior.

Correct: I think, both students and teachers have behavior responsibilities.

Explanation: When you say "responsibilities of behavior" behavior is responsible of something and it is the doer of the action. Since it is the object in the sentence, we better say "behaviors responsibilities" that means responsibility on one's behavior.