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I know that some instructors collect homework and "grade that on the basis of completion" (e.g., item #2 on this answer). In fact, I tried this myself for several years, based on advice from my mentor in graduate school. But I found it to be terribly frustrating, laborious, and unproductive, and I had to abandon it some years ago for my own sanity. That said, I'm still curious about how others manage to make it work.

Here's the main thing I never resolved: What should the criteria be for "checking off" (pass/fail, I presume) an acceptable performance on homework? Here are some examples that I encountered when attempting to apply this process:

  1. Student lists final answers only as shown in back of book; no work is shown whatsoever.
  2. Student has what appears to be work, but it is totally illegible.
  3. Student has some kind of work, but problem identifiers (labels/numbers) cannot be found that match the assignment.
  4. Student has work and answers that don't remotely resemble the correct solutions (e.g., exercises in simplifying variable expressions allege finding a value for the variable; work involving fractions or radicals has no such expressions at the end).
  5. Student's work starts with the answer and only checks that answer throughout, without exercising any real solution method (e.g., substituting solutions into an equation without solving it; multiplying factors back together without factoring a polynomial).
  6. Student's work exactly matches work on the next submitted page.

These are just some of the examples of what seem to be critical problems which are apparent at a glance, that I am loathe to give credit for. In fact, it seems to send a confusing and perilous signal to give students a passing grade ("you're doing okay") on work that is inherently flawed like this.

So: What criteria should be applied for minimally-acceptable performance when "checking homework for completion only"?

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  • $\begingroup$ I thought that the point of grading for completion was that it wasn't laborious? $\endgroup$ – Adam Jan 2 '18 at 13:24
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    $\begingroup$ Adam, Dan knows what it is supposed to be, but it is not working that way for him. (Great question, Dan.) $\endgroup$ – guest Jan 2 '18 at 14:03
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    $\begingroup$ Dan, my advice is to just use your judgment and give zero to the people that give only answers, have something that looks illegible or only complete a minority of the problems. Don't worry about justifying it--just put a quick note that it is unacceptable and move on. You will only have some very small minority that challenge you on it, but you can explain your decision with the paper at the time. You are the teacher, you control the grades. They will learn. Of if not, just keep hammering them. You're in charge. $\endgroup$ – guest Jan 2 '18 at 17:19
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    $\begingroup$ @guest I ain't no monkey. I'm an ape, damnit, and a great one at that! $\endgroup$ – Xander Henderson Jan 2 '18 at 18:15
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    $\begingroup$ Great question! I used to have the same problem myself, but I didn't try this "for several years", maybe two or three classes, after which I came up with other things (mostly giving lots of short in-class quizzes, which I've discussed several times in here before). There are just too many gray areas in this, and even spending a few seconds many times on each paper thinking about where the red line is adds up to a lot of time for what seemed to me wasted effort, as many students just copied stuff from others before class began --- I'd see students coming in for the class after my class do this. $\endgroup$ – Dave L Renfro Jan 2 '18 at 18:55
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This is going to look a lot like Jeffery Thompson's answer, with some slight modifications (I was working on this answer when his appeared).

First off, I agree entirely that you have to decide what you want students to get out of the homework first, then decide how you are going to grade those assignments. As I said in the answer to which you linked, I think that primary goal of homework in a lower division class is to give students a chance to practice the kinds of problems that I think are important, as this will help them to learn and master the material. Ideally, the students would be mature and engaged, and would do the homework and come to office hours to discuss problems even if no credit were given for homework.

That being said, the kinds of students who are typically in a college-level precalculus or introductory calculus class are often not mature enough to do the work without the promise of a reward. Thus, I collect the homework and assign marks, because if I don't, the students probably won't bother. This is why I give any grade at all to homework—I'm playing psychological mind games with my students.

