Is homework important? Should homework be assigned?

What does the research say

Does Homework Improve Academic Achievement? A synthesis of Research, 1987-2003

Summary: There is a positive correlation between doing homework and student achievement which means that students who did homework performed better on standardized test. Cooper also found that homework can cause physical and emotional fatigue which fuels negative attitudes about learning and it can limit family and leisure time for students.

Does homework affect student learning?

Myth 1: Homework increases academic achievement.
What researchers say: Cooper (1989a) argues that reviews on the link between homework and achievement often directly contradict one another and are so different in design that the findings of one study cannot be evaluated fairly against the findings of others.

Myth 2: Without excessive homework, students’ test scores will not be internationally competitive.
What researchers say: Information from international assessments shows little relationship between the amount of homework students do and test scores. Students in Japan and Finland, for example, are assigned less homework but still outperform U.S. students on tests (Organisation of Economic Cooperation and Development 2004). Other studies find a positive relationship in math, but not in reading (Fuchs et al. 2004).

Myth 3: Those who question homework want to weaken curriculum and pander to students' laziness.
What researchers say: Kralovec and Buell (2001) note that homework critics rarely question the work assigned but rather the fact that the work is so often performed at home without adult supervision to aid the learning process. Taken from here

Other findings

Paschal, Weinstein, and Walberg (1984) discovered through a meta-analysis of fifteen quantitative studies that homework did have a positive effect on achievement, especially in certain grade levels. Specifically, traditional, daily, and graded homework had the greatest positive impact on student achievement in the fourth and fifth grades.
Townsend (1995) examined the association between homework and achievement in language acquisition among third graders. Results from her study indicated that students who were assigned homework scored higher on vocabulary tests than those who were not.
Mikk (2006) examined the association between homework and math achievement in forty-six countries. Interestingly, student achievement was lower in countries where homework counted toward grades, where it was the basis of classroom discussion, and where students corrected homework in class.
Swank (1999) examined the differences in test scores among fourth graders who either did or did not do homework. Her findings indicated no differences in math achievement scores between students in the two homework groups. Taken from here

It seems that the research is clear. There are some advantages to giving homework and there are some disadvantages.... So what are teachers supposed to do?