## Monday, January 07, 2008

### Abolish the Grade Point Average

One of the things I'd like to do at my university is abolish the grade point system and just use percentages. We already give percentage grades for each course on our transcripts but these get converted to grade points for the purpose of calculating grade point averages.

The method of conversion is shown in the table below.

What do you think? Is there any good reason to use grade points and grade point averages in university? Do any of you go to schools where the GPA has been abolished?

1. My GPA looks more impressive than my average but I agree with you. Would you happen to know why they were used in the first place?

2. This is complete conjecture, but I have two theories as to why GPAs are used:

First off, it allows a composite of objective subjects grades with more subjective subjects. It's difficult to assign a precise number to a term paper, but letter grades are big enough buckets that you're usually pretty consistent.

Secondly, it allows different courses to curve differently. If every course uses the table you have there, this point is moot, but in my experience, in some courses a 89.6% yields you an A- while in others you need above a 95% to do so. If you were to just average percentages, you'd still need some course-level scaling (either with grading criteria or adjustments at the end of the term) to make similar numbers in different courses correspond to similar achievement levels.

3. I've been thinking about this for the past two years since in these past years I've narrowly missed getting either A or A+ in several classes (A+ is 4.33 at my school). It would make much more sense to use percentages and it would probably alleviate some professorial headaches when students like me come in complaining about our grades. Even in the hard sciences, there is no way grading is accurate enough to distinguish an A- student with a 90% from a B+ student with a 89%. Let's start the revolution!!

4. I thought the grade point system was the same everywhere, but here at Laval University (Quebec), an A+ is worth 4,33 and a D- is worth, well, 0.

Robert M.

5. matt r:

Wait a minute - A+ is 4.33? So how can you compare your GPA with that of someone from a university (such as my own) where the highest possible score for any class is a 4.0? Do grad schools take things like this into account when comparing applications?

As to the subject of the post, I'd rather see the elimination of curving; last semester the second best student in my genetics class (I was top, since you didn't ask!) had an overall score for the semester more than 25% lower than me, and yet still got an A.

I know this probably sounds arrogant, but frankly that's wrong.

6. We get percentage grades on tests but only letter grades appear in our records. This is just swell, IMO. The GPA system is fair because it smoothes out subjectivities and because finer grained marking would require more comprehensive evaluation methods than 2 exams (typically) which can’t reflect the breadth and depth of the course material. A is for excellent. The +/- modifiers are noise and frankly not just a little ridiculous. Also, where I go to school, the mapping between letter grade and percentage is not a rule; a professor can (for example) give you a C even if you scored 100% on the exam, or an A if you scored 70%.

7. Also, where I go to school, the mapping between letter grade and percentage is not a rule; a professor can (for example) give you a C even if you scored 100% on the exam, or an A if you scored 70%.
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I had professors in undergraduate who designed their exam to test how much their students know (depth of knowledge/thought/analysis) rather than if they knew X, Y, and Z. Based on that they did not expect students to get more than 80% on the exams. The course was designed accordingly. Those who did well usually got close to that level on the exams. The tests got you to think and were part of the learning experience. In answering questions you uncovered a new/deeper understanding of the subject.

8. The big thing with undergrads here at the University of Ottawa is the perfect 10.0 gpa. That means you got straight A+ in every course, even though your final mark in each could be as low as 90%. The university seems to think this is great. About 10-20 students in the biochem and pre-med programs are featured as "Perfect 10.0s" in the administration propaganda every year, and they get lots of graduates into med school. I think it's stupid. Are you telling me these kids already know everything there is to know about science?

9. I assume by "percentage" you really mean some sort of scaled score with 100 as the max (you don't fail 1/2 your students, do you?).

A better score system is one based on the student's score relative to the mean of the class, expressed in standard deviation units.

Nearly as good is a true percentile ranking.

For each you decide what merits different letter grades when that is required (e.g., within +1 SD = B, -1SD =C, beyond +1 = A, etc), but you always report the SD or precentile score for official purposes. Totally defeats grade inflation. (if a perspective graduate student's GPA is a 4.0 but their average score in all classes is +0.5 SD, you've got a graduate of a grade-mill.)

The advantaqe of either is it allows you do devise tests questions where the average student is correct only 50% of the time. Such a test is a much better discriminator between subtle differences in student performance than one where the average student gets 80-85% correct.

10. The University of Guelph publishes a letter-to-percentage scale in the calendar every year, which we (course instructors and TAs) are instructed to stick to firmly. One full professor I was TAing for told me it was our "get out of jail free card" because it was highly detailed, very clear, and very rigid.

Basically, the A range is anything above 80%, and can only be assigned to assignments that are considered "outstanding". The B range is for things that are "excellent", C is for "acceptable", and so on. +/- are treated much like noise, but not by the students.

In my experience, this system works reasonably well for written assignments, but isn't really applied consistently in tests, because most tests are easier to mark by subtraction - the student starts with a score of 100% and then loses marks by making mistakes (answering questions wrongly).