The next question is one of time; specifically, how much time do I have to grade? In a large lower division class (100+ students), there simply isn't going to be enough time grade all of the work in detail and give meaningful feedback. I would love to comment on all of the work, but my wife would probably kill me if I spent that much time in the office. Thus I will typically choose to grade on the basis of "completion," where completion basically means that the student wrote their name on the top of the page and wrote down solutions (note: not answers, but solutions which show work) to all of the questions. Typically, I'll make each assignment worth 1 point, and either give a 1 or 0. Either it is done or not. In your examples:

  1. Answers, but no work: I would give no points. The answers were given. It is up to the student to do the work.
  2. Illegible work: I would give points on the first couple of assignments, and make the comment that it is illegible, then stop giving credit after two or three assignments have been returned.
  3. Wrong problems: I would give no credit. If the student doesn't do the assigned problems, then they didn't do the work, and deserve no credit.
  4. Poor quality or incorrect work: I would give credit, but might ask the student to come to office hours. That being said, I might not even notice that the answers are wrong, since the whole point of grading for completion is that I don't have to check their work.
  5. Poor techniques: I would treat this the same as 4.
  6. Identical work to another student: Both students get full credit. Ideally, they were working together and therefore have the same answers. More realistically, one student copied off of the other, and was therefore "cheating." However, I assume that students will (to put it generously) "collaborate" on anything outside of class—I have no control over that, and don't want to arbitrate those kinds of disputes.

That being said, I rather like Jeffery Thompson's rubric, and my start adopting something like that (0 points for blanks, 1 point for the attempt, 2 points for correct solutions).

Note that all of the above applies to the kind of homework assignments that I call "Computational Practice." These kinds of assignments (similar to Jeffery Thompson's "Homework") are generally very computational in nature, and not terribly deep. They are meant to get students to master algorithms or computational tricks. These are not far from "drill-and-kill" (though I seem to recall from my ed certification program that there is some fancy jargon for this... "deliberate practice," maybe? that has the right ring to it...), and typically involve a large number (15–20) of problems that should all take very little time (2–3 minutes each).

I would like to specifically address this point:

In fact, it seems to send a confusing and perilous signal to give students a passing grade ("you're doing okay") on work that is inherently flawed like this.

I have had concerns about that, but I try very hard to make it clear to my students what the point of the work is. An example of the exact statement on my syllabus (from a stats class last quarter) is

Homework will be assigned daily. Assignments will be due on the Monday after they are assigned, at the beginning of class. All assignments will be posted on Blackboard. The goal of the homework assignments is to give you a chance to get some practice with the kinds of problems that might appear on an exam and to build your understanding of the concepts discussed in class. However, I do not have the time to give in-depth written feedback to every student, so your work be graded on the basis of completion. Answers to odd numbered exercises are in the back of the text, and I am available during office hours or via email to discuss any problems that you might have.

I then repeat something like that every time a hand back homework: "Remember, I am just grading your homework on the basis of completion. You should not assume that, because you got credit for the work, you are in good shape in this class. The exams will be much more important. If you are having any difficulty, please see me during office hours." This, coupled with the fact that homework is worth only 5–10% of the final grade, seems to get the point across.


As an addendum, I also tend to give longer "Written Assignments," but the goal of these if different, and they are worth a larger portion of the student's grade. The assignments typically consist of two or three more involved problems, and the solutions are graded in detail, with an eye toward good mathematical writing (this is inspired by the "writing across the curriculum" mandate that was all the rage when I taught high school—the goal is to (approximately) learn how to write in mathematician-ese).

I typically give seven or eight of these written assignments in a 10 week quarter, though it depends on the size of the class—it is reasonable to grade something on the order of 50 such assignments in a week, spending 2-3 minute per; in larger classes, I would assign fewer written assignments. The assignments are given out, and students have a week to turn in a rough draft. I then offer comments, and students have another week to turn in a final draft (though, to be honest, the final drafts have a "floating" deadline). I then award points as follows:

  • one point for turning in a rough draft on time
  • one point for turning in a final draft on time
  • one point for coming to office hours and discussing corrections to the rough draft (these three points represent the "completion" portion of the grade)
  • three points for writing mathematically correct solutions
  • three points for writing in legible, grammatical mathematical English, including the proper use of notation
  • one "bonus" point for TeX-ing up their work.

