What are the advantages and disadvantages of cumulative vs percentage grading?

Question

There are many ways to grade students. One is to provide a fixed body of student work and then give a percentage grade for assignments, with the overall grade representing the percentage achieved of some ideal. 90% = A, etc. The student is expected to work on each assignment. This is Grading by Percentages.

Another way (Grading by Points, Cumulative Grading) is to provide a body of assignments with a point total assigned to each part, preferably with small granularity but totaling, say 1000 points. The grading is done cumulatively with, say, 900 or more points required for an A grade. The instructor evaluates each assignment and gives points based on quality, etc. perhaps giving 40 points on an assignment that is "worth" 50. Here the student can work until they have enough points to achieve a grade that is acceptable to them. After that, they no longer need to do anything and can focus on other courses or commitments. It is, of course, good to warn students who are intending to go on that learning is still required to meet their greater goals and not to be too complacent.

In either case, the instructor may permit re-work on assignments. If Grading by Points the rework earns additional points, but perhaps not up to the full marks for the work, but some positive increment.

The writer used Grading by Points in the latter part of his career. What advantages and disadvantages are there of each scheme. What improvements can you make to either or both of these?

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For clarity, the real difference is that in Cumulative Grading, the rubric tells the student how many points are needed for each grade and they can choose to get them any way that they like, spread over the assignments, whose totals are also known. In percentage grading, especially with different things worth different "weights" it is (a bit) harder for the student to know where they are likely to wind up. They know their "average" perhaps, but every assignment affects the average. Therefore with Cumulative Grading, the student always increases their points, where with percentage grading, each assignment can get you closer or farther away from your goal.

Answer 1

I have done both percentages and points in my career, the latter being the most recent and preferred.

Percentages: The only advantage I can see is that, especially in high school, this seems to be the dominant way of grading, so students and teachers are accustomed to it. Disadvantages are that students can have a difficult time tracking their progress, or knowing, for example, how well they must do on a test to keep their grade above a certain percentage. In my experience, it also takes more time as a teacher - determining how many questions to put on a test or quiz so that percentages can be more easily calculated, for example.

As relates to programming specifically, I always struggled with the fact that I wanted programming exercises to count heavily but had a hard time making that happen with percentages. Students, parents, and administrators expect tests to be worth more than anything else, so if I gave tests the normal 40% weight, then that left programming exercises, quizzes, and classwork (study guides or worksheets) to split the remaining 60%, and I could just never get it "right", meaning feeling comfortable with the distribution.

Points: The major advantage of points the OP has already noted - students, parents, and teachers alike can instantly look at assignments and ascertain which assignments are worth more (I'm assuming all are using electronic gradebook of some kind), and students who want to remain at a minimum certain level find that easier to do.

Going to points solved the problem for me of knowing how much to weight each type of assignment - all assignments are weighted the same, and if I feel the assignment is worth more, I give it more points. So I can look at how many programming exercises I assign in one semester (depending on the course, 80 to 100), determine points for those (say 10 points each), and base the points for everything else on that total. If I determine a certain test is going to be worth 112 points because it has 56 questions, then the students see it as a large chunk, so they don't blow it off, but it is also not going to sink them if they fail it.

Rework: By extension, rework is made easier with a grading by points system. I've also found that "extra credit" makes much more sense for students in the points system, and they are more motivated to attempt it, because they can more readily see how the extra points are going to impact their grade.

Answer 2

The primary "pro" for cumulative grading is that it eliminates the math behind the weighted percentage system, making it easier to compute mentally. Imagine two friends in the same class. In a weighted percentage system, Alice gets 70% on homework and 90% on tests, while Bob gets 70% on tests and 90% on homework.

Later, they compare grades and discover that Alice got 78%, while Bob got 82%, a 4% difference, and an entire letter grade (assuming 90%=A...50%=F). At first glance, this sounds counter-intuitive, because they got the same numbers, but different letter grades.

It's hard for most people to naturally understand what happened here without pulling out a paper or computer and doing the math; the homework was worth 60% of the total, and tests 40% of the total. The instructor likely even told them how the grades break down, but it's harder to grasp mentally, especially for the majority of people that have problems with fractions mentally.

With the cumulative grading system, if Alice gets 420 points on homework and 360 points on tests, and Bob gets 540 points on homework and 280 points on tests, it becomes immediately obvious that Alice's 780 points got her a C, while Bob's 820 points was worth a B. This is the exact same grade as in the weighted percentage system, but the only math required is now simple addition. It's much easier to process mentally to see how the points translated to a letter grade, since we optimized out the multiplications required.

As you've also stated, it also allows a student to decide if the a unit is worth doing simply by comparing the numbers to a goal. In some classes, where assignments are worth different points, and those points are then converted to a percentage, then weighted along with other categories, you're now asking them to calculate how much each assignment point is worth, which differs based on the number of points in the assignment and the weight of the overall grade; this can even be further complicated if the assignments are "invisibly" pointed (e.g. the student only ever gets a percentage back).

It's a lot easier to figure out that an assignment is worth 40 cumulative grading points out of 1000 for a perfect grade, than it is to say that there are 8 questions, worth 2 points each, all homework assignments total 79 points, which is worth 35% of the total grade, while on a test with 8 questions, worth 2 points each, out of a total of 89 points on tests, which are worth 40% of the grade, versus a final with 16 questions, worth 2 points each, and a total of 25% of the grade.

