By Trevor Hedberg

Anyone who has taught even a single philosophy course has probably had to deal with borderline cases at the end of the term. A borderline case occurs when a student is right on the edge of receiving a higher letter grade in the course. Perhaps a 90% in the course is required for an A-, and the student has finished the course with an 89.8%. These cases seem common. In my own experience as an instructor, roughly 20-25% of students find themselves in this situation when the semester concludes. But here’s something that’s a little puzzling: beyond my own courses, very few syllabi that I have seen explicitly address how borderline cases are handled. In fact, I cannot recall seeing one course syllabus that addressed this issue during my entire undergraduate career.

From both first-hand and second-hand experience, I gather that what usually happens is the professor evaluates these cases on an ad hoc basis by looking at (1) the student’s perceived level of effort in the course, (2) the student’s body of work as a whole, or some combination of these factors. If the professor is appealing to (1) and the student appeared to put forth a lot of effort in the course, then that student gets bumped up to the higher grade; otherwise, the student gets the lower letter grade. If the professor is appealing to (2), then they examine the major assessments and see if the student’s body of work is indicative of a higher level of course mastery than the raw numbers indicate. Typically, if the student demonstrated improvement over the term, then they will get bumped up to the high letter grade; otherwise, they will receive the lower one.

The problem is that neither (1) or (2) will produce consistent or fair verdicts about these cases. Student effort is absurdly difficult to measure. Because we see our students for such a small portion of each week, we have little insight into how many hours they are putting into our course. Moreover, effort cannot be equated to quantity of in-class participation: students who frequently participate in class with half-baked ideas are not obviously putting in more effort than students who contribute rarely but with insightful thoughts and observations. Poor contributions to discussion may be evidence of a failure to complete the assigned reading or a failure to spend time reflecting on the material. But they also might just be evidence that the student is struggling to grasp the course concepts despite her best efforts. How are we to know how much effort the student is really putting into the course?

(In the prior paragraph, I'm conceding for the sake of argument that it is permissible to factor effort into final grades for the term, but I should not that this position is controversial.  See, for example, section 3 of Daryl Close’s “Fair Grades”.)

Assessing a student’s body of work is similarly ineffective. You already know that the student’s body of work produced an unclear result: that’s how the borderline case arose in the first place. If later assignments in the course are supposed to be weightier in determining a student's level of mastery, then that fact should be reflected in the actual weight of the assignments (i.e., their percentage of the final course grade) and affect all students rather than being applied selectively to certain students at the end of the term.

Moreover, higher grades on later exams and papers will not always be a reflection of improvement in knowledge of course material. A student may, for example, have bombed an early test because she had three other exams that week and was therefore unable to adequately prep for all of them. In such a case, her higher grades later in the term will be a reflection of having fewer commitments during the weeks those assessments are due rather than any meaningful improvement in her knowledge of course content. (Cases like this are quite common because college instructors have a tendency to schedule their assessments at similar points in the academic calendar.)

So what should we do about borderline cases? Well, here’s one easy solution: just don’t bump anyone up. Full stop. Such a policy treats all students equally and can be added to your syllabus with a single sentence. It also saves you work because you don’t have to puzzle over borderline cases at the end of the term. Sounds great, doesn’t it?

There’s just one problem: when you get that student who made an 89.8%, are you really that confident that a B+ is the appropriate grade? We all know that the difference between, say, an 84% on a paper and an 87% on a paper is difficult to judge. I feel that almost any fine-grained judgment I make on a paper or essay has a margin of error of +/-2%. As an illustration, if I gave a paper an 86%, I suspect that one could reasonably make a case that it should receive an 84%, and that one could reasonably make a case that it should receive an 88%. I’m skeptical of anyone who claims that they can make consistent judgments on philosophy papers or essay answers to the exact percentile, particularly since we often grade a lot of these and under significant time pressure.

