What a great question! Parents and teachers want to see students doing an optimal amount of work--enough that they progress without being overburdened. Of course, the factors in this equation vary for each individual student.
According to guidelines from Harris Cooper of Duke University, teachers should use the "10-minute rule":
"'The "10-minute rule," Cooper said, is a commonly accepted practice in which teachers add 10 minutes of homework as students progress one grade. In other words, a fourth-grader would be assigned 40 minutes of homework a night, while a high school senior would be assigned about two hours. For upper high school students, after about two hours' worth, more homework was not associated with higher achievement.'"
So, a third grader should have roughly 30 minutes of homework.
As a former classroom teacher, I would agree but with the caveat that this does not include study time. Some skills, such as foreign languages should be practiced for 10-15 minutes every night. And some time must also be set aside for steps in long-term projects, such as essays or science fair projects.
Additionally, I highly recommend that each child read a book of his or her choice for at least 20-30 minutes a night--though if you can find the right book, hopefully your child wants to continue reading more!
As a contrarian intellectual, I'm usually all too ready to laugh at most "expert" opinion, especially from elite educators! But I really did like this answer. The 10-minute rule. It rings true for me. I can't imagine that a half-hour would hurt or oppress a third grader. (Never mind what Alfie Kohn says!) Thirty minutes is just enough to create a rhythm of doing something at home. I note that 12th graders would be doing two hours. Seems to me I did almost three. But I would be quite pleased to find that typical high school seniors are doing two hours...On the other hand, if your child doesn't object, try the 12-minute rule. Or the 15-minute rule. Of course, you don't tell the kids that...Another way to go at it is to block out more time than you hope to get and say, "Well, it's like study hall. You do home work, you read, you think.." and hope the smarter angels will prevail.
I very much like the 30 min rule. My daughter is in 3rd grade and her teacher is homework crazy. It takes us 3-4 hours every day and on the weekend 4-5. It has been rough not just on my child but on me. I am a single working mom that has do housework. After getting done with the homework I have a rough time cleaning and cooking so we end up eating microwave dinners. My daughter has no time to play. Last week she had to write a book report, read 2 book and do 200 multiplications for math.