Friday, November 09, 2007


Ask My Readers: Pluses and Minuses

Becky Hirta's recent post about grades got me thinking. My college doesn't give 'plus' or 'minus' semester grades – you can get a B, but not a B-plus or a B-minus. The topic comes up for discussion about once a year.

The argument for pluses and minuses is basically that they offer greater precision. There's some distance between a B-plus and a B-minus, but in our system, that difference is erased. By the same token, if a student is on the border between two letters, there's more at stake in the decision which way to go.

The argument against, as near as I can tell, is based on false precision. The greater the number of gradations, the harder it is to get it just right. There's also the persistent ambiguity of the C-minus.

Since this argument is raring up for its annual go-round on campus, I'd like to get my readers' perspectives. Does it make sense to go with pluses and minuses, or are we better off sticking with blunt, whole letters?

My school also just has plain letter grades. Their argument for keeping it that way is that when students transfer, if for example, the new school doesn't award a B-, then how will it transfer?? As a B or a C?

Since the goal of most of our students is transfer, this is a pretty powerful argument agains them.

Personally, I'd like to see a +- system. It lets me more accurately reflect the differences in the B grades. It keeps me from having to give the same A to someone with 90% as someone with 99%, (the 90 would be an A-) and it motivates the B students to still work for a B+, even if an A is impossible.
The greater the number of gradations, the harder it is to get it just right.

I find that notion philosophically repellent. Pretending there is no difference between a 90 and a 99 for anyone is so wrong that it overrides the chance that someone might mistakenly get a 93 instead of a 94. I wish my grades were allowed to reflect that someone got an 89 instead of a 90, rather than just a B+/A-.

I can't find the post on grades that you mean? Not seeing anything directly relevant as I skim her front page.
My undergraduate school had a plus-only system. A is 4, B+ is 3.5, B is 3, C+ is 2.5, and on. That eliminates the most ambiguous grade in the system (C-) and also gives you a rational grade-point system, instead of the A- = 3.7, B+ = 3.3 monstrosity that most schools that go plus-minus use. I think there's a lot to be said for such a system.

But I *hate* *hate* *hate* a system without some kind of greater gradation. The gap between A and B in a system without pluses and minuses is simply punitive, and I find (amateur psychoanalysts, take note) I give out more A's in such a system than I would in divided system.

For what it's worth.
I decided a long time ago, back when I took my first course in testing and measurement, that when the error of measurement in the average exam comes out to be, say +/- 5 points on a 100 point scale, it's impossible to be precise within 10 points, much less to one or two points.

There genuinely is no difference between a 90 and a 99 most of the time. Anyone who thinks that even a well-crafted exam is giving them a system that shows real differences between a student with 85% and a student with 81% is fooling themselves, unless they're using items that have been tested and evaluated for reliability and validity. I know some faculty who do. They've spent years building a pool of evaluation items that are statistically sound, and those are the ones whom I would allow to give +s and -s. But otherwise? No.

My students and I usually devote one class period to discussing what it means to get a 76% on an exam; what is a "point?" How do I construct a test that fairly measures what they know? How do I assign credit for labs? (I teach undergraduate physics.) They are amazed at the notion of standard deviation!

We generally don't have the kind of precision needed to give As, Bs, Cs, Ds and Fs. We almost certainly don't have the precision to give plus or minus grades.
my cc gave end of semester numbers for each class, out of 4.0. I have no idea how faculty figured these things but they didn't go 3.0, 3.5, 4.0. No, I actually got end of semester grades like 3.1 or 3.4 or whatever. That was precise. Actually, my tendency to grade all my assignments numerically is probably owing to that first experience. I think letter grades are suspicious because they seem inherently imprecise. And I've TA'd for enough faculty to know how imprecise they can be and that some faculty really prefer it that way.
Vicki (or anyone), can you point me at an extended layman's discussion of this? I'm pretty confident that I can identify a lot of real differences between an essay that earns a 90 and a 99, although whether those demonstrate that the students are actually different is questionable. But I'm not sure which you mean, and I want to understand these issues.

But I'd also think that finer gradations reduce the cost of necessary imprecision. E.g., in med school admissions getting a B instead of an A could really make a difference--getting a B+ instead of an A- makes less of a difference--if the transcript showed an 89 instead of a 90, it's clear to the admissions person that the difference is insignificant.
My post-doc institution has an odd system. A AB B BC C CD D F. The same question as asked above, if someone wants to transfer, how is an AB received?
The University of Waterloo gives percentage grades. This is weird enough for undergraduates, but supremely bizarre (to me) for graduate students.

I think that A, B, C, D is just fine. (McGill, by the way, solves the C- problem by not having C-s).
I tend to think "grade snobbery" plays into this equation.

