The teacher I observed for my service learning hours mainly used behaviorism.
The children know that there are rules that they must follow. They also know where to put there assignments and when it is time to do certain activities. The student's must raise their hands, or when they can get up to get a drink or something. They're also split into "teams" so that if they are caught doing something good, they get bonus points. What ever team earns the most points gets something (although I haven't quite figured out what that something is). Participation points are also earned when they finish an assignment correctly or answer a question correctly for the class.
The students have a very structured schedule, that include task that are repeated daily. Some of the task that happen consistently each day include things such as; turning home work into a bin, journaling, subjects such as math, reading, and science.
The teacher I am working with addresses the developmental levels and different learning preferences by having "centers" that the kids can choose from. There are about 12 different things to do and each child quietly has their choice and each center, for the most part, has different levels for each individual child to pick from. She also has a library where the kids can go "shopping" for ten new books every week. Each book contains a reading level, and each child is assigned to their individual reading level.
I think she uses behaviorism very well. She does an excellent job implementing a routine that is consistent for her students. The expectations are set and managed through consistently adhering to structure of behaviorism. When children are young, it's important that they're in an environment that is highly organized, has daily task, and assignments. This type of environment helps the child understand in a clear and simple way what is expected of them, but also what they can expect each day.