A Necessary Evil?

This semester, I have found myself grading homework more often than working on any of my other academic duties. Some weeks, I have spent upwards of 15 hours just on grading, and I still have to prep for two classes, hold office hours, and supposedly get some research done. This is mostly because of choices I made at the beginning of the semester that I couldn’t later change. But it got me wondering about how important (or not) grading is for students, pedagogically speaking, and whether it is really all that helpful for them to get this kind of feedback.

The first question is probably why assign homework in the first place? In the past, I have taught Calculus I without it. Mainly, I suggested homework problems for them to work on, and then every couple of lectures I would give a short quiz covering the homework material. The idea was that to do well on the quizzes, they had to do the homework. But we get many students who have taken Calculus in high school and therefore assume that they don’t need to study for it. These students don’t do the homework (why work on something that is not due?) and later bomb the quizzes. But when they get a bad grade on the quiz they still believe that it’s not their fault, because they know Calculus, I’m just somehow being “picky” about how I grade or I’m making it confusing for them (this later comes out in evaluations for the course). So this semester I decided that they would have to turn in homework every day, and there would only be five quizzes, with questions that were slightly more involved than those in the homework. But with extra homework comes extra grading, so I decided to hire an undergraduate to grade the homework. This has worked out pretty well. At least I know the students are always doing their homework, and that someone is looking at it and giving them feedback.  At the beginning of class I have them vote on what they thought was the most difficult problem in the homework, and we will discuss it (that way I have some idea of what they are confused about without having to grade everything). They’re actually doing better on exams and quizzes.

Recently in our student paper there was an editorial piece about how it’s not a good idea for students to grade other students. The main argument is that professors have PhDs and are therefore more qualified to grade the students’ work. And I agree, we are more qualified, but we also have a lot of other, more important, things to do, like plan good class meetings/lectures and meet with students outside of class. But I think, at least in math, the most important thing about collecting homework is that it makes students think about the material and solve some problems on their own. The only way to learn math is to do it, and unfortunately, most people don’t do things that they are not required to do. Checking the answers is relatively important, but we give feedback in other ways. By talking to them during class (I assign worksheets frequently), giving quizzes and tests, we are still communicating with them and helping out with their mistakes and misunderstanding.

This problem changes slightly when teaching an upper level class, like Real Analysis, because here it is true that other students are not really qualified or prepared to grade the homework. Homework for this class is pretty difficult, and all of the problems are proofs, so it is no longer a question of whether the answer is right. At the beginning of the semester, while planning my syllabus (go here for more details on how that went), I decided that I would collect homework. They would turn in a first draft which I would grade for completion, then we would discuss homework in small group meetings (separate from office hours), and then they would turn in a revised draft, but only half of the problems, which I would grade carefully. Because it is IBL-style, we also always discuss the homework in class through their presentations, give feedback, etc. At the end of the day everyone has seen a correct proof of every theorem we see in class. The small group meeting idea came when I was trying to decide how much I could grade, and I figured it is more useful to them to talk with me directly than to see whatever notes I scribbled on their paper. But somehow I decided that I would also give them feedback on the first draft. So I write comments on every proof but don’t assign any points, this way they know which proofs need more correcting, and which are fine the way they are. This means that I am grading twice as much as I was planning to. The problem was that I wanted them to see feedback right away, and use that for their revisions (which have been of pretty great quality overall). It definitely helps them fix their existing proofs, but I wonder what actual impact this has on their proof writing skills. If anything, they might just get lazier about their writing because they know they have several chances and I will tell them what’s missing. However, I think they really appreciated and recognized this extra effort on my part, and it does help to some extent in their feeling that I have their back. But how much is that peace of mind really worth? Can I maybe accomplish that in another way that doesn’t kill me? I have 26 students, they write about 6 proofs per week, I grade half of those twice, so every week I’m grading 9 proofs per person, that is 234 proofs every week. It is no wonder some weeks I feel like I am going to lose my mind.