Someone who needs the satisfaction of knowing that they are 1 or 2 points better than someone else would argue for a +/- system.

Others would argue that an A is an A not matter where it hits within the range because they need all the help they can get (Hi!).

As an instructor, I vastly prefer a system with +/- instead of just "whole" grades. I think it is much easier to make decisions about the borderline cases when all that is at stake is a third of a grade point, instead of a full one. (Of course, with +/-'s there are more borderline cases, but that's a small price to pay.) In my experience teaching large math classes, the final grade distribution is essentially continuous (e.g. no clumps which can be nicely labeled as "A", "B", etc.). As a result, there will always be many people very close to the grade lines, who get assigned, essentially arbitrarily, one grade over another. So it's best the grade distinctions made by crossing these lines are as small as possible.

As for the worry about "false precision" and not getting the grad "just right" with more gradations, you are basically choosing to have many small injustices instead of a few very large ones, which strikes me as a good deal.

I also don't follow Vikki's argument that student assessment is inherently noisy (which it certainly is) means we should avoid assigning +/-'s. Like dance, I would argue conversely that if we should assign no statistical significance to the skills a students who received an overall scores of 78 and 82, respectively, then the last thing we should do is assign the first a "C" and the second a "B".

One thing I would recommend avoiding is a system with a "D+", which may be the cruelest grade in the world.
How about a system with an F+? The system I "grew up" in had a 0.5 that gave you a tiny bit toward your gpa even when you didn't earn any credit! I guess it would signal someone who took the final and failed, but it was abolished (after a wonderful year of academic arguments) along with the 4.5 grade that was creating issues between colleges that rarely used it and ones where it was common.

That was a system with numeric grades, but functionally equivalent to ones that use a B+ or an A- to assign a 3.5 grade. (You can guess which one the students prefer, but a D+ for 1.5 is clearer than a C-, because it is not a passing grade.)

I liked that system as a grad TA, and there is no grade inflation when some A's become 3.5 along with some B's. I don't have any political advice on the argument at your college other than to enjoy it and insist that proponents be clear about what problem they are fixing and which ones they might create vis-a-vis articulation agreements. It is certainly easier for all involved if a CC sticks to a basic system that requires no interpretation on the other end.

I can't imagine using the quarter point scheme some schools use, where an A- is 3.75 and a B+ is 3.25 ... and a C- is 1.75. It has fine divisions that do not uniformly sample your score distribution, and creates a nightmare for some colleges.

Example: A C- grade at 1.75 is considered a passing grade and cannot be repeated, but an engineering student *must* have a minimum grade of 2.0 in a required class for the program to be accredited! An elaborate scheme is then needed to substitute the grade in a harder course for that C- to demonstrate the required competency.

Students who transfer here see their + or - removed, raising a C- to a C but dropping a B+ to a B, but will see the original grade reappear (or be reinterpreted) when they transfer back to a school that has a fractional grading system.
In theory, my university uses GPA directly--instead of receiving letter grades, we receive a "grade" on a 4.0 scale. So in a given quarter, I can't receive an A or an A-, but I can receive a 4.0, 3.9, 3.8 and so on. I assume the logic is that this allows far greater precision than other systems. However, there is no university standard as to how grades are assigned. (At my previous schools, there were guidelines as to >.93% was an A, 90-93% A-, etc. How an instructor determined percentages was up to him/her.)

In practices, every class uses an arbitrary system to assign grades. (I've TA'd for many, so I've seen this first hand.) A 95% in one class may be a 4.0, in another is may be a 3.6. (Note that adding the magic of the curve makes this more complex.)

As a graduate student, I find this system hurts me when competing against students from other schools. My course grade when I received a 99% was a 3.9 ("4.0 is for perfection!"). At any other school, this would be a 4.0 (99% leads to an A, which is worth 4 grad points). When GPA's are calculated, mine will be lower every time.

This system leads to some undesirable behavior in students: they (and I!) will tend to grub for every single point on every single homework, because they all matter to the final grade. If a single point out of 500 in the course can keep me from a 4.0, you can bet that I (and any of my students needing competitive grades) will go and argue every point with the professor.
I vote for pluses and minuses. Without those options, grade inflation seems likely -- at least it does for me, anyway. If a student has a really, really high B, and the student after her has a very, very low B, I know I can't bounce the low B to C just to distinguish between the students; hence, I'm always tempted to bounce the very, very high B up to A because there has been a qualitative (if not quantitative) difference in their work. Call it giving the benefit of the doubt to the student who has indeed worked harder. I would much rather just have a plus handy to indicate that her B was not JUST a B. (Yeah, yeah, a B is an above average grade and all that...but sometimes it looks pretty stark. The plus gives more nuance to the grade.)