There are fewer of these, and each contains fewer problems. Even with a large number of students, it is possible to grade a couple of stacks of these each week (particularly since much of the feedback is offloaded to office hours, which is allocated time already).

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    $\begingroup$ Moral +1 (I am a second class citizen so can't give a real one). Great detailed answer. Keep the wife happy... $\endgroup$ – guest Jan 2 '18 at 19:22
  • $\begingroup$ Great answer. Love the details. Will definitely adapt parts of this into my mindset. $\endgroup$ – Jeffery Thompson Jan 2 '18 at 21:58
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    $\begingroup$ +1 I also think this is a great answer; thank you for addressing specifically each of the examples. The context and motivation is very closely matches my own; and the syllabus language is quite similar to mine, as well. Interestingly, my history is one of evolving from "completionary homework" in the first part of your answer, to something very much like your limited "written assignments" in the second part of your answer. But that too was a belligerent combat every week, with students copying in class in my presence and perennially not grokking why the careful writing was necessary. $\endgroup$ – Daniel R. Collins Jan 2 '18 at 23:31
  • $\begingroup$ It also seems like I would personally get frustrated (again) with the need to remind classes of the nature of the checking every week. Maybe you could fill in some workload scope: Number of sections/ students/ time per week spent on the grading? $\endgroup$ – Daniel R. Collins Jan 2 '18 at 23:34
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    $\begingroup$ @DanielR.Collins It varies, but last quarter it was two sections of precalc (50 students total), and two sections of introductory stats (another 70 students). I didn't assign written work to the stats class---only computational assignments. Grading generally took around 5-6 hours per week, plus another 4 hours or so of fairly well attended office hours. $\endgroup$ – Xander Henderson Jan 2 '18 at 23:47
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It depends on what you are assigning the homework for. The learning objectives of an assignment should determine your rubrics for assessment.

You need to ask yourself why you are assigning the homework, what is its point in the curriculum and the goal of completion of exercises for the students. You then need to ask yourself is homework part of the assessment of knowledge or is it a tool in the learning, or some combination of both. Design your rubric to match those learning goals and realize students use points and grades as an economy and your grading will shape some of the student behavior.

I am going to illustrate this with an example from one of my classes, this is not the format I use in all classes my upper level classes I rely on the students desire to learn the material being greater:

In my College Algebra Class I have three assignment types.

  • Homework
  • Notebook Problems
  • Project

The purpose of each assignment is different so the rubrics and assessments are different.

The homework problems are due each class period and consist of highlighted problems from the odd problem sets in the textbook. The answers are in the back of the book. The purpose of the assignment is for the students to practice the concepts introduce in the lecture and do enough problems that they can find where their questions, ask the questions, to begin to see patterns.

This is graded on a 3 point system. Was the problem attempted with sufficient work. Full marks for the problem. Was the problem attempted but insufficient work. 2/3 marks. Was the problem attempted by little on no work. 1/3 marks. And of course no attempt at the problem no marks.

Most of the grades are full marks. If there are attempts at getting to a solution they get the marks. Insufficient work would be the appearance of work but it is not relevant steps. Little or no work is when you get students copying the answers from the back on large sections of problems, usually when they run out of time.

The point though is the points come from attempting to solve a problem. My goal is to have the students get past the I do not know what to do hurdle, and to do problems. This is to open the door to dialogue on mistakes. Using the answers in the back of the book they have the ability to know if they are correct or not and can self correct or ask questions.

To test the knowledge from a homework set they will have a quiz on the day the homework is due on material that was assigned in the homework.

This gives an incentive for the students to do the homework, honestly and to ask questions when they are stuck.