A couple of weeks ago I tried to have them grade each others first drafts, and write comments as I would. I thought this would also be a good exercise for them, as they get to see how someone else thought of the proof, and even some mentioned realizing their own mistake when they saw it in someone else’s paper (it is easier to critique others than yourself).  But they soon got annoyed at this because it was not my feedback they were receiving, but a peer’s feedback, and they weren’t sure if the feedback was right or not (although by now they should have realized that I am also not always right). I think this experiment would have worked better if I had done it from the beginning. Now that they are used to getting so much attention from me it is hard to take it away.

Ultimately, the most important kind of feedback has been the oral kind. When they are in the small group meetings I get to talk to every one of them (the groups have 3 or 4 students), and nobody slips through the cracks. I also think the large class meetings are useful, since people present the proofs to each other, and they are mostly a very well-behaved but vocal class. Almost all of them feel comfortable saying that they don’t understand something, and I think some of them even realize that when they don’t understand something it sometimes means that the proof is missing some important detail. Those who are not so comfortable in the large group meeting have been pretty engaged in the small group setting, so they all get to voice their questions and thoughts. The small group meetings are 30 minutes long, but it might be worth it to try meeting them for longer chunks of time and not grading the first draft at all (only checking for completion). I mean, that would only add about 4 hours of work to my week, which compared to 15 is pretty good (and much more useful for everyone involved). I still have to grade their writing at some point, since that is an essential skill I’m trying to teach, but if I only graded the revisions carefully that might be enough for them.

Anyway, I open the floor to you, dear readers. What is your experience with grading? Do you have different policies for intro level classes and upper level classes? Any suggestion on giving meaningful and plentiful feedback and not dying trying? Thoughts on having undergraduates grade?

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3 Responses to A Necessary Evil?

  1. Avatar Dirk says:

    Probably I could add my experience in Germany both as a student as a teacher.

    In Germany we usually have obligatory homework which will be handed in and graded every week in most of the courses. The graded homework is discussed by the students and the corrector in smaller groups. In many courses there is policy that 50% of the total points throughout the semester are enough to either “pass the course” and “grant access to a final exam” (written or oral). In the end, the final grade depends on the final exam only. There used to be several courses for which you only get “passed” or “failed” but no detailed grade.

    What I like about this system: The students work on their own (or in groups) on problems and train the usage of mathematics (you emphasized the importance of this already). Moreover, they can try on every exercise but do not have to solve all of them. Hence, I usually put exercises of different levels on a sheet; some quite easy which just train definitions and easy calculations and some very difficult. In this way you can ensure that every student, from the weakest to the brightest, has the opportunity to learn something. I also like the low hurdle of 50%. In this way there is not too much pressure every week but you can not pass if you are very lazy. Finally, I like that the final grade does not depend on the homework performance. I think this is important: First, everybody has a busy week once in a while and this should not affect the final grade. Second, there are student for which learning takes a bit longer than for others. These students struggle on every exercise sheet but when it comes to the final exam they catched up. Third, it is easy to cheat on homework but its not that easy to cheat in a written exam (or even an oral exam…).

    Of course, one drawback is that grading takes a lot of time. We also have post docs, grad students and advanced students do the grading which works pretty well. Another drawback is, that the students are forced to do the problems you chose and this somehow restricts their freedom. However, at least for me, this was not as issue. I always had some trust in the professors that they would give me reasonable exercises which would help me to learn.

  2. Avatar Peter says:

    I haven’t taught in a while (the (dis)advantage of research grants), but this discussion happens regularly on other blogs, in particular among math teachers. So maybe these links are interesting for you:

    Casting out nine wrote about digital grading (the same day as this post incidentally) http://chronicle.com/blognetwork/castingoutnines/2011/12/01/experiments-in-digital-grading/

    Think, Thank, Thunk thinks about this frequently http://shawncornally.com/wordpress/?p=1838

    Lost in Recursion is both a teacher and a masters student https://lostinrecursion.wordpress.com/2011/10/11/grades-more-recent-experiences/

    Angels of Reflection also discusses this frequently http://anglesofreflection.blogspot.com/2011/11/homework-and-more-homework.html

    And of course, Dan Meyer once had a huge discussion http://blog.mrmeyer.com/?p=133

    (shamelessplug: I got these by simply using the custom search on mathblogging.org, searching for grading+homework)

  3. Avatar Adriana Salerno says:

    I just read this, and it’s very funny, and surprisingly accurate:


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