Case
Nonstop talking

I have a group of 12th grade students that just won't stop talking. I feel like I have tried everything and yet they still won't listen. I have tried positive reinforcement, enforcing punishment, and even ignoring it at times. What haven't I tried yet? I have no idea what to do next.

Solution #1
A great way to get a group to stop talking is to get them to interact with the lessons. Students aren't going to be quite, its impossible but if they're engaged in the lesson their less likely to cause stray off topic and instead be immersed into the lesson.
Solution #2
First, keep eye contact with the group's ringleader, also known as the student who influences all the other students to misbehave. Inform the student that you are taking names down of students that are not following directions to discuss alternative ways to support their academic achievement with their parents. Continue to take more students names down but only focus on one student at a time. This sends the message to other students that you are serious and the volume in the classroom should stop. Do not glare at students but maintain proximity with students who are not following directions.This lets them know you are aware of what they are doing. If the misbehavior continues give the student eye contact and tell them to meet with you after class. If you have tried parent conferences, you may want to implement collaboration activities and lessons into your curriculum. Students should have a clear understanding of rules and procedures. Follow guidelines and procedures with your school's district when moving forward with your next steps.

Singling out the ring leader is always a great first step to stop misbehavior in the classroom that involves several students. If you pick them out then other will probably quiet down in no time.

Solution #3
A possible solution to this problem is to move around the room while teaching. Taking time to stand next to the students that seem to be the chattiest and teach from there. This will discourage them for engaging in conversation since you are right next to them.
Solution #4
Proximity interference is a strategy you could test for this situation. It is a less invasive intervention approach that doesn't disrupt the class. If this doesn't work, I noticed that someone noted making the lesson more interactive to stimulate engagement. You could try using sites like kahoot! or use debate-style activities that involve the whole class. 12th graders are going to talk no matter what, and using that to your advantage by incorporating their need to talk into meeting objectives and stimulating academic achievement would provide a great opportunity to have the best of both worlds for yourself and your students in the classroom.
Solution #5
You can give them jobs that require talking, if that's what they love doing. For example, hand them a lesson plan, have them teach the class for the day and talk throughout the lesson to show how they are acting and go from there.
Solution #6
I think the first step is to figure out which group of students (or one) starts these conversations. I would walk around the class and talk about the lesson as I stand next to students. I feel like students chatter less when the teacher is right beside them. Seating charts can help and moving the talkative students next to the lesser ones could help too. Pulling students aside and holding them after class, let them know you will call their parents. If none of the solutions help, I think you should start handing out write-ups or detention slips. Warning the students beforehand that if it does not stop detention slips will be handed out.
Solution #7
I will directly seek out the person who initiates the conversation and then ask them to answer questions. If their conversation is still ongoing, I will continue inviting them to answer questions.
Solution #8
I think that a great idea for this age group is to have a lesson where you involve the class and let everyone participate.

That age is a bit tricky. But, you could sit the student in close proximity with you. Try including them in the lesson. If you are familiar with what they do, begin to include the students in the learning process. You could also give them responsible assignments that will engage them in conversations with other students (maybe leadership roles or something so that you are not constently talking to them).

Solution #9
Instead of trying to completely rid the students of talking in the class, try to re-direct it into something meaningful that contributes to their learning. Creating collaborative learning opportunities can allow students to socialize and learn, both of which are important for students.