The notebook is due every Monday. It is a choice of 5 problems from the homework sets. The students are required to rewrite the problem. Explain each step of their mathematics. And restate the answer in English. (Natural language of the classroom.)

The rubric is 5 points for format 5 points for the answer 5 points for Reasoning - clarity 5 points for Reasoning - logic 5 points for Reasoning - mathematics

The reason this detail is different than the homework is my reason for this assignment is not to practice and begin the dialogue around particular problem sets but for the student to show me the understand the methods and reasoning used in solving particular problems with mathematics.

The project is an extended semester long project that uses datasets to explore all the ideas of the semester with messy real world data. And I won't discuss the rubric here.

My point is the assignments are structured and graded as such because I am addressing specific issues in the classroom.

  1. Historically students did not self practice, I need to assign homework for them to practice, even if I quiz often.
  2. Historically students would stop if they did not know how to begin a problem.
  3. Some students when given odd problems would just copy the answers from the back and argue they did the work.

My rubric is designed to address these issues and specifically to highlight the need to practice, self correct, ask for help and communicate in the process.

Also the students see the importance of practice in the homework with minimal risk. They don't have to be perfect in the practice phase they have to start "to do". But with the quizzes they have to take the practice seriously it has to lead to an understanding.

Also the knowledge accumulates and they have the notebook problems to reflect and explain. To begin to own the thought process.

These are my goals with the assignments and I try to have my assessment reflect this. Yours need to meet your goals. And thus to answer your question the minimum criteria depends on where you expect your students to be with the assignments and how you use points/grades to motivate or encourage.

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  • $\begingroup$ Thank you for the detailed write up. Questions on workload: How often does the College Algebra class meet? How many students? Approximately how many problems per daily homework set? Do you do all the grading yourself, or have TA's? $\endgroup$ – Daniel R. Collins Jan 2 '18 at 23:21
  • $\begingroup$ ... and how many sections per term? $\endgroup$ – Daniel R. Collins Jan 2 '18 at 23:32
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    $\begingroup$ The class meets three times a week. I have no TAs. 10 required homework problems to be handed in. 20 suggested practice problems if struggling with the required problems. I have 3 other classes in this term that are not College Algebra. The notebook problems due beginning of each week are drawn from the 10 required homework problems and the 20 suggested practice problems. $\endgroup$ – Jeffery Thompson Jan 3 '18 at 2:53
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A high school teacher told me he stamped their homework at the students' desks, so he didn't have to collect it. I liked that, and for years used that system. (I bought a stamper at Staples.) At each test, they turned it all in, and I counted the stamps. It worked for me.

But apparently students didn't like it, which I heard about this summer from a friend who tutors. So I decided to try collecting homework, and spending as little time as possible grading it. I grade one problem, and the rest of the credit (maybe 3/4 or 4/5) is for completion. Only if they seem to be showing the work and doing the proper problems. Only if turned in on time. If I see someone working on it in class, I will remind them it was due at the beginning, and if it were to continue, I would stop accepting it. I did not accept late homework. I told them it was just too hard for me to keep track of. (True.)

It added 3 hours to my work week, I think. Bummer. But in two of my three classes, I think students worked harder than they have in the recent past for me. So, I will keep doing this.

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  • $\begingroup$ +1 These are similar to things I tried. I even bought custom stamps online for the process. $\endgroup$ – Daniel R. Collins Jan 3 '18 at 15:35
  • $\begingroup$ So it sounds like you just whiz through as fast as you can, and give the credit you think makes sense, and don't worry about explaining. This is my least favorite part of teaching. I am doing this senseless task because it helps students have enough motivation to do the homework. So I just try to do it quickly. I have always procrastinated in the past, and I felt defeated looking at multiple weeks' homework. This semester I managed to mostly stay on top of it. $\endgroup$ – Sue VanHattum Jan 8 '18 at 6:10

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