How much homework is enough?

As a tenure-track professor, my colleagues visit my class every semester to better get to know me. Aside from the fact that this is an evaluation with professional consequences for me, I find this to be a great practice when done correctly—in fact, I wish that tenured professors would make a habit of visiting each other’s classes. It is easy to become too familiar with one’s own teaching, and it is good to periodically have an outsider question your choices.

I recently had a visitor, and he was concerned about my homework assignments. It was a blessing that we had this conversation, because it reminded me about why I make some of the decisions that I do; I have internalized these, but it is good to make them explicit from time to time.

  1. I believe that any sort of upper-level mathematics that is worth doing is worth taking your time on. Upper-level mathematics is about ideas and problem-solving, not computations and memorization (for the most part). I believe that a well-written homework assignment should require that the student take time to complete it; it should require stops and starts, dead-ends, and sometimes flashes of inspiration. These problems cannot be churned out, factory-like, on a schedule. Because of this, I eschew the practice of giving proofs after every class period; rather, I prefer to give students a “cycle” (6 days—recall that my college/s is/are weird) so they can dwell, fail, try again, and ultimately succeed.
  2. I believe that the teacher’s job is to make him/herself expendable. I used to revel in the fact that my students would come to my office hours on a daily basis for help. However, I no longer think this is in the best interest of the student. While it does make me feel good to feel needed, I have (in the past) had a tendency to set up co-dependent relationships with my students, where the students never feel like they can do the mathematics outside of my presence. This, in my opinion, is the opposite of education, and I have been improving on this by leaps and bounds over the past eight years. My latest tool is cooperative learning, which has been considered a great success by my students. A second success is giving my students more flexibility in when the homework is done; again, I have found that giving students homework every cycle creates less dependence than making homework due every lecture—even if the amount of homework is the same in both cases.
  3. I believe in quality over quantity, if I must choose. I prefer to give fewer homework problems while expecting a higher quality (and giving a higher quality of feedback) than more homework problems of lower quality.
  4. I believe that mathematics homework is not just about mathematics; rather, this is an opportunity to improve writing skills, which will ultimately be used more than the mathematic skills for 99% of my students.

One of my main points is that I do not think that having homework due every lecture meshes with my values, but this does not mean that I do assign homework that is due the next lecture period. Rather, I reserve these homework questions for simple computational problems or problems that apply a definition.

These are ideas that I have come to in my years of teaching, although I make no claim that these are optimal. I prefer weekly/cycle homework to daily homework for proofs, but I feel like I could easily change my thinking on this if I hear a good argument. I would appreciate suggestions and other people’s rationales in the comments.

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3 Responses to “How much homework is enough?”

  1. Cong Says:

    I have some thinking about the homework. So far, I really like weekly/cycle homework more than daily homework. One of the reasons is I have time to play and enjoy the problems (just like point 1 in your post). Other reason is daily homework is so stressful, especially when high weight is put on it. Also I often struggle with reading carefully the chapter ahead to do daily homework or just imitating examples to just finish it. If I read the chapter ahead carefully, the lecture becomes so boring. But if I just do the example imitation, I feel like getting nothing from homework besides tedious algebra.

    However, I realize one problem with weekly/cycle homework. Weekly/cycle homework sometimes falls behind the lectures. So let’s say chapter 3 requires understanding of chapter 2, but I haven’t digested chapter 2 well enough and sometimes I feel lost in the lecture or I can’t appreciate the lectures.

    It’s tough to have the balance, but I have a suggestion. We’ll have daily questions and students don’t need to finish them before the lecture. They just need to read the questions in advance. Then they attend the lecture and figure how to solve these questions during the lecture or after the lecture. And this daily homework will be collected next lecture. The advantages are:
    1. Students know what to expect during the lecture and can apply immediately.
    2. The questions act as review for the next lecture when they are collected.
    The questions could be simple like proving a property of coset or proving a simple subgroup that are omitted during the lectures. And I think not much weight should be put on this. Let the students enjoy it like appetizer or dessert besides the lectures.

    • bretbenesh Says:

      I like the suggestion, Cong. In fact, I might even steal your name next semester: “Appetizer and Dessert Homework” instead of “Daily Homework!”

  2. Cong Says:

    The idea comes up when I usually try to prove one proof (in lecture) in different way and I often skim next chapter in the book (only note the new words and then try to see what’s cool with them in the lecture).

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