Yes, there are certainly mathematical savants out there that can tell you exactly what percentage of the final grade a particular assignment is mentally, but for most students, it just involves them scrambling to try and get as many points as they can; actually trying to figure out if the assignment is worth doing takes too much effort, so they may as well do it anyways, which might turn in to a time management issue since they may not know which assignment is worth more.

The only "con" I can see to a cumulative grading system is that it seems to be rarely used, especially in grade schools, so it will require explaining. However, I'm pretty sure most students would appreciate the simplicity of a single number instead of relatively complicated arithmetic just to try and manage their time.

Answer 3

Grading is one of those things that we have allowed to be far too complex. Trying to make a small change to how Moodle works, for example, exposes a forest of ever-changing alternatives, settings, approaches, customizations... Should extra credit only count if the student is above a certain percentage? Etc... Wow. As Thoreau said, "Simplify, Simplify" (which is already redundant).

What I tell my students, in a work training program for adults, is that basically they can relax about the grade thing because essentially the entire year-long program of study is pass-fail. He who endures to the end shall be certificated, and otherwise, not. The goal is to learn enough to be successfully employed, which is the goal of all learning. It is no use being a virtuoso and unable to pay your bills.

So, the minimum and maximum grade boundaries are just "rails" that they can only hit, like the concrete barriers on the sides of the freeway. If someone does not 'pass' an assignment, that means that they are missing essential knowledge. Too many such failures and they simply wash out. It does not matter if they are amazing at one aspect but abysmal at another: they must have basic competence in all areas or they will not be employable.

When they worry or do some point-grubbing, I basically ignore it and redirect them to the requirements of the next looming assignment.

Answer 4

The only real difference between the two, from your description, is timing of when assignments are due. In the traditional percentage format, assignments are due at a fixed time, whereas, it sounds like on the cumulative, you can turn assignments in at any time. Other than that, the only difference is perception.

Answer 5

Ultimately, it comes down to what you prioritize in your course and how you want your students to prove that they have learned the materials. What is critical though is if you use a course management/grade management system is that the syllabus AND the calculations in the LMS/CMS/GMS are in agreement with each other so that if a student does look at their grades it is calculated properly and accurately.

My full time job is administering our college's online course delivery system (Canvas) and training instructors on how to use it. I also teach a few classes as an adjunct, and while they are face to face I use the LMS heavily (gotta eat your own dog food).

In courses where showing applied knowledge and skill and ability is important - like my "Services with Linux" class - I use percentage based grading. This allows me to give 100 point exams, but since they are almost entirely based on readings and background information regarding the services, I can make them worth a relatively minimal part of the final grade (10%). I think it is more important for me to help produce a sysadmin who can actually configure a DNS server, a DCHP server, a Samba server, set up a LAMP server, or configure an email server and diagnose issues by reading headers, etc. In this course, I use percentage based grading - 10% exams, 15% discussions (relating to what and how to backup, security, pros and cons of various config options, etc), 25% projects (full documentation of local services setup, full documentation of internet services setup), and the other 50% in labs (all involving getting the various services configured, developing backup methods, etc).

For an "Intro to SQL" course I teach, I use a points based system. Mostly because I'm just an adjunct teaching with the course content provided by a lead instructor, but also because it makes sense. Doing the readings, understanding the different data types, understanding the differences between join types, etc. are equally important as being able to write the SQL syntax. Coincidentally there are 8 labs/projects with 10 questions/sql statements to generate at 5pts each, and there are 4 exams (each covering 2 labs/projects) worth 100 points each, so 400 and 400 respectively, and so it works out nicely that way. Of course, the same can be done with a percentage based system just as easily.

As far as the students go, I've seen a surprising number of them who never even check their grades in the LMS. And the rest of them just don't seem to be bothered between the differences of points vs. percentages. I've even had students in both classes in the same term and they either didn't notice the difference or seem to care.

One last thing - do not go crazy with conditional logic in your grade calculation - although this seems to mostly come from our Social and Behavioral Sciences department. "Well, if students score above 80 on exam 1 and submit paper 3 at least 2 days before the deadline then they can do either this bonus assignment or take an extra 10 points on exam 2 but only if they take the exam on a Thursday or on Monday before 10am."

Answer 6

The main advantage I see in using Cumulative Grading is that the student is always sure exactly where they are and what they need to do to obtain a grade that they will find satisfactory. An additional advantage for the individual student is that they can pace their efforts out over a wide range of courses and activities without undue stress. Not all students feel that the course I'm teaching is the most important thing in their lives, so it gives them a bit of freedom to pursue a variety of goals.

Of course, in some students this means that they don't maximize their efforts for my course. I can counsel them to higher and higher goals, of course, but I found that the superstars will still superstar.

I also permitted re-work on projects of all sorts, large and small. A student could improve their grade, but not up to the maximum for the exercise. The standard was that you could get back 90% of whatever you lost on the first trial. So if you got 70 on a project worth 100 you could get back about 27 points by redoing the assignment one or more times. For some students this rework, and the repetition-reinforcement it enables, is especially valuable. Point grading seems to encourage the re-work a bit more than percentage grading.

The possible down side of this, for a few students, is that they would re-do an assignment many times but spend less time on newer assignments, possibly reducing their effort there. I had to caution a few students on this and very occasionally had to tell a student that I'd accept no further re-work so they would focus on other things.

Overall, however, the combination of Cumulative Grading and re-work seemed to be liked/loved by my students. It also let me focus my office hours on the students who needed help the most.

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Some instructors also permit students to simply skip the final exam if their point total is sufficiently high at the end of the course. Of course, this can be incorporated into percentage grading as well. This benefits your best students who can then spend their efforts on other pressing concerns.