While there should be no absolute rule that teachers may never give homework to elementary school students, I think it is a good principle in general to keep homework at a bare minimum at this age.
First, we must remember the psychological effect homework can have on the child’s perception of school in general. No child enjoys homework; it involves working alone, without the productive and enjoyable atmosphere of the classroom (though this may vary depending on the school), and coping with problems independantly. While independant learning is important, the child should not feel isolated and alone when learning school subjects. Because the homework can be so unenjoyable, the child might start feeling negatively towards school in general, which is certainly counterproductive to the learning experience of the child. Homework also creates divisions between the students- those who did and did not do homework, those who got answers right and those who didn’t, etc.- which could add to the isolation of students.
Second, bringing schoolwork into the home could take away from the child’s free time, which in some cases could be a serious disadvantage. Many children enjoy productive extracurricular activities- from music lessons to playing Chess to reading books- and this time would be taken away by homework assignments. At this stage in the child’s development, such activities could be very helpful and enjoyable, and might be much more valuable than homework. Of course, the same can be said of social activities with other students, which shows again how homework can divide students; how common is it that a student can’t go to a friend’s house because he or she is stuck with homework?
Third, the homework itself can be very frustrating if the student has trouble. In a class, the child can ask friends or the teacher to help them with their assignments, and in general the child does not feel alone in failure, since there are bound to be others who, like him, are having trouble. At home, the only people the child can ask are his parents and siblings, and this is less optimal for two main reasons: first, these members might not always be available, and even when available might be bothered by continual requests to help with homework; second, these people do not have the skill teachers have in explaining how to solve a problem and fixing the problem, and so would be less useful to a struggling student.
All these problems grow less significant as time goes on, and in high school they are quite insignificant; homework assignments can be given accordingly. However, especially in the very first years of school, it would be wise to give homework only if absolutely necessary, and even then in moderate amounts and difficulties.