What this means is that you cannot be fully confident of your judgments in borderline cases. You may have been overly harsh on the student on a previous assessment or simply made an error when grading under conditions of fatigue or stress. And a small error or two like this could be what makes the difference in a student’s course grade. If we want students’ grades to accurately reflect their mastery of the course material, then this is a problem.

I’m still actively considering the best way to adjudicate borderline cases, but I have tentatively settled on using a system of Borderline Points to resolve them. Here’s an except from a recent syllabus that explains the system:

There is no extra credit in this course, but there are opportunities to attain Borderline Points. These points will be the determining factor in Borderline Cases (i.e., cases in which a student is within 5 points of reaching a higher grade in the course). If a student has accumulated (for instance) 936 total points on all the course assessments, then I will look at their total number of borderline points and add it to the point total. Suppose that after adding the borderline points, the student has 941 total points; in that case, the student would receive an A for the course (rather than an A-). If, on the other hand, the student did not have enough borderline points earned to reach 940 total points, then the student would receive an A-. Details on acquiring these points can be found on Blackboard in the handout “Borderline Point Challenges.”

My courses have 1000 total points possible, and these borderline point challenges allow students to accumulate a few points that will be added to their grade if they find themselves on the edge of receiving a higher letter grade. These challenges are usually short writing assignments that are graded on adequate completion. Each is worth 1-2 points.

One of the major advantages of this system is that the students control their own fates in borderline cases. I don’t have to make difficult judgments or worry about being biased in favor of students I have grown to like over the term. I just look at their borderline point totals. Suppose a student accumulated 896 points: if she got 4 borderline points or more, then she gets an A-; if she got 3 borderline points or fewer, then she stays at a B+. End of story.

It may not be an optimal system, but it’s the best one that I’ve devised thus far. I’m curious, however, what others think about this issue. How do you all assess borderline cases at the end of the term? And do you include that information in your course syllabus?

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9 responses to “How Should We Handle Borderline Cases?”

  1. In the UK, borders for individual classes are sharply fixed, and cannot be changed. Borderline cases are resolved holistically. If a student is within .5% (or maybe 1%, I don’t remember) of a border, then the board of examiners has the option of bumping them up to the higher grade class. This can be done on the basis of two criteria:
    1. Preponderance: Are the majority of their individual class marks in the higher grade category? Maybe they had one really bad class that they bombed, but did really well in everything else.
    2. Trajectory: Has their mark gone consistently up over the course of all three years? If you take their course work in the final year alone, would they be in the higher category? If they wrote a thesis, was it in the higher category?
    These criteria can be individually sufficient, but sometimes jointly necessary.

  2. Michel X.

    What if a student has 3.5 borderline points? =p
    Is there any harm, really, in bumping every borderline grade up? One could do this by singling out all of the students on the cusp of a higher letter grade and bumping up that way, or even just by saying that at the end of the semester any partial credit gets bumped to a full percentage point (so, e.g., 89.3% turns into 90%), or anything above .5 (normal rounding rules apply), etc.
    That would be my inclination, at any rate. It’s easy and seems perfectly fair to everyone involved.

  3. Daniel

    I don’t announce point thresholds in advance. That lets me avoid borderline cases. I’ll explain.
    I say on the syllabus how much of the final grade will be determined by each component of the class. At the end of term I come up with percentages for all components of the class. Then I look for gaps. If, e.g., there is nobody between 89 and 91, then that’s a good spot for a gap between B+ and A-.
    This is a form of curving, which I’m fine with. Of course it’s not guaranteed to work–if there are lots of students and the grades follow a non-gappy normal distribution, then it won’t work. But given the numbers of grades I usually have to come up with (typically in the 10-20 range per class), that doesn’t usually happen.

  4. Michel X, I have known professors who handle it that way, but I worry that strategy just pushes the issue back a bit. If you round all scores, then you run into a similar problem with a student who makes something near an 89.4%: how confident can we really be that this student didn’t make the magic 89.5% threshold and shouldn’t get the bump up? Part of the reason I like my system is that the students have control of their fates in these circumstances, and it doesn’t come down solely to my fine-grained judgments on a few assessments.

