Students should have to do homework at home because it not only keeps their minds working while they aren't in school, but keeps them busy so they have a harder time getting into trouble. It's important for students to continue to work with their minds even after the school bell rings in order to not lose interest in school.
Yes, schools should give students homework, but teachers should go out of their way to make sure the homework they assign is not just busywork. When sixth graders end up spending hours to color maps, they are wasting their time. Homework that makes students read, research and think is valuable and should be continued.
While teachers should not give students hours of homework each night, some individual study outside of class is essential for learning the material. Material done outside of class forces the student to think critically and use the skills he learned in class. This practical application of skills and learning helps the student understand and remember the material.
Few students enjoy homework, yet such work helps them apply the lessons the learn during the school day. By applying the lessons in practical exercises, they master the skills, much in the same way that drills in sports help athletes master the sport. Homework also teaches students to be responsible, for at home no teacher is standing over them ensuring that they complete their assignments.
Students should have homework for them to apply concepts they learn in the classroom. Homework is a more involved form of learning than simply listening to a teacher, because homework is interactive and doing rather than listening. It also helps students to learn techniques such as critical thinking and research, which is important for the real world.
What lessons are there to apply to every day life? Obedience? Conformity? Submit to absolute authority?
I know what people think: "But how will they ever learn the quadratic formula?". Simple. Let them teach themselves. Give them the guide and the resources, and students will out-learn every previous generation. I remember a comment from Ron Paul's theory on public education- Give a child YouTube, books, and Wikipedia, and the child will eagerly accept the challenge.
You see, homework is only necessary for the -modern- system of education, the indoctrination system force fed to our children in order to produce the "machine" of society. When our children could spend their time developing immaculate minds, we standardize their minds through busywork- homework.
Homework can actually be a disadvantage to many children. Their parents might do it for them. They might get other students to copy their answers or even pay them to do it. Many might live in neighborhoods or even dysfunctional homes where homework is not doable. Schools are meant to be the educational environments and the learning should take place there, not over the weekend
Homework is often just busy work and is just there to give the teacher something to grade. If the teacher wants the student to apply what he or she has learned, they should have those assignments completed during class hours so that the teacher can help in the process. That's the whole point of school, after all.