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The Grade Point Average (GPA): An Exercise In Academic Absurdity

Tomorrow's Teaching and Learning

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Below is the sixth posting in a series of selected articles from the

National Teaching and Learning Forum newsletter reproduced here as

part of our "Shared Mission Partnership" announced in March of this

year. The article, by William Cohen of Hunter College in new

York,looks at the negative aspects of the grade point average (GPA)

evaluation system prevalent in higher education and suggest some

opportunities for improvement.

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National Teaching and Learning Forum Newsletter

Sept. 2000, Vol. 9 No. 5

William D. Cohen

Department of Biological Sciences Hunter College


Evaluation of college student performance is a working necessity for most

of us who teach college courses, including many who dislike this aspect of

the profession. While evaluation methods can vary among and even within

institutions, some are widespread, and one of these is the Letter

Grade-Grade Point Average (GPA) grading system. After three decades of

college teaching, during which I have dutifully utilized letter grades and the

GPA system, it is time for the truth. The GPA system, foisted upon so

many professors and students in so many colleges for so many years, is

unfair, inaccurate, irritating, and unnecessary.

The GPA grading system has certainly always been applied in good

faith, so I am neither complaining about my institution nor speaking

for it. However, in my opinion the GPA has also been applied by rote,

and both a critique and a better way to gauge student performance are

sorely needed. Since evaluation of students has been an important

ongoing topic in The National Teaching and Learning Forum, my

objective here is merely to add to an ongoing critical dialog on this

still popular grading system. My arguments and a proposal follow.

Grades in Perspective

Like the mechanisms involved in admissions screening and choice of

courses, grading is a selective system at the college core, with

major impact on students. Beyond determining who earns an academic

degree, grades decide academic honors and strongly influence faculty

letters of recommendation that are critically important to an

undergraduate's future.

Because grades have important consequences, grading systems should be

examined periodically to assess their accuracy, fairness, and logic.

The GPA System: A Quick Review

The letter-grade GPA system is based on the fact that we all find it

convenient to lump things, including people (perhaps especially

people), into categories. Thus, "A" work is excellent or superior,

"B" good or solid, "C" average or mediocre, "D" bad and below

average, and "F" poor and failing. Letter grades are determined

either by conversion of numerical percentages from exams and other

work, or by direct letter evaluation without first assigning

numerical percentages. The "Grade Point Average" or GPA or overview

of student performance derives from averaging these grades weighted

according to the credit hours involved. As an example, the number of

credits in each course is multiplied by the number of "quality

points" (QPs), with 4 points for A, 3 for B, 2 for C, 1 for D, and 0

for F. The QP total is then divided by total credits taken, so that

GPA = the QP average per credit. For example, if student X takes 5

courses, with #1, #2, and #3 at 3 credits each, #4 at 2 credits, and

#5 at 4 credits, and receives an "A" in each, the GPA = (15 x 4) ?

15 = 4.0. If student Y, taking the same courses, gets an "A" in

#1-#3, and a "B" in #4 and #5, the GPA = ((9 x 4) + (6 x 3)) ? 15 =

54 ? 15 = 3.6. And so on.

Letter Grades: The Pluses and Minuses

My institution voted some years ago to add pluses and minuses to the

letter grades, without changing the GPA calculation. Our present

letter grades, percentage ranges, and quality points (QPs) are shown

in the following table:


Letter Mid% Quality +% -%

Category Range Points Range Range

A+ 4 97.5-100

A 92.5-97.4 4

A- 4 90.0-92.4

B+ 3 87.5-89.9

B 62.5-87.4 3

B- 3 80.0-82.4

C+ 2 77.5-79.9

C 72.5-77.4 2

C- 2 70.0-72.4

D+ 1 67.5-69.9

D 60.0-67.4 1

F 0


What do these + and - letter grades mean? A+ is truly outstanding,

the best of the best. However, A- is just fine with most students,

because they realize that they just squeaked past a B+ and still

receive 4 QPs. While a B+ certainly looks much better than a B-, it

represents an A- near miss, earning only 3 QPs. It is thus agonizing,

particularly to pre-professionals vying for medical or law school

admission, as the GPA calculates credits x3 rather than x4. And a C+

is equally agonizing, because the respectable B was barely missed.

But what of a D+? Not quite so agonizing because the near-missed "C"

isn't very impressive either; the D+ is surely one of the silliest

grades ever invented: it announces that, among students who nearly

failed, this student is superior! Mercifully, at my institution, no

D- grade is permitted.

What about the F category? Since everyone from 0.0% to 59.9% gets 0

QPs, "F" is not really a grade but a label stating that the student

is below the minimum acceptable threshold. But is it really fair to

give zero quality points to one student who just misses a D with

59.9%, and to another who does no work and gets perhaps 30%? And is

it fair to a student who does well in all courses but this one? The F

grade is reconsidered below.

