How do I fairly assign partial credit?
November 2, 2010 6:06 PM   Subscribe

How do I assign partial credit consistently?

I teach in a university statistics department. My exams tend to consist of a relatively small number of relatively complicated problems, and I like this style. As a result I give partial credit on exam questions.

And on the last exam I gave I had some students who believed they didn't get enough partial credit. It turned out, when I reviewed their exams, that they were right, and I gave them some points back.

But I don't want to make these mistakes! I have a rubric where I say "if student does X, give Y points" but students often do certain steps of the problem partially right, so get part of that Y... and I want to be consistent, but it's very difficult to keep track of who did what.

And on a related note, how do I make sure the students believe I'm fair in assigning partial credit? This is different than actually being fair - even if I am fair, some students will inevitably think that they got cheated. And I don't want the bitterness that that causes.
posted by madcaptenor to Education (24 answers total) 3 users marked this as a favorite
I've never been in this position before, but having taken a lot of tests, my idea would be to predetermine some checkpoints that one must pass through in order to arrive at the answer. Assign a certain portion of the problem's points to each checkpoint. And of course don't forget to forgive errors propagated from a previous checkpoint if later work is internally correct.
posted by Salvor Hardin at 6:09 PM on November 2, 2010

This is basically what I do, but they keep finding other ways to do things! And I try to propagate the errors but I run into situations where the error makes the problem simpler. So say a problem divides naturally into five equalish parts, and they do the third one wrong. And the result is that this makes the rest of the problem easier. So I might give, say, six out of ten. And they insist "I only made one mistake, I should get eight out of ten!" - what then? I kind of want to just tell them that I know more than they do and in particular I can tell from their answer they don't understand the material that well. But they care about their grades a lot and so I don't want them to think they're arbitrary.
posted by madcaptenor at 6:16 PM on November 2, 2010

Are you grading 1 question at a time? (That is, doing question 1 for each person, then question 2 for each person) That always helped me a lot when I was doing tricky grading, because if kept just that question and what I was doing on that question in mind.
posted by brainmouse at 6:18 PM on November 2, 2010

I don't know if this will help, and it is an entirely different subject (biology or some type of biology, insert the advanced biology topic of your choice), but I used to go through great pains to grade consistently.

Here is the solution that eventually worked for me:

Make a list of points that you should see addressed (I guess in your case it would be how many steps should you see, but let’s pretend you should see 6 steps—then I would decide that I needed to see 5 to give the student full credit, whatever, but write down those steps).

Quickly skim the tests from people who normally do well – can they hit those points? If they don't you may need to revisit your rubric.

Then skim the test from a few people who do not normally do well – do they hit any of the points or say it in another way (so that they could get ½ a point at least?)

I went through 10 or so answers to the same question so that I had a well-developed rubric in advance.

Then I scrambled up the tests, cover up the names, and went through all of them. If you find a new point that a student addressed part way through (or something that you think is worth partial credit), add it to the list (and glance back to make sure that no one else had the same point – fortunately I had a good memory for this).

Let me just say in advance that I feel that I was extremely fair, but to grade like this took several hours to get through a few essays. If you had 20 to 40 students, then it meant that it took days to grade an exam. No matter what you do, someone will still argue.

I eventually shifted over to multiple choice and only 1 or 2 essays, because in the end, people only saw the points and a reason to argue, but YMMV.
posted by Wolfster at 6:25 PM on November 2, 2010

Just reread your reply to another poster. Your rationale describes exactly why I shifted to multiple choice versus essays and partial credit.

They don't understand the material, and at the end of the day, if they are using that math to calculate how to dilute a drug, for example, and don't get it, well, they just killed someone if they use it in the real world (there is no "partial credit").

Also, what bothered me most of all - if you do give in to some of the students who beg and plead to give them more points, then 1) you are reinforcing the whining behavior, not mastery of the material and 2) it really, really isn't fair to the other 95% of the students who are not at your door insisting that they get points for partial whatever, and 3) for the students who did bother to learn all the material very well, if everyone gets so much partial credit that it = their grade, is it fair to them?
posted by Wolfster at 6:31 PM on November 2, 2010 [1 favorite]

A high school teacher I worked with would break problems down into stages or major steps and evenly break down the credit across the stages, then either give the full stage value for each stage completed correctly or around 50% of stage value if the student at least attempted the correct (or a somewhat feasible) approach to that stage. Evidence of checking answers garnered some credit too.

When I was at university myself I'd frequently get to the point in an exam problem where I knew I'd screwed something up but I didn't know how. I would write little notes explaining how I knew I had the wrong answer at this point and what I would have done if I'd gotten the correct answer. This actually got me an astounding amount of partial credit; I got the impression from my professors that this sort of feedback was unusual.

