Sunday, October 9, 2011

Homework

Have you ever read any research about the effectivness of homework? I suspect not. I have not. Yet math homework is an integral part of many mathematics classes, and I suspect that the expectations, rewards, rules and circumstances surrounding this part of the learning experience are as diverse as anything we do. Teachers have strong feelings about homework. How many times have you heard it explained that a student "doesn't even do his homework, so how could he possibly succeed?" But I know that there are a lot of students who succeed without doing much, if any, homework. Many of my best students did as little homework as they could get away with. Many of my best students did all of the homework carefully and then did extra problems.
I think it is clear that many students will not do very much homework if there are no immediate consequences. Will this lapse stand in the way of their learning? Sometimes. After forty-two years of teaching, there is nothing I am as confused about as the value of homework. So I would like to bring up a few things about homework. I do not have answers to any of these questions and welcome logical arguments that will convince me, or anyone else, of a logical path.
Why do so many math teachers believe that students need to work on math homework every night?
I suspect the most common answer is that students need practice in order to master something. Do all students need the same amount of practice? I doubt it, but most homework is designed as if every student needed thirty minutes of practice every night, or every student needed twenty problems every night. I don't know how to insure that students work on math for thirty minutes every night. If I assign twenty routine problems, some students will finish those problems in five minutes, while others may take an hour. If I assign three challenging problems, many students will never make progress on any of them, and other students will give up after two minutes and will be angry because I did not show them how to do the problems. If I don't assign challenging problems, then students will never practice problem-solving skills and will never encounter interesting problems that will capture their imaginations and lead them to the excitement of mathematics. And the homework will always be tedious and boring.
How should I assess homework? I could create a list of important problems and tell students that they should do these problems in order to learn the material. I can then make solutions available somehow so they can check their work. Or perhaps I should collect all homework and grade the problems so I can give students feedback on their work. I could check to see the homework has been done and then not collect it. I could collect it and grade some of the problems. I could collect it on random days. I could give a homework quiz where they can use their homework paper to copy a specific problem that I would then grade. I could give a quiz containing a homework problem or two but not let them use their homework. There are lots of variations. I know some master teachers who use each of these systems, and others.
How do I know, in the end, if my method of assigning and assessing homework is valid?
I think if my students know the material, as assessed by some sort of legitimate final exam at the end of the course, that perhaps my method works. I am particularly positive if they do well in subsequent courses, and in subsequent work.
I can tell you that I spent considerable time trying to find a way to make homework work for me. I tried most of the things listed above in some form or another, and found one system that seemed to work for me and for my students. It did not over-burden me and seemed reasonable to my students, and so I used it for most of the classes I taught for the last twenty years of my career. A key aspect of my plan was that doing homework every night gave students a bonus at the end of the quarter. If a student had no more than one missing assignment at the end of a quarter (about 35 assignments), that student's lowest test-score was raised by a grade. I determined grades using letter grades on tasks, not points. If a student missed more than five homework assignmets in a quarter, that student's highest test score dropped by a grade and continued to drop a grade for every subsequent missed assignment. I did not collect homework, but I looked at it every day as they worked on the opener for the day. I gave frequent quizzes to inform myself and my students whether they were making progress. More to the point, I spent almost all of every class walking around listening to them work problems, so I knew whether they were learning or not. This system worked very well for my students and for me.
I think the best advice I have is: devise a plan that you are comfortable with and tweak it until you are happy with it. Then: share what works with others.