A math student may write very long and detailed answers, just because he or she does not know what to look for, for example in Geometry proofs.

Or - a student may just write an arbitrary step without explaining.

Overall, it can become tedious and even frustrating to grade math homework or exams.

Do you share the same frustration, and how do you handle it in the best possible way?


7 Answers 7


I have found that, for myself, implementing standards based grading has eliminated this frustration entirely. I now find grading to be enjoyable.

I have a collection of standards for my course like

"Evaluate the truth value of an expression such as $(T \Leftrightarrow F) \implies (F \wedge T)$"


"Give a Fitch style proof outline for a theorem such as $\forall x \exists y (A(x,y) \wedge (\neg B(x)))$ "


"Prove simple statements about parity and divisibility such as 'The sum of any two odd numbers is even'."

The students are first given "rehearsal sets". These are like "homework". They try their best, submit their attempt to me by a certain date, then gain access to the solutions, make corrections, and resubmit. Grading these is basically for completion and takes no time at all.

They are then given a "performance set" for the standard. These are collections of problems which I believe demonstrate mastery of the standard. They are grouped into "attempts". I might have 15 problems grouped into 5 attempts of 3 problems each. So each student will submit the same 3 problems as their first attempt. If they demonstrate mastery, then they are done. If not, they should get help, read my feedback, and then attempt the second set. They continue this until they either give up on the standard, or master it.

The grade in the course is 15% homework, 10% "honest attempts" at mastering each standards, and the remaining 75% of the grade is derived from mastering standards. There is no such thing as partial credit: either I believe you really understand what you are doing, or I do not, on each standard.

I learned that a lot of my frustration with grading stemmed from the feeling that it wasn't fair, and that my feedback didn't matter. If I deduct 3 points on a problem, and write a paragraph explaining why there was a problem, the student has little incentive to correct the issue: maybe this kind of question will not come up again. The whole course is a guessing game: what kind of question will the instructor ask?

SBG eliminates all of that. I lay out my expectations in extraordinary detail. There is no guessing what I want the student to know: it is all extremely explicit. My feedback is not wasted. When I give feedback, I learn about the present state of knowledge of the student, and the student learns what they need to fix on their next attempt. The student has to persist in learning the content until I deem their understanding suitable. There is no "good enough".

  • 5
    $\begingroup$ Getting rid of partial credit is a great way to streamline the grading process, help students focus on which skills they need to work on, and make it easier to determine what skills are actually contributing to students' final grades in what amounts! $\endgroup$
    – TomKern
    Commented Apr 15, 2021 at 16:00
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    $\begingroup$ As someone who has previously graded formal logic assignments, I'll note that formal logic is especially well-suited towards this approach. It's very easy to distinguish between systemic errors and local errors. Mind you, in my case I streamlined homework grading of proofs by partially automating it. In hindsight, I could have gotten rid of partial credit; students were given a copy of the grader program, so errors were typically indicative of lack of mastery. $\endgroup$
    – Brian
    Commented Apr 15, 2021 at 16:32
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    $\begingroup$ @Brian I have also had a lot of success in an elementary number theory class. There the standards were divided into computations, definitions, and proofs. Computation standards included "calculate the GCD using the Euclidean Algorithm" and "Evaluate Legendre symbols and use them to make decisions about squareness mod n". Proofs were mostly of the standard results (prove the correctness of Euclidean Algorithm, etc). $\endgroup$ Commented Apr 15, 2021 at 17:16
  • $\begingroup$ How would this work when there's standardized testing and government control over the curriculum that's expected to be taught? $\endgroup$
    – nick012000
    Commented Apr 16, 2021 at 2:46
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    $\begingroup$ I just wanted to say, in engineering school I had a professor who did his courses using a "mastery system" very similar to what you've described (frequent exams featuring all topics covered, getting a topic correct 100% counts as mastery of that topic and means you don't need to do it again on future tests) and it was absolutely the best testing/homework experience I had in school. Now as an engineer in the field, the concepts from those 3 classes have stuck with me better than any other course I took. Not to mention it made the class much less stressful and enjoyable. $\endgroup$
    – PGmath
    Commented Apr 16, 2021 at 19:40

I actually get excited to grade my students exams. I see the test/exams as the whole point of the class: the chance for the student to demonstrate what they know or don't know about certain problems. It's like the chance to get inside of my students head and see "oh, that's what they were thinking."

I also feel that grading is a responsibility that teachers owe to their students, ideally as soon as possible. I once heard a high school teacher say "I am giving them the unit 5 test today...but I haven't even started grading their unit 4 test." Can you imagine being a student in that class? Being held accountable for new information when you don't even know how you did on the older information?

