Homework assignments typically have one or more purposes. The most common purpose is to have students practice material already presented in class. Practicehomework is meant to reinforce learning and help the student master specific skills.Preparation homework introduces material that will be presented in future lessons. These assignments aim to help students learn new material better when it is covered in class. Extension homework asks students to apply skills they already have to new situations. Integration homework requires the student to apply many different skills to a single task, such as book reports, science projects or creative writing.
In particular, math homework has been shown to be more important in the middle to high school grades and less important in the elementary grades. It starts to become important in the fourth grade and is increasingly important in the upper grades.
http://www.ed.gov/parents/academic/involve/homework/part.html
