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Author Topic: Calculating grades: virtues of letters vs. numbers  (Read 4203 times)
shenanigan
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« on: December 05, 2007, 3:44:43 pm »

I apologize if this issue has been discussed before.  I searched for variations of "calculating grades" and didn't come up with anything on this issue...

I teach a humanities class.  All the assignments are papers.  I assign letter grades (B+, A-, etc).  I calculate their averages just as one would a GPA.  A B+ is 3.333 points, an A- is 3.667, and so on (each weighted according to how much each assignment counts).

I have a colleague who assigns number grades on papers.  I rejected this method because it just didn't make sense to me.  I'm not sure how I would go about deciding between an 87 and an 89, for example.  But I just discovered a MAJOR problem with my grading system.  I have a couple students who will receive "0"s on assignments they failed to turn in.  But within my grading system, that's an F, not really a 0.  So if a student, say, received two Cs and then got two Fs for failing to turn in two assignments (and suppose all are weighted equally), that student would receive a D in the class (2.00 x 2 + 0 x 2 / 4 equally-weighted assignments = 1.00, which is a D!).  But if you used number grades, (2 x 75 + 0 x 2 /400 = .375), the student would get an F, which sounds like the grade they deserve.

How can this be?  With my grading system someone who only turns in one assignment could scrape by with a D-.  It seems like both systems would work the same as long as people turn things in and get at least a D-.  But it's trying to factor in the Fs/0s that's throwing me off. 

Any ideas?  I can't even just decide to calculate those B+s as if they were, say, 87s and then go from there, since I clarified my grading system in the syllabus (i.e. that a B+ = 3.33).  I also neglected to put something in my syllabus about having to do all the assignments in order to pass. 
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dr_dre
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« Reply #1 on: December 05, 2007, 3:51:15 pm »

I'm confused. What is the difference in your system between an F and a zero? If someone takes an exam, but fails it, I count that as 55 points, most times. If someone does not turn in a paper, I count that as zero points. Is that a distinction you can make?
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professor_pat
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« Reply #2 on: December 05, 2007, 3:55:13 pm »

This is exactly the reason I went back to numerical 0-100 grading after trying the 4.0 scale. It gives me the flexibility to assign a zero when appropriate, or a 15/100 or 40/100 so the student can get some credit if they did some small amount of the work. It also establishes a standard of a higher minimum performance for passing the course: students have to earn at least 60% of possible points.

But that's for the next time you teach the course. For this time, I think in fairness you have to stick to the syllabus and award students the D, and just count it as a learning experience for yourself.
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t_r_b
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« Reply #3 on: December 05, 2007, 4:37:29 pm »

If the syllabus says an assignment is required for the class, and a student doesn't hand in the assignment, why not fail the student as a matter of course? In other words, why not have a rule that says "in order to pass this class, you need to complete the required assignments." Instead of marking the assignment grade as a zero, mark it as an "X" or some other non-quantifiable mark (just as their performance on the assignment is not quantifiable, because it is non-existent). If at the end of the semester you have an X on your record, you get an F because you haven't completed the basic requirements for passing.

As was mentioned, this may not be viable for your current situation, but if you otherwise like the 4.0 scale (as I do, for the same reasons), then a policy like this could avoid this problem in future courses.
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miss_m
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« Reply #4 on: December 05, 2007, 5:16:21 pm »

OP,

I grade with letters as well, though as has been mentioned, I don't give any points for work never done.  I give a 0 for that, and an F for work done unsatisfactorily.  I have stayed away from points grading on papers in particular because of several years of students asking about how many points they lost for this or that error.  I want to emphasize the holistic quality of the work rather than have them think about making a few less grammatical or typographical errors on the next paper.  That is also why I don't mark such errors on exams--they start to think they can get points back or fewer points off when the answers only reflect a certain level of knowledge.  Before going to numbers, think about how students view that quantifiable judgement in your field--and what arguments you will have over an 87 instead of an 89.

