For me, motivation and engagement means that students actively participate in lessons and are excited for each new day of school. Having students be excited to learn is such a key factor to creating a healthy learning environment with limited disruptive behaviors.
One theorist that I relate to is B.F Skinner. Skinner did a lot of work in shaping behavior. I think that although there are some issues with Skinner's behaving shaping (it not being great at teaching students what NOT to do) it has a lot of benefits within the classroom. It allows for the teacher to increase praise to students which can help students create a growth mindset. It's important to remember that when you are constantly reprimanding a student they are going to begin seeing you as an enemy instead of a teacher and will only continue to demonstrate behaviors and pushback against your instruction. Its important to let students know what they are doing well, not just what they are doing wrong.
Another theorist that I relate to is Linda Albert. Albert believed that if students are not involved or interested in what's going on in the classroom behaviors will increase. Allowing students to be able to play a role in the classroom while learning will help decrease the amount of misbehavior. I think that this is such an important thought process because it highlights the idea that if our lessons are not reaching our students in terms of interest they are going to misbehave during the lesson.
One way to help increase motivation and engagement is to introduce external motivators to practice specific behaviors. One way I would do this is to introduce a classroom behavior tracker that allows the class to work as a team to reach a goal and earn a reward. It can also be changed and innovated depending on the age group and/or season/theme. It can be a marble jar, or a board game inspiredtracker where the class gets to move a piece when exhibiting good behavior. It not only allows the teacher to monitor and manage the entire classroom behaviors but also allows the students to work on SEL skills by keeping each other accountable on the self created classroom rules.