  5. Michel X.

    Trevor,
    If you round all partial percentages up to the next whole number, however, then the 89.4 becomes a 90. Seems fairest and easiest to me, and nobody gets partial percentages any more.

  6. Good post, Trevor, and good discussion.
    I have an explicit policy in my syllabus, as follows: “The letter grade cut off for, e.g. an A- is 90.0, not 89.5 or 89.9. But I may choose to round up in exceptional cases, if (i) I feel you’ve done better or worked harder than your grade suggests, and (ii) your grade is not due to excessive missing assignments. This is a courtesy, not an entitlement.”
    As you can see, it basically just codifies the problem you’re asking about. Technically, cut-offs are strict and well-defined, and there’s no obligation on my end to consider rounding-up in borderline cases. But I may do so in certain cases.
    In practice, I’m much less strict than the policy makes it seem. This is mainly because, as you note, grading is highly fallible. So, in practice, I think its safe to assume that I could have given them an extra 0.n points somewhere during the term. And the way I run my classes, students have to really try not get the grade they want, so its usually pretty clear who deserves rounding up and who doesn’t.
    One point about effort: you’re right that its hard to discern how much effort a given student is actually putting in, let alone how much that effort should determine their grade (We wouldn’t dock points from students who don’t have to study for lack of effort, after all). I set up my classes explicitly so that you can get an A just by working hard consistently: there’s basically a threshold above which high quality work doesn’t make your grade better. At least, that’s what I do for lower-division courses. Upper-division/ grad courses are different, but in lots of ways that make rounding-up less of an issue anyway (at least in my experience).

  7. One more thought, about avoiding the problem rather than addressing it. As you mention, putting the students in control is good for both student and instructor.
    I often will allow for extra credit assignments that put the rounding-up burden on the student rather than on me. I think they’re a lot like your Borderline Points system, except I just treat them as extra assignments. For example, I’ll let them do a small number of one-page response papers or something, worth 1% of their final grade each (so, much more work for these points than normal). Anyone who is in range of getting rounded up can choose to do some more work in get over the hump, if they want. But its on them.
    I also like to allow re-do’s on certain assignments. For instance, if I assign three short papers, I’ll let them R&R them if they get a C or worse, with a new grade of up to 80%.(And I do mean R&R: they have to write a cover-sheet explaining what they fixed and why). Its a very powerful teaching tool, and it also lets them do the work to ‘get rounded up’ themselves.
    Third, for lower-division courses I have small, low-stakes quizzes every day. They’re worth about 1% each, but I’ll offer more than I grade; this semester, I give 38 quizzes, but you can only get 35 points total. This build-in curve allows students to miss a few quizzes’ worth of questions throughout the term without penalty. This means that they’re less likely to end up with just a point or so less than they needed, and if they do they have a clear explanation of why (e.g. they blew off 5 quizzes instead of 3).
    One principle underlying all these approaches is to give the students several opportunities to get the grade they want, and if possible more than one avenue for doing so. Done right, you minimize cases where one assignment is directly responsible for the grade. And putting the students in charge of their own grade as much as you can makes your life a lot easier, not to mention making the students happier.

  8. Jerry, I also incorporate rewrites and exam retakes into my courses, but I hadn’t made this connection to how it could impact the frequency of borderline cases and how students feel about them. It sounds like our overall outlooks on these issues are quite similar.

  9. Joe

    If a student has a course grade of 90.1%, is that student questionable to deserve an A? Why should a student with two points less out of a 1000 points course with a course grade 89.9% be considered for less or scrutinized MORE? It’s simple math. If your syllabus says that 90% is an A, math tells us that anything from 89.50 to 90.49 is considered 90% (using mathematical round up/round down principals). Just give the student that best rewards the student and don’t look to punish border, because that is totally counterproductive to encourage students to work hard and learn. And some of the hardest working students are those on the border that will do anything to get those those 5 or 10 points that make the differ. Use some common sense and don’t judge students so harshly.

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