MM
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lemondrop
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« Reply #5 on: December 05, 2007, 5:21:09 pm »

Here's what I do:  I put letter grades on student essays.  However, this is just what the student sees.  In my grade book, I give students numerical grades out of 100, so that I can make fine distinctions as students improve in increments.  That also takes care of the difference between bad work (50 or 55 or something) and non-existent work (0).  I submit their final grades as letters and calculate the letter grades rather loosely:  F is below 60, D- is 60-63, D is 64-66, D+ is 67-79, C-is 70-73 etc.  This has considerable benefits, without the problems of ever having to discuss why an 88 vs. an 89, or of placing emphasis on how many points a comma vs. a good idea is worth.

I do agree, though, that if you have already explained your grading system to your students you can't change it this late in the semester.  Live and learn.
« Last Edit: December 05, 2007, 5:23:13 pm by lemondrop » Logged
finallyfullprof
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« Reply #6 on: December 05, 2007, 5:40:09 pm »

Numbers are easier for me to use and the students to understand.  I went to a point scale several years ago and never looked back after one semester with three grade challenges in which I spent a huge amount of time explaining how to convert letter grades to proportions of the total grade.
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shenanigan
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« Reply #7 on: December 05, 2007, 5:42:26 pm »

miss_m,

How do you calculate grades then?  It seems to me the problem with the letter system is that there's isn't a real difference between an F and a 0.  If you use a numerical system, you could, say, give someone an F (maybe a 60) on an assignment they turn in, but which completely did not meet the requirements, while you could give a 0 to someone who just didn't turn it in.  But with the letter system, you can't make that distinction.  So I'd be interested to know how you make that distinction in calculating your grades.

Now, as others have pointed out, the simple way to keep using the letters system, but keep the possibility for this distinction, is to specify that all work must be turned in to pass the class.  I will probably just do that next time, because the numbers system sounds like a pain too if you have to explain to a student how much you "took off" for a spelling mistake or what the difference is between an 87 and an 89.
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balancing_act
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« Reply #8 on: December 05, 2007, 5:42:38 pm »

Numbers are easier for me to use and the students to understand.  I went to a point scale several years ago and never looked back after one semester with three grade challenges in which I spent a huge amount of time explaining how to convert letter grades to proportions of the total grade.

Agreed, for all the same reasons.
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postmodern
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« Reply #9 on: December 05, 2007, 5:49:40 pm »

As others have mentioned, numbers are easier to understand and more concrete than letters. Many people seem to be using the point system, but I use numerical grades that are averaged together. This is the system that all my professors used in grad and undergrad, so the point system is sort of unfamiliar to me in general. Actually, if someone could humor me and explain the point system, I'd appreciate it.

While I grade some papers, I mostly grade projects, and find that I can distinguish between an 87 and an 89, for example. I place the projects into A, B, C, etc. categories and then determine the type of A, B, C, etc. from that, based on the project's criteria.

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heronhouse
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« Reply #10 on: December 05, 2007, 6:58:39 pm »

I'm a big proponent of numbers for grading, whether is a cumulative point system or whether it is a series of 0-100 grades that are averaged at the end of the term.  The reason I support this is because ultimately you must be able to determine a student's grade at the end of the term.  I think it is also reasonable and important that the students themselves be able to calculate their grades.  What is a student to make of an A-, C+, B-, A when trying to figure out his/her final grade?  How would you figure it out?  On some level, I would think, you need to use numbers, so why not make them explicit rather than implicit?

If you don't feel comfortable determining the difference between an 87 and 89, then use a point system.  The way this works (since someone asked) is to designate in the syllabus the number of points that all assignments are worth.  Add those up, and you get the total possible number of points for the class.  Then, you, the professor, indicate how many points equals what letter grade.  So, a paper might be worth 30 points, so you give the paper a score out of 30.  You can then add up all of the student's points at the end of the term to determine his/her final grade in points.  Then use your scale to convert that to a letter grade.

