What would happen if every teacher decided what to teach?
One of the major difficulties we have in the community college is that students enter courses without knowing the prerequisite material. I am not suggesting they were not taught the prerequisite material, just that they don’t know it. In theory, they can go on to the next course knowing 70% of the material, but that means that there is 30% that they don’t know. To make matters worse, a student who crams, might forget half of what he knew when he took the final exam.
Most teachers review constantly. When I demonstrate a calculus problem, I don’t say, “The rest is algebra, so I’ll skip it.” I show them the algebra, and their homework requires them to practice the algebra. Suppose the students were never taught some of the prerequisite material, because their teachers thought something else was more important. This means the students would know less of the core material, making it harder for them next semester.
I understand that the teacher may be right and the curriculum committee may be wrong. Maybe it is less important to learn adding rational expressions than, well, almost anything else the teacher could teach. However, the class is not taught in isolation. The students are expected to be able to add rational expressions. When I teach partial fractions in Calculus II, I expect them to remember some of it.
Teachers have to remember they are part of a system. Ideally, students enter a class with a certain skills and leave with additional skills. If a teacher decides to substitute other skills, it does not benefit the student in the next course.