As an adjunct who is also taking classes well outside my field (I'm liberal arts; I'm taking advantage of the "free class" benefit to take all the sciences I never did when I was a college student), I sooooooo appreciate that 90-100% is an A.

Knowing that a 94% on a test isn't going to ruin my grade point average is an enormous relief.

I've attended places where percentage points mattered, and it didn't so much result in the reward of the most superior students; it resulted in high-achieving young women bursting into tears while studying convinced a 99% would ruin their lives and too stressed to learn because the grade mattered too much.
For student feedback, we got satisfactory/unsatisfactory, and that was it. If your grade was a C or higher in a class, you got an S, and if not, you got a U and some paperwork to fill out depending on how bad the U was.

Grades were assigned, sure, but we didn't see them without having to ask our advisors, and depending on how much they bought into the 'learning for its own sake' thing, they would or would not grant the opportunity. So I don't really know how any of that worked.
I'm sorry, Dance, I can't. Maybe someone else can. It's something that I've carried with me through a 30-year career in education.

I also don't follow Vikki's argument that student assessment is inherently noisy (which it certainly is) means we should avoid assigning +/-'s. Like dance, I would argue conversely that if we should assign no statistical significance to the skills a students who received an overall scores of 78 and 82, respectively, then the last thing we should do is assign the first a "C" and the second a "B".

My brother! (Or sister.) You're right; the last thing we should do is give one a C and one a B, and yet The Man forces us to do exactly that. I hate it, it's the worst part of my job. I want to give Pass/Fail grades and be done with it. I tell my students that the difference between a 78 and an 82 really is meaningless, and that a 78 can be a B and an 82 can be a C and the way I will decide is through what I have learned about them as scholars through the quarter. (My students all share a disability, so my classes are very small; my quarter student-load is between 20 and 30. This clearly would be impossible for large survey courses.) They can come to class, talk to me, participate, come to office hours, ask questions, send me e-mail and give me a basis upon which to make the determination, or not. It's their choice. But in 30 years, I've never had one grade challenged, not one.

OK, no. There was the student who SWORE that I'd told him that we had an under-the-table agreement that if his lab reports were good, I'd ignore his test grades. Um, no.
MIT has an interesting compromise--they give pluses and minuses as part of internal grades (which can be used, e.g., by faculty committees deciding on nominations for Rhodes Scholars, etc.) but for external transcript purposes and GPA calculations, they only report A, B, C grades.
If we absolutely, positively have to give+/- grades, the MIT system is probably the way to go. At my institution, we can give them, but I tend not to, telling them I have a hard enought ime distinguishing between an A and a B, let along A+/A/A-/B+/B and so on. I do give the occasional "+" grade, so I do succunb to "grade inflation" here. But I hate the +/- system
My school doesn't have plus or minus grades. Coming from a quantitative discipline, everyone computes the range of their possible final scores religiously as the semester goes on. I gather that at some places talking about one's grades is something of a taboo subject; here it is quite common to hear people people enthusiastically announce that, for example, they would have to get the implausibly low X% from now on to get a C, or the unreachably high Y% to get an A, there is already no point in caring about the class any more.
1) I think the transfer argument should end the discussion. Standard grades will transfer anywhere, and non-standard won't.

2) The use of pluses and minuses does create artificial gradations which truly do not correspond to student talent in any meaningful way. There's an old joke -- "Why do economists calculate CPI to tenths of a percentage point? To prove they have a sense of humor?" If there's a curve, pluses and minuses are pretty silly. If you must use them, then definitely use A B+ B C+ C D F, to avoid the meaninglessness of C- and A+/- grades.
When this was discussed most recently at my current institution, which reports plain letter grades only, the group most firmly opposed to adding a plus/minus option was high-achieving students. They feared the loss of the 4.0 GPA, recognizing that some of their A grades might become A-minus grades. I would prefer a plus/minus system so as to differentiate levels of achievement in a given class, but I also agree with those who argue that the addition of plus/minus would be unlikely to produce any significant difference in students' GPAs except for those at the very top and the very bottom.
I use a rubric for assignment grades at the end of term. This rubric will have + and - grades.

The grade on file will be rounded off to the standard ABCDF.
All schools would have to change, or none, to allow more precision.

I went to a college that only had Pass or High Pass for grades. Didn't want to hurt the little students' feelings you know. As a result it was literally impossible to transfer out. Luckily, I did not.
When this was discussed most recently at my current institution, which reports plain letter grades only, the group most firmly opposed to adding a plus/minus option was high-achieving students.

A few places deal with this problem by having A+ grades be worth more than 4.00 when computing GPA. This way the occasional A+ balances out the occasional A- for such students.
It looks like "standard" grades aren't as standard as many people assume.

For example, an "A" up here translates to a numerical mark of 80-100%. A "B" is a mark in the 70s, and so on down to "F" (<50%).

