A response to the question:
What purpose(s) does math homework achieve? How do we make math homework effective in helping students learn? I am interested in hearing different philosophies about the purpose of giving homework in math. Thanks.-------------
When I assign homework in mathematics I try to make sure it is to REVIEW content we have already learned, to provide some independent practice. Because it is practice, I don't grade it for correctness (even though we DO correct the work the next day). I want my students to be able to take some risks, and I find they are much more likely to do that if they aren't penalized for being wrong, so the homework grade is mostly an effort grade. (In my school system homework counts for only 10% of the total grade, so this isn't a problem for me.)
I try to assign something that will make them think, and will help them review more than one thing at a time. If we are doing some computation work, maybe I will ask them to use their estimation skills to select 5 problems on the page that will have answers over 5 (since I HAVE all the answers it isn't too hard to figure out a limit) and then just solve those. Or I might ask them to do the first 4 and then write new problems that have the same answers as the first four.
To grade the homework I have groups of students talk together about the answers they worked out, justifying their ideas with proof (rather than with loud voices -- we spend some time discussing how to do this!) They are just fifth graders, so this is a great was to give them ownership of their work, and empower them to be math "experts". Then we talk about the problems the small groups couldn't come to a consensus on.
I should also say that I rarely assign more than 10 problems, usually less than that, actually. I believe that if they know how to do they work, it is a waste of time to do a whole page worth, and if they don't know how to do it, they are practicing mistakes, and imprinting THEM instead of correct procedures.
Often, the work I assign can be completed quite easily, too, but with a bit more effort, could be a challenge. For example, last week the homework was to write an addition, subtraction, multiplication and division problem that all had the answer 2.46. When we checked the work in small groups, I found (as I listened) that several students had used 1 and 0 to achieve their answers (1 X 2.46 = 2.46, 2.46 - 0 = 2.46 etc.). I used the whole group time to ask students what they thought was necessary to earn an "outstanding" on the assignment, then, when they said the answers should all be correct, I put the four equations on the board and asked them to decide what grade they would give the work.
To my delight, most decided the work was correct, but didn't show them much about what the student knew, since the identity elements were something they had learned in earlier grades. They said it didn't take much effort to do that work, so it shouldn't get more than a satisfactory grade. I then countered with the question, "How many of you were able to choose answers that worked on the very first try?" and many hands went up. I reminded them that if they could "do it quickly in their heads, it wasn't very challenging, either, so that wouldn't be worth more than a satisfactory grade either... and we spent some time discussing how to show effort.
Mind you, this is just a 10 - 15 minute time period during my total math time. I find I learn a lot about what my students are thinking as I listen to their discussions, though, so it is well-spent time.
So, to sum it up briefly, I think homework is an opportunity to reinforce what is learned in the classroom, and can be more than busy work, if the problems are chosen to help students think about the mathematics they are doing, and they are required to justify their responses.
-Gail, for the T2T service
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