(On the other hand, I never argued over the grades... if they're getting down to fighting with you over the value of particular problems that seems like a bit much. I mean seriously, complaining about a six out of ten when they completely blew the actual answer to the problem? I'm not a teacher or a student any more but I would say screw 'em.)

I would think that one thing that might help, as far as the classes' perceptions, is if you clearly explain and give them explicit goals for how to achieve partial credit. They'll probably feel that it's fairer if the rules are clear and it may generally help with morale - y'know, that sort of sinking feeling you get when you know you aren't on target in a long, complicated problem... there's some hope to be had if you can do damage control by at least making a fair bid for partial credit. (Although from what you're saying it sounds like they're basically taking partial credit for granted at this point... in my day we would feel lucky to get any partial credit at all, lucky I tell ya.)
posted by XMLicious at 6:32 PM on November 2, 2010

It is likely that your rubric can be simple, if you add a bit of a stick to your carrot: a question answered correctly is full credit, a question answered partially correctly that went off the rails or was left unfinished is partial credit earned if they stay after and learn to work through the rest of it with you, and anything less is no credit.

The upshot of this is that you'll be assigning partial credit to students who demonstrate they had the right idea (at least at first) and care enough to learn where they went wrong, and someone who doesn't want to put in that effort won't get the partial credit. You effectively assign partial credit for a combination of having paid some attention and being willing to put in effort where their knowledge failed them. Without that one-two punch, I can't imagine why anyone would expect partial credit, personally.

However, I'll agree with Wolfster that this is effective for questions with fuzzy answers, or without life-threatening consequences, but if we're talking about mixing drug formulas or calculating stress loads, partial credit may hurt more than it helps (except as a motivator to get 'em to stay after class and learn what they've failed to learn previously.)
posted by davejay at 6:53 PM on November 2, 2010

In graduate school, I had a professor whose policy was if you made a mistake that trivializes the problem, you lose more points than othewise---thus, the answer to the student who complains that the 6/10 should be 8/10 is that the mistake made the rest of the calculations significantly easier.

In general, I:
--grade one problem at a time
--have a partial credit assignment on my solutions for each problem (not for student eyes)
--tend to write problems with multiple parts, so that the partial credit assignment is mostly clear because of the part division

But honestly, I typically have very little pushback on my point assignment (on math tests). My own rule if thumb is that if a student cares enough to bother to come argue about points and can make some sort of compelling argument, I'll typically give a point or two.
posted by leahwrenn at 6:59 PM on November 2, 2010

some students will inevitably think that they got cheated

I'm not sure this is a useful way to think about the issue. It sets you up immediately in an adversarial relationship with your students via a via grading---instead of you're trying to assess their work to the best of your ability. And if you make a mistake, or if you don't notice a subtlety of their work, then you're happy to rectify the error and make sure they get all the points they're entitled to. And you can say as much to them.

I don't have hordes of students in my office grade-grubbing, even with such an approach, although Your University May Vary.
posted by leahwrenn at 7:03 PM on November 2, 2010

Another way to help even things out is to grade one question at a time, as suggested by brainmouse, plus read the answers from 3 or 4 students without marking anything and put those papers back at the bottom of the pile to be graded. This kind of gives you a feel for what sort of answers you're going to get, without penalizing the first few. I usually found I was harsher on the first few papers because I expected the students to do better than they actually did, so this kind of levels the field a bit.

After seeing a few answers you'll probably have a better idea how to apply partial credit impartially. Do you give extra credit for bad puns?
posted by Quietgal at 7:12 PM on November 2, 2010 [1 favorite]

You might find this source helpful in thinking through your options: Effective Grading: A Tool for Learning and Assessment in College, by Barbara Walvoord.
posted by 5Q7 at 7:33 PM on November 2, 2010

Basically everything I'm hearing is things that I already do. Except for davejay's suggestion that I give partial credit for students who stay after and learn to work through the rest of the problem with me. I like this idea but my classes are large enough that it's impractical.

I just want to clarify that I don't actually have a huge number of students asking to get some points back. This is mostly because I had the foresight to say that they had to submit requests for regrading in writing; I think this stops the most frivolous ones. But I find myself imagining that for every student who asks me about grades in a somewhat hostile tone there are N more who are silently bitching and moaning.

leahwrenn: to your first comment, my policy on trivializing a problem is essentially the same as your grad school professor. But this is not in writing. And I teach large classes (60 in one, 100 in the other) so even if I said this some substantial number of students wouldn't hear it.

My own rule if thumb is that if a student cares enough to bother to come argue about points and can make some sort of compelling argument, I'll typically give a point or two.

I usually do this, too.

I'm not sure this is a useful way to think about the issue.