As for GPAs, getting back on topic, I agree that they seem outdated, and differences between universities render comparisons very difficult. My undergrad was at the University of Victoria, which used a 9-point scale; my M.Sc. was at Simon Fraser University, which used A+ = 4.33. In my experience, the admissions process for graduate schools does take these differences into account, though of course mistakes happen. I've heard unpleasant rumours about the scaling calculations used at the University of British Columbia's medical school.

11. This is a totally bizarre system - I never realised North Americans were burdened with something like this. I'd be surprised if it is used anywhere outside of your crazy continent.

12. Ian B Gibson says,

Do grad schools take things like this into account when comparing applications?

Grades don't count for that much when applying for graduate school. As long as you meet the minimum requirements, your application will be considered. In most cases, it's the other parts of your application will determine whether you are accepted.

As to the subject of the post, I'd rather see the elimination of curving ...

"Curving" is unethical, indefensible, and stupid. It's okay to add marks to everyone to bring up a class average but it's not okay to differentially adjust marks relative to each other.

13. anonymous says,

Also, where I go to school, the mapping between letter grade and percentage is not a rule; a professor can (for example) give you a C even if you scored 100% on the exam, or an A if you scored 70%.

Change schools immediately.

14. divalent says,

A better score system is one based on the student's score relative to the mean of the class, expressed in standard deviation units.

Nearly as good is a true percentile ranking.

I disagree. I think those systems are stupid and naive.

Let's think of a hypothetical example to illustrate the problem. Imagine that you have a rigorous honours program and students must have a 75% average to get in. Your department offers two introductory courses in the subject; one is for the high achieving honours students and the other is for everyone else who needs to learn the subject at a lower level.

Imagine that you have one student in each class who scores exactly the class mean. The honours student gets 77% in the honours class of high achievers and the other student gets 67% in the lower-level course.

Do you mean to tell me that both students deserve the same mark on their transcript and that they should have the same chances of getting into graduate school?

15. anonymous says,

This is a totally bizarre system - I never realised North Americans were burdened with something like this. I'd be surprised if it is used anywhere outside of your crazy continent.

Richard Dawkins has a nice comment on the bizarre British system where everyone is divided into just three classes: first, second, and third.

See The Ancestor's Tale pp. 257-258.

16. Let's think of a hypothetical example to illustrate the problem. Imagine that you have a rigorous honours program and students must have a 75% average to get in. Your department offers two introductory courses in the subject; one is for the high achieving honours students and the other is for everyone else who needs to learn the subject at a lower level.

Imagine that you have one student in each class who scores exactly the class mean. The honours student gets 77% in the honours class of high achievers and the other student gets 67% in the lower-level course.

Do you mean to tell me that both students deserve the same mark on their transcript and that they should have the same chances of getting into graduate school?

I don't see the problem. If it's the same course, but different "peer" group, you pool the score across the different sections of that course. If it is a different course (additional material, more depth, etc) then call it something different, like "Honors Biology" or "AP Biology", and make sure the course catalogue accurately describes the rigor.

I think most people that evaluate grades will recognize that an average grade in an honors course is worth more than even an above average grade in a non-honors course. (Just like most people will prefer a B-student from Harvard over an A+ student from Liberty "University".)

[there used to be a time when "C" meant "average"]

17. Ian,

I think that it's fairly standard for U.S. Universities to give 4.33 to A+ students. At my university, the total/cumulative GPA is truncated at 4.00 so nothing higher than that will be reported on transcripts, but an A+ in a class helps to offset a lower grade received in another class. As to whether our GPAs can be compared, I don't have an answer for you...

18. I think it protects the teacher from failure. My first semester teaching a graduate level microbiology lecture, every single student in my class (16 of them) failed spectacularly. I would say that means that *I* failed spectacularly to present the material, or that I failed to ask reasonable questions. Thanks to the GPA, I can correct that by setting the top grade in my section as an A. Through tweaking, I've managed to improve my lecturing considerably, but for the early students, they don't end up bearing the brunt of my own learning process.

19. Adjusting the grades of an individual to fit some sort of expected average (let alone a standard deviation) is statistically indefensible with the sizes of most classes I've been in... right now I am not in any classes with more than 25 people. With that size of sample, you would expect massive variation in class average any give year. Trying to standardize to an expected value would unfairly penalize classes with a high proportion of strong students.

for example: I was just in an upper year econ course. This course has been taught by the same person for 13 years, generally with an average between 56% and 65%. With the same tests, and same professor, our year averaged 78%. Should we have had our marks penalized simply because we were all fairly strong students, and happened to end up taking the same course at the same time?

I was just in an upper year econ course. This course has been taught by the same person for 13 years, generally with an average between 56% and 65%. With the same tests, and same professor, our year averaged 78%. Should we have had our marks penalized simply because we were all fairly strong students, and happened to end up taking the same course at the same time?