Two things help me look forward to grading:

  1. I started to put a rather difficult question the students had not seen before as the last question of a test. This was always worth 7-10 points, so I explained that it was the "A student question." If you could mimic the formulas and regurgitate some memorized steps, you could get a B. But if you wanted an A, you'll need to earn points on the last question. This made me excited to see what solutions the students came up with, especially if it was different than mine. That gave me something to look forward to when grading.

  2. I started to collect data on every test question. I think most teachers unofficially get a feel for how the whole class did after grading a test or perhaps they might even keep track of everyone's final grades so they could report the class average and median. But I took this a step further and collected data on every student for every question. Then I could keep track of what the hardest questions were and which students were getting them right (or if the whole class missed what I deemed an 'easy' question!). If all I did was keep track of the final grades, then seeing the class average of 75% didn't feel like it meant anything to me. But if I see that on problem #4, the average score was 3 out of 8 points, then I can go back and find ways to re-iterate this concept. So I saw grading not as "what scores should I put in the computer" but more as "what didn't I teach so well and need to go back over." Adopting this mindset made it easier to begin grading a large stack of papers because it was ultimately about me doing my job better, not just attaching numbers next to student names.

I haven't done this myself, but I have seen teachers that do this:

  1. You could not hand write specific feed back in detail on each test (maybe just underline or circle where the student lost points). Then write up a document that shows what the most common mistakes were on each problem. That way, you're correcting everyone's mistakes in one document instead of over and over again multiple times on different tests. If the students aren't sure why they lost points or if they lost points for reasons that aren't on the "common mistakes document," then you can meet with them individually to discuss it.
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    $\begingroup$ It's important to note that collecting data on each question doesn't have to be a lot of extra work! Back when I had large exams with partial credit on each question, I was entering something like =10+5+7+3+3+8 into my spreadsheet. Replace the + keypress with tab or enter and you can enter these numbers into separate rows or columns to perform data analysis on. (including fun correlations and principal component analyses!) $\endgroup$
    – TomKern
    Commented Apr 15, 2021 at 16:07
  • $\begingroup$ I had one professor who could clearly predict student performance on an exam. Others may have been able to, but did not demonstrate it. I took a class from him and as he handed out the midterm he said "there are three problems. If you get two right, you will be doing pretty well." The scores were a uniform distribution from 0 to 100, so a 67 was not so bad. Later I audited a course from him, again three midterm problems, but "if you get one and do some of another you will be in good shape.". 15/30 was 70th percentile. $\endgroup$ Commented Apr 17, 2021 at 5:25
  • $\begingroup$ "I see the test/exams as the whole point of the class". To me this is a complete degeneration of the educational process. Examination is necessary for accreditation and institutional motivations require it, and as a teacher one must do it and do it well, but it is not and should not be the objective of an educational process. The objective should be to facilitate and guide the learning of those motivated to learn. Evaluation is not a necessary part of this process (doctoral programs normally have no evaluation), rather in part a recognition that many students are not motivated by learning. $\endgroup$
    – Dan Fox
    Commented Jul 6, 2022 at 6:50
  • $\begingroup$ @DanFox You're missing the second half of that sentence. To me, the tests/exams are my students' feedback to me, not just a score I type in the computer. That's what motivated me to grade any assessments quickly: 1) the students need to know how well they understood the content and 2) I need to know how well I delivered that content and what misconceptions they still have about it that I might need to potentially revisit. I agree with your sentiment that teaching is not just coaching students to do well on a particular exam. $\endgroup$
    – ruferd
    Commented Jul 6, 2022 at 19:25

Overall, it can become tedious and even frustrating to grade math homework or exams. Do you share the same frustration, and how do you handle it in the best possible way?

Some random ideas I have heard others use:

  • Choose a small subset of proof questions to grade in detail. You're right that proofs can be long to write and difficult to parse for the grader. Maybe just grade the "most important" one from a homework set and then post solutions to the others after they are turned in.
  • Develop (early) a set of expectations that include the things you want to see and the things you won't tolerate. [e.g. "Making any claim, such as "angle $A$ is $25^{\circ}$, without supplying written evidence or justification, will mean a deduction in points"] Then use a short-hand for marking these various things so you're not writing a ton to point out the same kinds of issues on every paper. This can help with your grading time, and it may reduce the number of occurrences of these things in your students' written work.
  • Do something else while you're grading exams. I knew someone who said they graded one student's proof, then did 5 push-ups, graded another student's proof, then did 5 sit-ups, etc. [This was during the pandemic lock-down when they weren't getting enough exercise, and apparently this kept them motivated to get the grading done.]

