Most learning happens in class, and one should not overdo homework. Too much homework only antagonizes kids and in most cases, it does not help their learning.
On the other hand, a small amount of homework is a good thing:
- It is a form of differentiation, as it allows kids to take different amounts of time to do the same assignment. (The nature of what happens in class in a cooperative learning culture is that racing is discouraged, and kids work more or less at the same pace, with the faster students slowing down to help others.)
- It gets the message across that it takes work to learn anything substantial, and that while in class we work in groups, the ultimate goal is to understand the material well enough to deal with it on your own.
- It’s a place to do the often necessary but often boring work of basic drill and review, thereby saving class time for more interesting and substantial engagement.
In my class, a powerful argument in favor of homework came from the students themselves. In course evaluations, it was common for students to tell me that what helped them learn the most was going over the homework with their classmates. I usually allowed about 15 minutes for that at the beginning of class. During that time, I walked around and recorded a 0 (did not do it), 2 (great job), or 1 (somewhere in between). Students helping each other is far more efficient than me explaining things to the class, because it allows different tables to focus on the parts of the assignment they each need to focus on. True, there’s a risk that all the students at a given table are doing something incorrectly, but that doesn’t happen very often. Besides, after a quick homework check, I’m walking around, ready to intervene if I see this.
A teacher explanation at the board is sometimes needed, particularly if there is a similar question at more than one table. However in general it is not a good idea as it is boring for students who did the work correctly at home, and a waste of precious class time. Asking students to write solutions on the board does allow others to focus on the ones they need help with, but live conversation is more effective than silent copying of ill-understood techniques.
I don’t count daily homework as a significant part of the grade. I see it as a helpful part of the learning process, but not so much a valid assessment tool. However, because not all students work well under time pressure, overemphasis on quizzes and tests can be unfair. Thus, I give substantial weight to test corrections, plus a couple of major at-home assignments per trimester (projects, reports, and/or very tough problem sets — more on those in a future post.)
This is part of a multifaceted strategy to teach heterogeneous classes.
Read about it in this article: Reaching the Full Range.
–Henri
Homework links:
Lagging Homework
New Practical Advice Document
NY Times special issue
Henri's Math Education Blog 
A correspondent writes: “Some years ago Marilyn Burns wrote that homework could benefit from being something unique to the home. Volume is a good example—developing understanding, comparisons, etc. can be done easily at the sink with water or in the garden with sand or dirt. Great for home but harder in the classroom.” Good point! But perhaps more difficult to implement in high school?
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