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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Tomorrow's Teaching and Learning

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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