Oh, I don't think it is either. But the students seem to think of it this way.
posted by madcaptenor at 7:41 PM on November 2, 2010

I have experimented with a couple of different ways around this problem.

One is instead of having a rubric that gives marks for certain parts of the problem, have one that gives marks for demonstrating certain types of understanding, which the problem is designed to test. As a really simple example, imagine you have the problem: 1+2=3. This is designed to test that students understand the concept of addition, and that they can get the correct answer when applying addition. So you might give 1 mark for showing understanding of the concept, and 1 mark for the right answer. Students who give the answer -1 or 2 or 1/2 probably didn't even understand the concept of addition and were trying to apply subtraction, multiplication or division instead. Students who got an answer like 4 probably were trying to add but screwed up. That is not a very good example, but hopefully it shows what I mean. Usually a big complex exam problem would be designed to test five or six different components of understanding. And even a correct answer, if they don't show any working, might not illustrate sufficiently that the student understood all of these. If you are going to take this approach, you have to explain it to them in advance, and preferably have a couple of smaller assignments that are marked this way before a final exam.

Another solution is to sort all the exam papers for each question before starting marking them. Usually there will only be five or six different ways that a student can screw up a problem. So sort them into piles for each type of error. Then you might be left with one or two "special" papers that have an error completely their own. They usually fail. Then you can rank the error types - i.e. error 1 is not very serious, error 2 is worse, because it shows they didn't understand concept X, error type 3 is a disaster, because it shows they didn't understand ANYTHING, etc. Then assign marks for each error type, (error type 1 will get 18/20, error type 2 will get 15/20, error type 3 will get 8/20, etc). Then adjust individual marks if necessary for other small problems (not showing working: deduct 2 points; not using the right units, deduct 3 points, etc).

I find that the first solution is better for large groups (200 or more papers) because it's faster. The second solution works well for around 50-100 papers.
posted by lollusc at 8:08 PM on November 2, 2010

lollusc: I think I'd need to see some examples before doing your first scheme. And I'm not convinced that it would give much different results than a "conventional" approach.

And even a correct answer, if they don't show any working, might not illustrate sufficiently that the student understood all of these.

Yes! I've gotten a lot of "where did my points go? I got the right answer" questions to which the answer is that they didn't justify the answer properly (or at all), and that that justification is pretty important.

As for the second scheme, that actually seems like a good idea. In my experience, the number of different errors students can make on a given problem is fairly small. And this is what I essentially try to do, except without the physical device of actually sorting into piles. So I end up thinking "wait, what did I give the last person who made this particular mistake?" and going back and trying to find that one, which is frustrating, especially since sometimes it turns out there was no such person.
posted by madcaptenor at 8:23 PM on November 2, 2010

So I might give, say, six out of ten. And they insist "I only made one mistake, I should get eight out of ten!" - what then?

You say, No. You get six.

You're starting down the "too nice" road. It's ok to be in charge and set the standard. They're the ones who did the problem wrong, not you. Of course they're going to try to weasel as many points as possible out of you—they'd be fools not to. That doesn't mean you have to give them any more.

If you want your standard to be that you stop giving away points (or only give 50% of the rest for correct procedure, or whatever) once the error significantly simplifies the problem, then that's what it is.

Sometimes my written exam questions are based on scenarios with action levels - I might ask what radiological concerns are going to result and what actions will be necessary from some ridiculous casualty like a radioactive vacuum cleaner getting dropped down the stairs and busting open. Part of the problem requires some judicious assumptions - how much comes out? How much of that gets dispersed into the air? What is the volume of the space?

I try to make it difficult to do, but it's possible that some of the assumed parameters could be manipulated to always result in no actions required, yay! I'd take off a few points for that if the math was otherwise ok. The problem is, when they then have to calculate exposure to the person involved, no fair saying "since airborne worked out to less than the limit, exposure is negligible." I still want to see the math, since that was kind of the point of the exam question. I don't feel bad about not giving away any points for part B, even though it was error carried forward from a previous part.

Maybe reference your rubric to your learning objectives, so instead of grading by the answer, you grade by what knowledge they showed you. In my scenario questions, when I get thwarted on my point breakdown by errors I hadn't thought of, I can at least fall back to something like:

Did I get to see:
That they knew there was a problem and what it was? X points.
That they knew the methods to calculate what they needed to (correct answer or not)?
That they know what the action levels are (I make people write "answer which is less than/more than the limit of limit" so I can grade that knowledge, too.
If they took correct actions for wrong results, some points. Not all.
If the assumptions were so ridiculous that the problem was greatly simplified, no more points. (Volume of the room is 1 x 10^3 ml, really? Come on, now.)
and so on.
posted by ctmf at 10:28 PM on November 2, 2010 [2 favorites]

Basically, no points for knowledge you wanted to test, but didn't get to see. If I want them to show me that they know the actions for an airborne concentration above the limit, and I don't get to see it, no points for that portion. Doesn't matter if it was error carried forward, or if my question was poorly worded, or if they forgot to write that part, or any number of ways that might have happened - I didn't get to see what I wanted to see.

