Some recent discussions on twitter and on google plus got me thinking about my own homework policies. An Alfie Kohn article that I had read back in grad school and now reread as a result of these discussions posits that homework at any level is at best, useless, and at worst, actually detrimental to learning. In my Algebra classes (which is primarily what I've been teaching the last two years), I give about a page's worth of homework four times per week. Students are expected to check their odd answers at home, mark the problems that are incorrect, and fix them if they can. At the start of the next class, students check any even problems (usually only one or two of these), and discuss with their group the problems that they did incorrectly, but that they couldn't fix on their own. Then, as a class, we discuss any questions that the group couldn't resolve, as well as problems that I just thought were interesting or that bridge to the next lesson. Students turn their homework into group folders and get back their graded homework from the previous day.
The first thing that I do with a homework assignment is determine whether every problem was attempted, the answers checked, and incorrect problems were corrected in a way that demonstrates understanding. I look at the work and write notes if the thinking demonstrated was creative or elegant, or on the other hand, unnecessarily laborious. If there are skipped steps in work or problems that are incomplete, I circle the problem number. If there are errors, either of understanding or careless in nature, I circle and make a slash through the problem number. Each homework assignment is worth 3 points, and I grade based on how well I believe the student understood the lesson. A score that is less than 3 means that I want the student to correct that assignment and turn it back in to me (they will need to fix the circled and the circled & slashed problems). A student can correct and turn in work as many times as they want until the unit is over. They can ask me or other students questions in class to get help with an assignment or they can see me outside of class (there are designated times in the schedule for students to meet with teachers). Almost every assignment, whether it scored a 3 or not, has comments on it that I want the student to read and think about.
Homework is about 20% of a student's grade in my class, but I find that there is a very high correlation between homework grades and grades on quizzes, tests, and projects for most students. (Yes, there are exceptions... for those students that legitimately don't benefit from the homework because their in-class work is sufficient, I handle homework differently.) At the beginning of the year, students are not great at checking and correcting their work on their own. I emphasize homework corrections as a way to understand their errors and deepen their understanding, but I push them in the direction of checking their work and learning to ask for help before they turn their assignment in so that they ultimately are not dependent on me for going through their work and giving them feedback.
One of the pros of my system is that students take homework seriously. They know that I look at every problem and that I use it to assess their understanding of the content. I think that the detailed feedback they get on assignments and the emphasis on correcting and understanding, rather than just completing, is helpful for their learning. The main con of my system is that it takes so darn long for me. I do spend about 30 minutes per class per assignment (this varies between 45 min at the start of the year and 15 min at the end of the year). I also wonder if it's a helpful system if their future Math teachers treat homework very differently (most of the high school teachers either spot check a few problems a few times a week or collect homework at the end of the unit and grade on completion or sometimes, don't count homework at all), but my goal is that by the end of the year, it is internalized and seen as helpful for their learning so that they will continue to do their best work regardless of how it is graded. And isn't that the point of most techniques and habits of mind that we teach?