No, your marks should not have been lowered if your explanation is the correct one.

However, your explanation is improbable. Personally, I would have tested the hypothesis by checking your transcripts to see if the members of your class were scoring consistently higher in other courses.

21. Well, it is pretty anecdotal, so take it with a grain of salt. However, out of the 15 or so people taking the class, I know at least 3 of them got accepted to pretty good graduate programs the next year. Also, from what I remember of the midterm marks, they were somewhat bi-modal, which is what you would expect if you had a disproportionate number of high-marked students in the class. I know that with my mark at least, curving it down would have pulled the mark below my normal average.

Honestly, I still think that it's not a good idea to curve down marks in classes. I certainly don't think that one somewhat high scoring class, with few students, out of 13 years, is surprising at all. The only way to make it even half-way defensible to re-curve small classes would be actually using a regression on each person's other marks, and demonstrate the the class mark would be a significant outlier in their transcript. Curving without at least testing the null hypothesis that it's just sampling error causing the problem is silly.

22. The Fractician says,

I think it protects the teacher from failure. My first semester teaching a graduate level microbiology lecture, every single student in my class (16 of them) failed spectacularly. I would say that means that *I* failed spectacularly to present the material, or that I failed to ask reasonable questions. Thanks to the GPA, I can correct that by setting the top grade in my section as an A.

You could do the same thing with percentage grades. Just add marks to every student's grades until the highest mark is 85% or whatever you want. I do this quite often.

You don't need to work with grade points in order to do this. When I advocate abolishing the grade point system I mean getting rid of A's, B's, C's, etc., not abolishing marks altogether.

23. eric says,

Honestly, I still think that it's not a good idea to curve down marks in classes. I certainly don't think that one somewhat high scoring class, with few students, out of 13 years, is surprising at all.

I hear students say this all the time. Whenever the class average on a test is higher than normal they always claim that it's because they are smarter than students in previous years.

On the other hand, whenever the class average is lower than normal it's because the Professor made the test too hard. In that case the grades are unfair and need to be raised.

Most of my colleagues know that accidentally making a test too easy is much more of a problem than making a judgmental error in the other direction. That's why we always err on the side of a difficult test.

We can always add grades without the students complaining that they are getting marks they don't deserve but we can never subtrate marks.

BTW, Eric, "curving" is not the same as adding or subtracting marks to every grade. "Curving" is never justified but adding marks to every student is justified and we do it all the time.

If adding marks is fair and justified then it follows, as a matter of simple logic, that subtracting marks should also be fair and justifiable. We always rig our tests so that we never have to subtract marks because students will never see that as being fair.

I consider that attitude to be a failure on our part to teach students how a university works.

24. I am curious exactly what about my tone suggested to you that I in any way supported arbitrarily raising grades, and only was opposed to lowering them. I do not want either: all I ask is that a professor be willing to say: "these grades are statistically different from the expected average, and these factors point to this stemming from errors in the test, rather than sampling error or some sort of group effect". Why should we be taught to demand rigour and evidence in every place except our marks?

I consider this sort of attitude to be a failure on our part not to demand the same standards in our learning as we expect from a scientific study.

I do apologize for mixing up adding or subtracting marks with recurving. It was a stupid mistake on my part. However, this does leave one question open: if you support moving the mean of the class up or down, why not the variance as well? Or the skew? Why is adjusting the mean any more defensible than any other part of the mark distribution?

I know most professors are extraordinarily concerned about ensuring fair grades. Most grade adjustments, up or down, are likely justified. However, ideas such as divalent's, where all classes are adjusted to have the same average, are patently insupportable. There is going to be sampling errors, especially in small classes , so arbitrarily fixing averages unfairly penalizes or helps students in those classes. Any sort of adjustment should be backable by some sort of evidence, rather than arbitrarily applied. I had brought up my particular class simply as an example of where this would be a bad idea. I know that the professor in question had both the knowledge to evaluate whether the grade was too improbable, and would have been perfectly willing to change it if need be. I have been in classes with particularly low averages as well, and I think it would be just as indefensible to arbitrarily raise those marks to meet some imagined ideal average.

25. eric says,

I know most professors are extraordinarily concerned about ensuring fair grades. Most grade adjustments, up or down, are likely justified. However, ideas such as divalent's, where all classes are adjusted to have the same average, are patently insupportable.

If I interpret this statement literally then I agree with you.

This does not rule out some kind of guidelines where every Professor in the university is aware of typical class averages. I support that sort of system.

26. Honestly, I think we both agree on what kind of grade adjusting would be considered fair. Knowing what the expected average should be is vital tool in marking and preparing work. If the marks of a particular assignment, or in extreme cases, all the assignments in a class indicate that they were too easy or too difficult compared with the expected achievement, then I heartily agree with adjusting. All I object to is the idea of automatically scaling all classes so the average always matches the expected outcome, without some indication that the mark wasn't overly low or high due to chance.