Rethinking Math Homework

In all my time of teaching, I think the thing that has changed the most has been my approach to homework. I remember my own experience in high school, especially in Algebra 2 with Ms. Callahan, who assigned “every problem in every set” for each lesson in the textbook. Completing 30 or 40 tedious, monotonous problems seemed pointless to me at the time, and in hindsight, I’m sure it was pointless for just about every student. For most classes, lessons, and concepts, one has to wonder who benefits from so much practice. A student who understands the lesson well the first time will probably benefit from a small number of varied practice problems. A student who gets the main idea of the lesson would most likely benefit from a slightly larger homework assignment with a bit more repetition. A student who doesn’t have any idea what the lesson was about wouldn’t have any luck with a homework assignment of any size.

While some practice is absolutely necessary to reinforce concepts, procedures, and algorithms in math, my class assignments have become much smaller. Some of my algebra assignments are only 3 or 4 focused problems. However, it isn’t only the size of the assignments that have changed in my classes. An even bigger change has been my assessment of homework. Each homework is worth 10 points, but the points awarded are not a straightforward percentage. Instead, the focus of the points is on the process. A student who completes every assignment, and shows work, automatically receives at least 8 out of 10 points, even if they get every answer wrong. If they make some minor errors (arithmetic errors, forgetting units or negative signs, etc.), they still get 9 points. The awarding of points has encouraged students who may be unsure if they are doing a problem correctly to at least put something down on paper, and sometimes the act of starting a problem is enough to trigger the memories of how to finish it. Either way, they know that they have the ability to get 8 points, which is a perfectly fine grade.

The next steps that I have taken have had dramatic results. I started to require that students complete all of their homework assignments before taking a unit test. In fact, they have to have turned all homework in and had it returned to them before taking that test. This was met with some resistance at first, but students have come around because it leads to less wasted time and better overall results. I had too many students in the past who took (and failed) a test, and then did the homework and figured out what they had missed on the test. Worse yet, I had students who took and failed a test, and then took and failed a makeup test, due to never understanding or properly practicing the concepts on the test. So encouraging students to have their homework complete by making it a requirement, plus giving credit for attempting every problem, was beneficial. Even more beneficial, though, has been my policy on making corrections to homework. I now allow students to resubmit every homework assignment, multiple times, for full credit, up to and even after taking a test. I thought that it would benefit them, but wasn’t prepared for the dramatic difference in quiz and test scores. I may have small classes, but the data is quite telling. The average quiz grades of my trigonometry students who did not complete their homework (which isn’t a requirement for quizzes – only tests), has been 48% so far this year. For students who completed homework assignments, but did not submit corrections, quiz grades averaged 78%. Students who submitted corrections had average quiz scores of 91%! Even more impressive – when I first told students about some of the trends I was seeing, the number of students who didn’t submit homework on time dropped, and the number who submitted corrections grew, so these results are even more impressive than the original results earlier in the semester (44%, 81%, 88% for no homework, completed homework without corrections, and completed homework with corrections).

I am continuing to collect data and hopefully will submit these findings to a publications at the end of the school year, so more teachers can maybe think about how they are assigning and assessing homework. After all, the point of homework should be to give students the practice necessary to solidly understand the concepts that we are teaching, and if awarding more points gives them the motivation to keep improving, as teachers, we should be willing to do that. I’m not suggesting that every student should be given an A, but given the right tools, I can imagine a class where every student earns an A. At least, that’s one of the main things I strive for as a teacher.