What is the Purpose of Homework?

This week has involved multiple conversations about homework, in two of the classes I teach, in my office talking with our pre-service teachers, and in my house, where my 7^th grader brought up the topic.  Apologies if this post is all over the place because all the conversations led me to truly think about why we assign homework.

I have been using an online homework system in math courses for several years—in fact, I was the first person in my department to try using one in calculus. I love online homework systems, mostly because I hate grading.  However, I struggle with them because students are only graded on their final answer.  My philosophy has always been that math is NOT about the answer.  How do I deal with this struggle? I also include paper and pencil quizzes and tests in my courses to see if my students truly understand the concepts and to give them feedback on their problem solving process. 

Having both parents as teachers has exposed our children to lots of conversations about education.  In fact when we were looking at my son’s grades in his courses, he was disappointed that he did NOT have an A in one of his courses. As we looked more closely at his points in the course, we noticed that his homework (B average) made up more of the course points than his quizzes and tests (A average).  He said, “I don’t know why my homework makes up more of my grade in this course. Homework is for practice.”  As a teacher, my children know that I am always more likely to take their teacher’s side if there is any sort of complaint or disagreement.  This time I wasn’t sure what to say because my son was right—homework is to practice.  In fact, I used to put the following on my syllabus. “Math is very much like a sport—you improve your ability with a lot of practice.  It is not a spectator sport but rather a full contact sport.

This brings me back to my own class, Calculus I Lab. This week as I was grading my students’ quizzes and they were not doing well, I realized that they may not be doing their homework to learn but rather to get it done.  So I went into class and asked the students how many of them were doing their homework just to get it done.  There were a couple of brave souls who raised their hand and admitted it.  I designed the Calculus I Lab course as a just-in-time review of algebra and trigonometry skills that they use in calculus.  I reminded them that the purpose of lab was to make them a better calculus student.  So then I asked them if they thought it was making them a better calculus student—some said yes, but some said no. Now I need to really think about how I can improve the lab—another summer project.

In our assessment course this week, we had planned a Homework Debate. We assigned students into two categories—Pro Homework vs Con Homework. Then we assigned some common readings and asked them to do some of their own research and come to class ready to defend their position.  First of all, we concluded that math majors aren’t the best debaters, especially when deep down they don’t believe in the position they are assigned.  The students went back and forth and rebutted each other, but in the end, we all felt like we were somewhere in the middle and it likely would depend on our class and our students.  We wrote the following items on the board at the end of class under Homework. 

• Reasonable time for doing homework. 
• Feedback (timely) is critical. 
• Different forms of homework: group and projects. 
• Personalized.

Later that morning one of the students from the class was in my office and she made a comment that really resonated with me.  She works as a tutor in the department’s help center and helps students every day as they work on their homework.  In our courses that use online homework, we have put restrictions on the number of attempts the students have for each problem.  Her comment was, “Why don’t you just give them 100 attempts?”  She feels like restricting the number of attempts puts added pressure on the students and often leads them to cheating on the homework by typing the problem into Wolfram Alpha or Chegg.  Her comment really resonated with me and I even passed it on to our calculus coordinator as an idea to propose to the instructors.

Homework is really a formative assessment to help students determine if they understand the concepts and to help teachers see where the students are struggling.  When we use an online homework system, we make homework about the answer.  When we restrict the number of attempts, we make homework high risk.  When we assign a large portion of the grade to it, we make homework summative rather than formative.  As teachers we really need to think about the purpose of homework and what the students should gain from it—it isn’t about us!