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Next semester I'm teaching a course where I want to grade a significant chunk of the homework for completeness without checking whether the answers are right, and separately post the answers and encourage students to check the answers themselves.

This is largely for homework early in our coverage of a topic, so part of the goal is to make the homework less stressful, and indicate that we don't expect them to understand the topic completely at this stage.

My concern is that, especially in the middle of the semester when they get busy, students will be tempted to just write out nonsense knowing we don't check the answers. (Students sometimes do this when we do check the answers.)

I know other people have tried similar things, so I'm curious about methods that worked for getting the students to take the homework seriously.

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    $\begingroup$ Another option is to still grade HW but on a coarse holistic scale. A few problems would get graded on the scale 2 = an honest attempt, shows some understanding of what was covered in the chapter/class but isn't necessarily correct, 1 = judgement call, you possibly read the chapter or attended class but don't really understand what you are doing, 0 = appears to be intentional BS or extreme misunderstanding. I have used this scale before with great success. It's course enough to make grading easy and lower stress, but still motivates students to try hard. $\endgroup$ – WetlabStudent May 6 '14 at 18:50
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    $\begingroup$ Tell the student that the exam will contain some question that are very like some of the homework question and that any student that can answer all the homework questions while understanding why the answer is correct will do very well in the exam. $\endgroup$ – Ian May 7 '14 at 11:46
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    $\begingroup$ @corsiKa: Why? My students aren't (mostly) of legal drinking age, but that certainly doesn't stop them. $\endgroup$ – Henry Towsner May 7 '14 at 12:48
  • $\begingroup$ My high school teacher used to allow students with A's to do only 2 problems on each homework. I ended up doing the 2 hardest problems on the homework and that was the end of that. I think this works well because it avoids wasting students' times when they've already understood the materials, while also motivating them to do well in the class. $\endgroup$ – user541686 May 8 '14 at 3:59
  • $\begingroup$ The point of reading their homework is not just to motivate them to work. It's also to give them feedback on their educational progress, give them feedback on whether their work meets your standards for this course, and track their progress. Posting solutions doesn't necessarily accomplish this. Many students will never look at the solutions. If they do, my experience is that they cannot necessarily tell whether their own answer is also correct or not. They may write severely flawed work, e.g., prove a theorem by giving an example, and believe it to be just as valid as your solution. $\endgroup$ – Ben Crowell Feb 21 '19 at 2:10
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We tried something that worked nicely (though not for all students).

At the beginning of the course we announced that there will be a quiz during the semester, and the questions in the quiz will be taken from their HW assignments. This way they had to check the answers to these assignments.

The downside is, as we noticed while checking the quizzes, that some students just memorized the answers without understanding the most basic ideas.

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  • $\begingroup$ the other option would be to post more limited solutions, have the students talk to their peers and use office hours to figure out if they did the problem correctly. Potentially you could post hints or fill in the blank style of solutions, or see problem #X for a similar solution. This forces them to potentially think a bit more. $\endgroup$ – WetlabStudent May 6 '14 at 18:41
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    $\begingroup$ Don't ask the exact same questions, change it a bit. Memorizing "solution to homework problem 15" (perhaps done by somebody else, asked at MSE, ...) doesn't help in such a case. $\endgroup$ – vonbrand May 6 '14 at 22:06
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The following answer is just my opinion and might not address your particular situation. To oversimplify a bit, most students either

  1. want to do the homework for their own reasons (enlightenment, fun, or preparation for the exams,) or

  2. only do the homework in order to receive credit.

To get group (1) to take the homework seriously, you don't need to do anything at all. So let's just consider group (2). If you want them to take it seriously, then you need to grade it carefully and only give credit for work that demonstrates understanding. If you grade based on "completion" then they will (rightly) understand this to mean that a nonsense answer is as good as a correct answer. A nonsense answer is easier to write, so the choice will be clear to them. Also, they will think "if the instructor can't be bothered to grade properly, then why should I bother to write a proper answer?"

So if you want more students to take the homework seriously, but you don't want to grade more carefully, you will need to make more students from group (2) move over to group (1). The straightforward way to do this would be to make the homework more enlightening, more fun, or more relevant to the exams. You can make sure the homework is relevant to the exams when you write the exams, so let's think about how to make it more enlightening and fun.

This is a hard problem in general, but one easy thing you can do is to simply give fewer problems that are less tedious. This makes it feasible for more of the students to turn in their own work, rather than giving up and writing nonsense or copying the answers from another source. It is hard enough for a student to understand one new concept per week, so the instructor should focus on making that happen rather than assigning dozens of exercises with the unrealistic expectation that the student will understand them all simply by virtue of being forced by the grading scheme to "do the work."

To summarize, a simple way to get the students to take the homework more seriously may be, paradoxically, to make it easier. (The downside is that you will have to select the problems more carefully and make sure the students understand that they need to understand all of the problems in order to be prepared for the exam.)