The other hobby horse I'll bring out here is rubrics.  Rubrics make it much easier to explain to students why they received a certain number grade rather than another.  You don't have to make your scale as fine as 100 points; you can make it 15 and demonstrate through your rubric what each level of paper looks like.
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t_r_b
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« Reply #11 on: December 06, 2007, 12:02:36 am »

Just to be clear here: I think all the posts basically agree on the importance of having some numerical scale for grading. The question isn't "letters vs. numbers" so much as the 4 point scale vs. the 100 pt. scale. The OP is using the 4 point scale, which avoids the absurdity of 89 vs. 87 and makes the math a lot easier for us number-phobic humanities folks. Each assignment gets a letter grade, which has a numeric equivalent on the 4 point scale, just like for the GPA, and you just average it all together to get the final grade. As OP notes, there is a problem because a zero on the 4 point scale hurts the student much less than a zero on the 100 point scale, but as I mentioned above there are viable workarounds to solve this.

You can run into the same problem with a 100 point scale, by the way. I had a student once who disappeared for most of the semester and missed the midterm, but showed up towards the end and made a half-hearted effort to get a passing grade. He failed, but if he'd really gotten his act together it would have been possible for him to pull off a D or even a C (the midterm counted for 20% of the grade, so even with a zero there he had 80 points to work with). That's why I favor making a passing grade contingent upon completing all course requirements - if you skip something entirely, you shouldn't pass the course. That is the meaning of requirement, right?

I'm not crazy about the cumulative points system because it usually involves assigning a large number of points to major assignments, which invites some of the same bickering over minute point differences that you get with 87 vs. 89. The nice thing about the 4.0 system is that it separates the grading scale for individual assignments from the assignments' proportion of the final grade. Just because a paper is worth 30% of the grade doesn't mean you have to grade it on a scale of 1-30 (or 30% of the total points of the course). Grade the assignments on a scale that makes sense for you, and then run the averages from there.

Does anyone out there grade on a 10 point scale? In other words, give each assignment a grade between 1 and 10 and average them out? This offers another way to make the zero count more (or rather, less) than it does in the 4 point scale, while avoiding the 87 vs. 89 problem. In OP's scenario of two Cs and two zeros, they'd average out to 3.75 and garner the F they deserve (assuming that a C gets a 7.5 and not handing it in gets a zero).
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scienceprof
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« Reply #12 on: December 06, 2007, 1:16:51 am »

To the OP:

If you want to keep the letter system, but adjust for nonexistent work (zero) vs merely failing (say a 50%), you could add an F- , for example, assign a -1 for work that is not turned in.
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heronhouse
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« Reply #13 on: December 06, 2007, 1:47:05 am »

the_raised_bar, I do something like you're talking about.  Most of my assignments are worth between 10-15 points.  I don't average them, though.  I just add them up and then use my pre-designated scale to determine each student's grade.  I'm not sure why you think cumulative points systems are more likely to generate discussions about the difference between an 87 and an 89, as you stated in your post.  Whether it's a 4-point scale or a 100-point scale, there is always room for students to complain and question why they received one number (or letter) instead of another.  This is why I am a big proponent of rubrics.  They can provide a real aid to those discussions.  I like the cumulative points system because it's a bit easier (no averaging!), and it allows me to make rubrics on my own terms.  In other words, rather than saying "This kind of paper is an 87 and this is an 89," I can instead say "A 15-point paper has these characteristics..."  "A 14-point paper has these characteristics" etc.
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t_r_b
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« Reply #14 on: December 06, 2007, 2:14:48 am »

My concern about the cumulative points system is that it can require that major assignments are graded on a many pointed scale: if a pop quiz is worth 10 points, say, then a major paper might be worth 50. I don't see much to be gained by distinguishing between a 37 and 38 point paper, for example (for other teachers, and other kinds of assignments, a 50 point scale might be quite appropriate, but in general I don't think that the weight of the assignment in the final grade should dictate the grading scale used).

I entirely agree about the value of a clear rubric explaining what kinds of papers receive what grades. I just think it keeps things simpler when the grading scale for each assignment is small.

I TA'd once for a professor who wanted us to grade on a 500 point scale. There were four components, each worth 25% of the grade, or 125 points. So I was supposed to grade their take-home essay on a 125-point scale. I told the students I'd grade them on the 4.0 scale and just average the results: no one complained. If they had, I'd have simply done the same thing and then multiplied out the results to fit the 125 point scale. The only purpose the large scale served was to create the illusion that the students' work was being graded more precisely than it actually was: it's not like there were 125 particular points they could score on their essays and we'd count them up to get the right total.
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