So, it looks like one of our students, transferring down south, would be viewed as better than they indeed were (assuming that the standards for earning the marks were equivalent, which is a HUGE assumption!).
Ibid to the comments of Vicki and Kimmitt.

Grading and standards of evaluation will be argued until Sol burns out. Yes, precision is always preferable to ambiguity. No, we certainly do not wish to create transfer issues for our students moving to another institution of learning. With these comments, this tired old curmudgeon is very comfortable with the whole letter system. One of the most frustrating things for me professionally is to explain to an incoming student why her +/- on the sending school transcript matters not a whit in our admissions decision. It is lopped off and the whole letter melded to our whole letter system. Commonality trumps precision.

a tranquil Mighty Favog
At our cc grades are assigned based on a percentage scale: 90-100% is an A, 80-89% is a B, etc. (no +/-) A group of students challenged that they were given a B grade for 89.6% which they felt should round to an A grade. The Provost upheld the appeal and determined that the method of grading was not precise enough to be able to make that fine a distinction (echoing Vicki's comments above). Now that program uses 1000 points per semester: If you only have 896 points you get a B, if you have 900 points you get an A. And now students argue for every single point, as has been mentioned, since only a single point will separate a B (899) from an A (900).

I am curious vicki, how you can make such subjective grading decisions. Do you specify in your syllabus that you give points for students who come to your office hours? Treating two students differently based on behaviors not included in the grading parameters would get us in hot water.
I am curious vicki, how you can make such subjective grading decisions. Do you specify in your syllabus that you give points for students who come to your office hours? Treating two students differently based on behaviors not included in the grading parameters would get us in hot water.

Not explicitly. As I said, we spend a two hour class period talking about grading; testing and measurement and the limitations. I explain how I assign points, I explain how I make the absolutely unavoidable subjective decisions that must be made, and most of those center around students who are on the edge between two grades.

We've already discussed standard deviation and error of measurement, so they get that an 89 is actually somewhere, say, between 85 and 93. A 92 is between 88 and 96. So, how do I decide? That's where the other factors come into play, and they boil down to "Am I convinced that you gave me your best work?"

I've never had a student yet who didn't understand that. A student who misses a lot of class, doesn't participate in the group lab activities and never comes to ask questions about homework or lab work is probably not giving it his best. So his 88 isn't going to be bumped up to 92; he probably could have earned a 92 with a bit more effort. The student who asks questions, works with his lab group and contacts me (or another tutor) when he's having problems is much more likely to be showing me his best work. So I'll break the measurement uncertainty his way.

Students at my school who complain to the grading committee without coming to the instructor get a very firm direction to go talk to the professor about the grade first. I'll be happy to sit with any student and explain in detail how I determined it. So far, as I said, I've never had a serious complaint.
Someone mentioned institutions that give more points than a 4.0 for an A+; I went to such an institution for undergrad, and I'll admit to being biased in favor of the +/- system, and it turns out that just about the only way to raise your GPA when you're pushing 200 semester hours is to get the 4.333 points for an A+. I also got an A+ from a professor who was notorious for not giving them, and I'm still proud of that.

The +/- system encourages most students to work harder, I think, because they know they can get more points for that +. Why bust your butt, one could reason, if a 90 is the same as a 99 or more? It's a good compromise between flat ABCDF and the percentage system, which would make anyone neurotic.
May I ask a question? I teach (a) in the UK and (b) Mathematics, which means that I work in a different system, and in a subject where it is easy to allocate percentage marks precisely.

Why do you need both percentages and grades? It seems to me that much (all) of the debate would disappear if students were only given a grade for an assignment, rather than a percentage which is then converted in to a grade.

(In a previous existence I taught History. Matching assignments to grade descriptors in the rubric was easy; when the exam board required us to use percentages we first decided on the grade and then converted to a percentage!)
I work in the UK in Geography, which is largely assessed by extended writing (essays, reports, exams, call it what you will). And we have to assign a percentage mark to the pieces of work, and mark the entire module on the basis of 2-3 pieces of work maximum. Trying to assess an essay as worth 56 or 57 is really stressful, and it is really hard watching students taking those nubmers very seriously - but they have to, the class of the degree at the end of the day depends on mark averages. I WISH we could go to a marking scheme with fewer categories, it would deal with so many problems. But this is how we've always done it, apparently, so...
The great B+?+ was my favourite undergraduate grade. And that's a Beta, not a B! Besides which, A/B was different to B/A... Sadly the (English) university in question has since moved to percentage points. And I do mean 'sadly' - at least one knew what a tutor meant by 'A/B', while what someone wants one to take from 68 or 69 is trickier. IMHO.

The greater the number of gradations, the harder it is to get it just right. There's also the persistent ambiguity of the C-minus. home tutor
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