That said, I try to write my questions so that they can't be sabotaged in this way too badly. If it's critical that I see part B, I might just break it into two questions - one asks to calculate the airborne, and then the second says "assume that instead of your previous answer, your spill resulted in an airborne concentration of blah. NOW what, tough guy, eh?"
posted by ctmf at 10:40 PM on November 2, 2010

I don't know how well this will apply to stats, but in physics I had a professor who had what I thought was a very fair system of partial credit: you got partial points up until you made a mistake. So the student who'd made an error on step 3 of 5 would get points for only the first two steps, despite working the last two steps "correctly" based on the error in step 3.

As he explained it, the beginning steps of the solution are the most important. If you misunderstand a problem and choose the wrong formula/approach, then it doesn't really matter if the rest of the problem is "correct." This might seem harsher, but he offset some of it by having earlier steps worth more.

I may be influenced by the fact that he took the trouble to explain it, rather than just saying "I give partial credit, so show your work!"

I did have another math teacher (high school) who had "approach" and "execution" points - pretty self-explanatory.
posted by clerestory at 10:43 PM on November 2, 2010

Consistency is not anywhere near as important as an accessible, transparent appeals process. If your students know that
  • you welcome being approached when they're unhappy with their marks
  • you will review your marking if asked to do so
  • such a review might actually result in a lowered mark if that is what the facts warrant
  • everybody only gets one appeal for one test
  • students unhappy with their post-appeal results are welcome to raise the issue with your head of department
you should end up respected.
posted by flabdablet at 10:44 PM on November 2, 2010

I find myself imagining that for every student who asks me about grades in a somewhat hostile tone there are N more who are silently bitching and moaning.

As long as the ones who are silently bitching and moaning are also the ones who haven't bothered to do the work, you're doing fine.
posted by flabdablet at 10:47 PM on November 2, 2010

Oh, and get a little diary book or something to keep a log while you're grading. Every time you have to make a judgment call on one, write it down and what you decided. Include the question number (from your question bank, if applicable.)

That will help you apply the judgment calls consistently (since you can look up previous ones easily). It will also jump out at you if one of your questions just sucks. Sometimes it IS the question, and it can be reworded or reorganized in a way that cuts down on some of those errors. Other questions might just need a giant table of all ways to screw it up, and how many points they get for that. (I'd sooner just get rid of that crappy question and find a different way to test that knowledge, though.)
posted by ctmf at 10:49 PM on November 2, 2010 [1 favorite]

I love flabdablet's answer and 2nd those thoughts.

When I taught, I would share the rubric with the students (making it vague enough not to reveal answers - 1 point for trying the problem, 2 for using the correct formula, 3 for getting the 1st part, etc), which settled disputes quickly because we could use the common language of the rubric. "Where do you think your work falls on the rubric?"

Tangentially, I had a prof who hilariously gave this challenge:
You have two deadlines: an early deadline and a late deadline. If you choose to turn your work in on the early deadline, I will grade it while drinking a fine wine, after enjoying a delicious meal. If you choose the late deadline, I will grade it after I've had a rough night of sleep and an argument with the neighbor.
posted by jander03 at 11:33 AM on November 3, 2010

Late to the party but: I have found over the years that it's better for problems to be worth few points rather than many points. Then, in a complicated problem in Statistics or Calculus, I can grade based on how far into the problem you got, and if the problem is only worth 5 points, it's pretty easy to figure out whether you get 5, 4, 3, 2 or 1 point.
posted by wittgenstein at 10:51 AM on November 4, 2010

wittgenstein: that's something I forgot on the last exam I gave. It was four problems, each out of 25 (so the whole exam would be out of 100). There's no reason I couldn't have made the whole exam be out of 40, or even 20. It's a math class, the students can handle weird numbers.
posted by madcaptenor at 11:31 AM on November 4, 2010

Very late to the party, but it's my party: I gave an exam yesterday. I made all the problems be out of 2 or 3 points, as opposed to the 6 to 8 points I would have given before. Seriously, this reduces the stress involved in grading a lot. I spent a lot less time agonizing over "how much partial credit is this worth" while grading.

And I teach probability, so this also inspired a future homework problem about the probability of the roundoff error in such a scenario being really large. (This is part of my "look, probability solves real-world problems!" series of problems, which is fun.)
posted by madcaptenor at 10:21 PM on September 29, 2011

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