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  • $\begingroup$ Well, some people might want do part of the homework for learning, and the rest for credit. See my comment on the question for more context. $\endgroup$ – user541686 May 8 '14 at 4:00
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    $\begingroup$ I think "if the instructor can't be bothered to grade properly, then why should I bother to write a proper answer?" is less likely than "I have other classes with homework that IS graded for credit, so it would be more beneficial to my GPA to expend minimal time and effort here when it would be better spent elsewhere." $\endgroup$ – LinearZoetrope May 17 '14 at 2:59
  • $\begingroup$ Have you tried this and how did it go? $\endgroup$ – Tommi Feb 21 '19 at 6:16
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    $\begingroup$ @TommiBrander I haven't tried it in the sense of doing what the OP plans to do, because I always check homework solutions for correctness. However, I do tend to assign few problems and keep them simple (or make the complex ones extra credit.) This seems to help students to take the class seriously in the sense of trying to write correct solutions (which are not necessarily very long) instead of long solutions that are mostly BS. $\endgroup$ – Trevor Wilson Feb 22 '19 at 5:05
  • $\begingroup$ @TrevorWilson Thanks for the answer. Adding it into the answer proper would improve it, I thin. $\endgroup$ – Tommi Feb 22 '19 at 11:02
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This won't directly help you, but the way I was motivated to do my homework as an undergraduate was that I had one-on-two tutorials every week. If you haven't done the homework and your tutorial partner has, then you can't really hide in room of three people. There was no formal sanction for missing a small amount of homework unless you count sarcasm. I didn't always do it (or do it all), but I certainly didn't skip it lightly.

You can't hold tutorials (I confidently assume), but I think you should be looking for other ways to prevent the students from hiding. Busy or lazy people will drop your apparently-optional homework unless there are consequences for dropping it, so you're looking for a way to persuade the students to make an honest effort.

As you've noted, grading for completeness without regard for content doesn't do this, since there's no difference between a wrong answer and "Lorem Ipsum". But you could for example:

  • Make clear that you will randomly sample homework and fail anyone you catch gaming the system. Of course this is "unfair" in the sense that someone might still take a risk and avoid getting sampled.

  • Include some really easy questions that can be answered pretty much directly from the course material, and check that they get those correct. You probably need this to be non-obvious or else it can still be gamed by those who've at least attended lectures. But the inclusion of the easy questions should at least make things less stressful and ensure that even if they feel they don't understand everything they do at least understand something properly. Up to you whether you count it a win if someone looks at all the questions but only bothers answering the ones they think are the easy ones.

  • Grade the homework for effort instead of completeness (which requires finding someone to actually read it and distinguish nonsense from failed effort).

  • Create an indirect means by which the homework is obviously necessary in order to pass the course. Ludolila already suggested an exam involving a subset of homework questions, and you can prevent people memorising the answers by setting an exam involving questions very similar to the homework but not quite identical. Students could then be persuaded to view homework as exam preparation, and that it's easier to do it than skip it.

  • Set normal graded homework on the easiest parts of the material, plus advanced questions that are explicitly optional since the students aren't required to have mastered the material yet. However, stuff that's optional at the start of the course could be introduced into the normal questions in later weeks. Maybe you could even figure a way to set questions in week N+1 that are easy for anyone who has seen the sample solutions to the questions from week N, which motivates the students to check the answers. That might still result in students never attempting the optional questions, though. Just reading the solutions is a poor substitute for trying to do it yourself and only reading the solution after failing.

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  • $\begingroup$ I can vouch for effort-marking, which I do pretty much every day. I give a mark out of 1 for a homework, and I spend just a few seconds per student glancing through it. This gives them acknowledgement for their work and is easy. Telling comments from a good student I teach about a colleague: "You work really hard and then he never checks it. It makes you want to not do it." and from some students a couple of years ago who were leaving: "If we think there's a chance you won't check it, we'll take that chance, every time." There is NO credit for my homework, but hardly any homework is missed. $\endgroup$ – AndrewC May 6 '14 at 20:56
  • $\begingroup$ It is hard to check if they try to game the system. I came to the conclusion that I'm not really interested if they did the work or copied it from elsewhere. So a "randomly selected" sample of students is called for a interrogation on what was handed in (and the general topic). The resulting grade replaces the grade of the written work. This has tended to make them at least aware what they turn in. $\endgroup$ – vonbrand May 6 '14 at 22:04
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In a (small, graduate) course we got weekly homework. Four questions, only one ("selected at random") was graded (rigurously), and the resulting homework grade was a minor part of the final grade. Partial answers (mostly hints) were published.

Worked nicely. Hard part is to come up with four equally interesting, and equivalent in work required, questions each week.