Distorting the Record

Consider students X, Y, and Z once again. Suppose X gets an "A-" in

course #1 with 91.0% and 3 x 4 = 12 grade points. Student Y, taking

the same course, scores 89.0% for a B+, with grade points 3 x 3 = 9,

and Z scores 81.0% for a B, also 9 grade points. Comparing X and Y, a

2% difference in original course performance has produced a 25%

difference in grade points! In other words, the difference between

students has been grossly magnified, with a difference magnification

factor greater than 10X! Yet, comparing students Y and Z, an 8%

difference in score has produced absolutely no difference in grade

points. Is this logical or fair? Absolutely not, because the ability

demonstrated by student Y is much closer to X than to Z.

Given the fact that my college grading system includes one decimal

place in the percentage scores (table, above), how close could

students X and Y be, and still receive different letter grades? My

biology course has 1000 total possible points, 600 from lecture

exams, and 400 from laboratory quizzes and reports. Suppose X gets

900 points out of 1000, and Y gets 899. According to my current

college grading system, student X receives A-, and student Y a B+.

The difference in their performances, 1 point out of 1000 or 0.1%, is

utterly trivial, the equivalent of one incorrect guess on a single

true-or-false question. Yet, a grading system using quality points

records the difference as 25%, with a difference magnification factor

of 250X. How absurd!


What effect does such a system have on people? First, students worry

excessively about every point lost for fear of a borderline near-miss

at semester end. Second, professors are disturbed by excessive

student worry, challenged by complaints about points lost, and nagged

by conscience when assigning borderline final letter grades. The

syndrome can affect final letter grade distribution in a very

negative way, because many professors plot final numerical

percentages of all students graphically, then look for natural

"breaks" in the curve so that borderline grades are minimized. Since

a natural break might occur at 86% rather than 90%, the result is

grade inflation. Third, recognizing that the system leaves something

to be desired, institutions periodically spend inordinate amounts of

time attempting to modify the system to make it more fair. Hence, the

most recent vote at my college is to count the + and - in the GPA

numerical calculation in the future. What is the significance of

adding + and - to letter grades and counting them numerically? This

is akin to improving N, S, E, and W compass points: NE is more

accurate than just E, and NNE more accurate than NE. So B+ is more

accurate than B, and, presumably, B++ even more accurate. By doing

this, what we really hope to achieve is letter grades that reflect

the original numerical percentage evaluations more accurately.

Likewise, NNE really represents only a 1/16th wedge in a 360 degree

directional circle, whereas N represents a far less precise 1/4 wedge.

Is There a Better Way?

Given students X, Y, and Z with 91%, 89%, and 81% respectively, in

the same course, what letter grades are really appropriate? None. No

letter grade will be as fair and accurate as the original percentage

grade. By definition, the percentage grade has at least 100 units of

assessment, and it typically has 1000 units by including one decimal

place, as in my current system. Thus, the ultimate absurdity: the

deserved performance assessments are, of course, simply the original

91%, 89%, and 81% scores.

What happens, then, if the professor never uses numerical

percentages, but rather uses letter grades directly on exams and

papers? These letter grades should be converted into percentages,

using current percentage-letter grade conversions (table, above) in

reverse. Should students receive QPs for these percentages, and

would a GPA be calculated? Absolutely not! Fairness demands that

there be no QPs and no GPA to magnify student differences. Since we

must still take into account the number of credits per course and all

courses taken, performance overview should be determined as

percentage per credit, or PPC. For example, suppose students X and Y

take the same five courses: three 3 credits, one 2 credits, and one 4

credits. Suppose also that student X gets 91% in every course for a

91 PPC, and Y gets 91% in the three 3 credit courses and 89% in the

other two for a 90.2 PPC ((9 x 91%) + (6 x 89%)) ? 15 = 90.2%. Both

students would thus be in the "A" category using a 90 PPC standard,

whereas the traditional GPAs of 4.0 for X and 3.6 for Y are

misleading. The situation can be even more ridiculous: if Y received

98% in each 3 credit course, and 89% in the other two, Y's PPC would

be 94.4, clearly showing superiority to X. Yet the GPAs remain as

before: 4.0 for X and 3.6 for Y.

Now, let's reconsider the F grade, with zero QPs for anything below

60%. Suppose student X takes five 3 credit courses, and gets 79%,

79%, 69%, 69%, and 59%. The PPC will be 71 (classical C category),

but the GPA is 1.2 (much closer to D). If Y gets the same grades in

the first four, but 30% in the last, the GPA remains 1.2 but the PPC

is 65.2, correctly reflecting the difference in level of F

performance. One more extreme example to make the point: suppose

student Z takes five 3 credit courses, receives 99% in four, but has

one very bad day and gets 59% in the fifth. Clearly, this is a

superior student (PPC = 91), but the GPA is a so-so 3.2.


Some may argue that the GPA is nevertheless acceptable because

borderline grades may not make much difference in the long run. But

why not just get it right? Why begin the grading process with an

accurate numerical evaluation, convert it to a less accurate letter

grade, and back again to a still less accurate number? With its

potential for producing distortion and unnecessary agonizing, the GPA

should be discarded and the PPC, or something better, should take its



Professor William D. Cohen

Department of Biological Sciences

Hunter College

695 Park Avenue

New York, NY 10021

Telephone: (212) 772-5312