Classroom Management in Bath

I just completed my sixth day at St. Andrew's yesterday, which is sad to think about as my time here is starting to go by so quickly. Since I have been teaching there for six weeks, I have been able to see a lot of different classroom dynamics and have had the opportunity to really observe the actions of my CT and her students. I have definitely noticed an emphasis on conduct and discipline at my school, as good behavior, respect, and paying attention in class are highly valued and monitored throughout the school day. I consider myself to have a more laid-back teaching style than some of the teachers at St. Andrew's and I am nervous about how this will translate in my lesson that I am teaching next week.
St. Andrew's is a beautiful school, the students are wonderful and the staff is well-trained, attentive, and are some of the best teachers that I have ever seen. My CT is wonderful, the amount of love she has for her students is obvious and her level of skill and expertise is really impressive. I feel so lucky to get to observe her and I am learning a lot from getting to watch her teach and interact with her students.
My CT, Miss. Sandey, has high expectations for her students as she constantly tells them, "you are Year 5 and I expect more from you". They are expected to be on task, respect each other, and listen to the teacher, which I have found to be very similar values to ones that I have seen in American schools. While the values are the same, I believe that the promotion and regulation of these values is more strict than back in the states. The teachers are not likely to give out warnings or to let things slide, they are quick to be on a student when they are misbehaving and are not weary to embarrass them in front of the class if it means that it will facilitate good behavior. I find that this method of discipline works on the students as they are not only used to it since the majority of them have been in the school since Foundations; but it also is obvious to me that it works since even the worst behaved students are pretty well behaved, in my opinion. Therefore, I find it hard to discipline the students to the extent that my teacher wants me to because, compared to American students, I find them to be really well-behaved, courteous, and kind.
One of the major problems that I have found in my classroom in terms of behavior is their lack of eagerness to learn. Many of the students, upon being given a task, will choose to ignore the instructions and not participate at all if they see the task to be unfair or a waste of their time. I spend a lot of time throughout the day convincing students to do their work and trying to get them to engage with the material in the way that Miss. Sandey wants them to. I find that this type of behavior is more distracting and damaging to their ability to work in the classroom than other types of behavior; however, I feel as though other types of behavior are focused on more heavily by teachers than some students' lack of motivation. I come across this lack of motivation to do work often in my class and I wonder why it is so prevalent in British schools but not so much in American schools. I also am curious as to what I can do as a teacher to motivate and increase the learning outcomes of my students.