Last term (at the suggestion of one of my TAs) we started having tutorial sessions with three questions. One to be solved as an example by the TA, but active participation by the class is expected; another one to be solved in open discussion by the class, with hints from the TA as warranted; the third one is written up individually and handed in, to be graded as 0 (no work/completely irrelevant), 1 (looks related to the topic), and exceptionally 2 (very well done). This is a 5% of the final grade. Grades (and percentage of passing) soared. We are repeating the exercise this term.

Both alternatives cut down on the grading work, and (given good problems) do engage the students.

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The purpose of homework is to demonstrate understanding.

So what about offering your students the chance to come up and solve/explain a question demonstrating their understanding to the rest of the class, and if they do so successfully they get full homework grade without having to do the homework assignment.

Its a win for all parties involved.

  • You get to go through individual questions in class, like you originally planned
  • You'll have less homework to grade, since kids who understand the stuff won't be submitting any.
  • Students get an opportunity to demonstrate their understanding during class time, and don't have to waste their free time solving the the same problem repeatedly just to demonstrate to you that they understand it.
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  • $\begingroup$ Unfortunately this sounds to me like it will motivate the A students to skip the homework -- probably transforming them into B students before your very eyes! $\endgroup$ – Chris Cunningham♦ May 7 '14 at 18:46
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    $\begingroup$ @ChrisCunningham I would love it if I could have skipped my homework... I almost always understood the material and I hated the fact I needed to waste my free time by demonstrating this by writing out many versions of the same problems. Based on some comments from other classmates (things like "Its stupid, I already know this stuff so I'm not doing it", or "I wasn't really paying attention in class - I'll just figure it out later when I do my homework"), I think this could actually help improve student attendance and paying attention in class :) $\endgroup$ – Rachel May 7 '14 at 18:52
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    $\begingroup$ I find that students don't tend to be very good at board work. Even if they understand the math, their presentation may not be as helpful to classmates as the teacher's own presentation would be. I don't find student board work to be a good use of class time. $\endgroup$ – Frank Newman May 21 '15 at 2:33
  • $\begingroup$ Solving lots of problems adds to fluency and is important for later development of more advanced skills. $\endgroup$ – Tommi Feb 21 '19 at 6:22
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I think my system solves your problem

  1. Assign homework due by date $X_1$ and time $t_1$. The submission is accepted electronically until that date and time.
  2. The solutions to this homework are automatically released on date $X_1$ at time $t_1$.
  3. The students now have until date $X_2$ to correct their homework using the supplied solutions. I need to see evidence that each problem was compared to the given solution. This might be a check-mark if it was entirely correct, all the way to completely redoing the problem if the original solution was not salvageable.
  4. I can very quickly "grade" their correction on essentially a binary scale: for each problem, have you shown me evidence of an initial attempt and a revision.

The first step is needed to prevent people from just tweaking the solutions and making it look like their own work. If I suspect that is happening, I can look at the electronic submission which was accepted before the release of the solution.

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    $\begingroup$ That's an interesting approach, but I'm trying to figure out how the mechanics work. Do your students type their assignments? If not, how are you handling electronic submissions? $\endgroup$ – Henry Towsner Feb 20 '19 at 21:02
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    $\begingroup$ My school uses blackboard. The students just upload pictures they take with their phone. I made the first assignment due by the second class and it was just a bunch of silly things (draw something awesome, tell me your favorite movie, etc), so they could practice submitting for a low stakes assignment. There are generally a few hiccups at first, but it is pretty smooth by week 2 or 3. $\endgroup$ – Steven Gubkin Feb 20 '19 at 21:05
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    $\begingroup$ Can the down-voter explain their downvote? I would be grateful to learn if this practice is damaging in some way, so I can fix myself. $\endgroup$ – Steven Gubkin Feb 22 '19 at 19:48
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My answer/suggestion is in the form of a question. I'm new here, so please forgive me if this is not with the zeitgeist:

I'm curious whether anyone out there has ever tried a version of the following idea: have the students grade each other's homework, by hand and eye with a red pen, but penalize the grader if the work of the person he's grading does not correlate to his exam score on a proctored exam. The exams would of course need to closely resemble the homework!

Novel here would be the new cost: in this case any significant gap between a student's performance on the homework and the grader's evaluation of that homework would be expensive.

This would place a premium on accurate grading, which is a great way to learn math!

Of course, the homework would be worth points and a poor performance would garner fewer points, and the exams would still be worth what the exams are worth.

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    $\begingroup$ This seems like it creates more clerical work for both the instructor and the students while also reducing the accuracy of the grading. Maybe I am confused about what you mean. $\endgroup$ – Chris Cunningham♦ Mar 6 '19 at 16:56
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    $\begingroup$ I was sort of wondering whether it would be better than no homework being taken seriously at all (except for the students who are self motivated), but I see your point for sure. $\endgroup$ – DeepFriedTurkey Mar 6 '19 at 17:28
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    $\begingroup$ Do you think some students would object to other students seeing their work especially if it's poor? $\endgroup$ – Amy B Mar 6 '19 at 20:41

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