In addition to all the other GREAT advice, I would just advise to do it ASAP and do it fast (quick and dirty). And give yourself a beer afterwards. Students really appreciate the prompt feedback. It is HUGE to them. Tests are big events. And they want the info ASAP. I would always do it same day and post the results (clear names for students in the military, code names for...ugh..snowflake civilians). In addition to the benefit to the students, you don't have that awful hanging weight on your soul. Just done.

Um. And don't grade homeworks (assign it, but don't collect/grade it). And don't assign projects.

The other thing that helps you (and your kids) is regularity. Do tests on the same day (ever FRI for HS, every second FRI for college). It seems so arbitrary, but routine is helpful for managing the animals, to include yourself. Plus it makes that FRI beer taste even better.

Don't do (much) written feedback on test papers. And develop an acronym set--you can publish it. Things like SF-1 (sig figs minus 1). Or NWNC (no work, no credit). Or ACF (answered carried forwards). Learned that at nuke school in the military. The kids will learn it and get a little fun out of it. Like that badge of experience from Mr. Hardoof's class.

Take the test prior to giving it. Then take it again during the exam, while proctoring the students. You will be fast and it will be easy. But it gives some empathy, some brothers in arms, with the participants. And one of the repetitions can be used as your published solution.


Here's a short grab-bag of ideas; things I've found useful.

  • Design the test for gradeability. As the instructor, you have the power (hopefully) to design a test that you look forward to grading. Some of us get locked into legacy traditions from examples we've seen, or things mentors dictated. We don't need to necessarily follow those same habits if they're depressing to us. Think about what you can manage to reasonably grade, that makes for a quality assessment, and take responsibility for something you're eager to grade and get results from.

  • Use a reasonable point scale. Joel David Hamkins suggested that one use a 5-point qualitative scale to grade any mathematical question. I started using that and it made my process much easier. For some reason I can't understand, a lot of people get stuck on a 10-point scale for questions of any type. That's unnecessarily granular and you wind up wasting time debating over "6 points or 7?". Consider also the magical number 7±2.

  • Minimize writing feedback. From recollection, studies show that written feedback on graded tests is mostly ignored by students. It seems really hard to avoid (I still have not really succeeded to date), but of course the written feedback is the most time-consuming part, and arguably should be avoided. Provide a common solution sheet and refer students to that. (I do that, but still to date can't avoid giving individual feedback. Maybe someday.)

  • Consider digital testing. This is really an adjunct to the item above. I've learned in the last year, re: feedback, that I can save a lot of time with an online test, and a text FAQ/common errors file to the side, from which I copy-and-paste common feedback observations. At least for some of my classes I'm going to continue having students, in the classroom under my proctoring, log on to the computer system and take digital tests in the future, partly for this purpose.

(In addition, I use some multiple-choice questions on definitions and terms, and fill-in-the-blank numerical calculations, which can be digitally auto-graded. Forbid the thought of an all-multiple-choice test, though.)


I grit my teeth and do it. Skimming long answers for the relevant parts is a skill.

One way of handling the frustration is talking about it with someone. If that someone is also grading the same exams or homework, or was/is involved in teaching the course, this can even be genuinely useful.

But really, on the scale of frustrations, this is not a big deal. At least to me.

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    $\begingroup$ "this can even be genuinely useful." Or required, to ensure that all teachers at a given school are marking a given subject consistently. $\endgroup$
    – nick012000
    Commented Apr 16, 2021 at 2:49

Grading may be tedious. But overly long answers can be averted. A student may write a lot, hoping that the mostly irrelevant text will contain whatever the teacher is looking for. But in doing so, the student demonstrates a lack of knowledge – and won't get full credit. No matter what truths are hidden in the sea of irrelevant wrapping. Students write this way only because teachers let them.

Telling the students that you grade this way, should help even more. "If you are unsure, don't write down every irrelevant fact you know of; this will be punished." The point of an exam is to have the student demonstrate their knowledge. Including lots of irrelevant stuff, means they don't know what is relevant for the question. Such an answer gets a bad grade; even if it also includes a correct answer to the question.

  • $\begingroup$ One of the students I tutored had a professor that took off points if extraneous information was written down. I explained to my very weak student that writing everything that he knew about this type of problem would earn a deduction in points. He was disappointed but wrote less. $\endgroup$
    – Amy B
    Commented Jul 4, 2022 at 19:49

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