Written and designed by the staff of the Center for Teaching and Learning. Reproduce with permission only.
April 1991
The subject of grading is rarely
discussed among faculty members, except perhaps for the occasional debate about
grade inflation. But many teachers privately confess that grading is one of
the most difficult and least understood elements of their job. Often, professors
have little confidence that their grading systems accurately discriminate between
different levels of achievement and they differ widely on the components that
should constitute a final grade. As a result, grading standards and criteria
are so idiosyncratic that an "A" from one teacher may be the equivalent
of a "C" from another. Part of the problem with grading arises from
the fallibility of the tests and assignments used to measure student performance.
The three previous FYC's focused on ways to improve assessment techniques; in
this article, we will survey several different methods for calculating final
grades and point out their strengths and weaknesses.
First, it helps to make a distinction between grading and other forms of feedback. A grade is a "certification of competence" that should reflect, as accurately as possible, a student's performance in a course. If this goal is achieved, then grades will have the same value from semester to semester and from year to year. Trouble arises when we include grading components that are difficult to measure accurately (such as effort or participation) because these elements reduce the strength of the relationship between grades and academic achievement. Furthermore, when we use grades for reward or punishment, give extra credit for additional work, or grade on attendance, we contaminate the meaning of grades and reinforce the students' belief that a course grade has less to do with academic performance than with fulfillment of arbitrary requirements.
Of course, we must give students
feedback in many of these areas of behavior, but using the grading system to
convey this assessment is inappropriate. Moreover, we often complain that students
are excessively grade-oriented, but by attaching a grade value to every aspect
of student performance we actually reinforce our students' preoccupation with
grades. Teachers should avoid using grades as incentives for performance and
seek out non-graded methods for motivating students. For example, verbal "rewards"
in class, individual conferences, and written critiques can provide positive
and negative feedback without contaminating the grading system.
A good grading system must meet three
criteria: (1) it should accurately reflect differences in student performance,
(2) it should be clear to students so they can chart their own progress, and
(3) it should be fair. Performance can be defined either in relative or absolute
terms (comparing students with each other or measuring their achievement against
a set scale), and each system has its defenders. But whichever grading scheme
you use, students should be able to calculate (at least roughly) how they are
doing in the course at any point in the semester. Some relative grading schemes
make it impossible for students to estimate their final grades because the cutoff
points in the final distribution are not determined until the end of the course.
A complete description of the grading system should appear in the course syllabus,
including the amount of credit for each assignment, how the final grades will
be calculated, and the grade equivalents for the final scores. Also, students
should perceive the grading system as fair and equitable, rewarding them proportionately
for their achievements. From the standpoint of measurement, many different kinds
of assignments, spread over the entire semester provide a fairer estimate of
student learning than one or two large tests or papers.
Relative (norm-referenced) grading
systems are probably the most widespread in higher education. In relative grading,
students are in competition with one another for a limited number of grades
in each category, and a student's grade is based on his or her relative position
in the class. By contrast, absolute (criterion-referenced) systems use an unchanging
standard of performance against which student performance is measured, so a
student's grade is related to his or her achievement of particular levels of
knowledge or skill. No grading system is foolproof, for the integrity of any
system depends on the teacher's ability to devise valid and reliable measurements
of student performance. Measurement error is therefore the greatest hindrance
to effective grading.
Relative grading is based on two assumptions: (1) one of the purposes of grading is to identify students who perform best against their peers and to weed out the unworthy, and (2) student performance more or less follows a normal distribution -- the famous bell-shaped curve. Teachers who use relative grading point out that these systems correct for unanticipated problems (e.g. widespread absences due to a flu epidemic, tests that are too hard or too easy, or poor quality teaching) because the scale automatically moves up or down. Students like relative grading for much the same reason.
One of the most common relative grading
systems is "grading on the curve." The use of the normal curve as
a grading model is based on the discovery, earlier in this century, that IQ
test scores over large populations approximate a normal distribution (Figure
1). Although it is true that the larger the class, the more likely that student
performance will begin to look something like a normal curve, the assumption
that performance is normally distributed is usually unjustified, even in large
sections. In the first place, college students are a highly selected group,
not representative of the general population with respect to background or intelligence.
Second, we cannot be sure that our tests accurately measure student achievement
-- even standardized exams are suspect in this regard.
Fortunately, few teachers adhere to a strict normal distribution, since it will
fail a fixed percentage of the class and award "A's" to a fixed percentage,
without reference to the overall level of performance. Forcing students into
this scale tends to wreak havoc with their motivation. Consequently, many people
use a "skewed curve" in which the distribution is shifted upward slightly,
resulting in fewer grades below "C" and more in the "B"
category. However, few teachers base their modified curves on statistical principles
or cumulative performance data; they simply select a distribution that "looks
right." Typically, the rationale for grade cutoff points is based on tradition
rather than on analysis of student performance over time. The major problem
with any curve is that one cannot be sure that differences in performance are
real or simply artifacts of the distribution -- was the performance of the top
5 students who got "A's" substantially different from that of the
15 who received "B's?"
Statistically speaking, the soundest relative grading system is the standard
deviation method. In this system student grades are based on their distance
from the mean score for the class rather than on an arbitrary scale. To calculate
the standard deviation, the teacher creates a frequency distribution of the
final scores and identifies the mean (average) score. Using the formula in Figure
2, the standard deviation is computed so that cutoff points for each grade level
can be determined (note: spreadsheets can be programmed to perform the math
automatically).
Cutoff points for "C" grades range from one-half the standard deviation below the mean to one-half above. Adding one standard deviation to the upper "C" cutoff will yield the "A-B" cutoff point, and subtracting one standard deviation from the lower "C" cutoff will provide the "D-F" cutoff point.
| Class I | Class II | |
|---|---|---|
| Mean of final scores | 79.2 | 60.76 |
| Standard deviation | 12.79 | 9.85 |
| Upper "C" cutoff | 85.6 | 65.69 |
| Lower "C" cutoff | 72.8 | 55.83 |
| "A/B" cutoff | 98.4 | 75.54 |
| "D/F" cutoff | 60.0 | 45.98 |
Absolute (criterion-referenced) grading is based on the idea that grades should reflect mastery of specific knowledge and skills. The teacher sets the criteria for each grade, and all students who perform at a given level receive the same grade.
The simplest absolute grading scheme is "percent of total points possible." The teacher decides on the total number of points that a student could earn in the course and sets arbitrary achievement levels based on the total. The cutoff for "A" grades might be 90%, for "B's," 80%, and so forth, and it is assumed that a student who makes 83% knows 83% of the material. If every student scores above 90%, they will all receive "A's." Although this method does provide clear performance targets for students, there are several problems associated with it. First, the rationale for the cutoff scores is usually murky and often based on intuition rather than analysis. Second, the system is based on the assumption that the teacher can construct valid, reliable exams and assignments at consistent levels of difficulty throughout the course. Third, some teachers apply the same performance scale to every evaluation component, a practice which does not take into account the variability of the assignments or adjust for particularly difficult or particularly easy assignments. Finally, some students may achieve a high number of points simply by doing well on many small, less important assignments.
Objective-based grading is perhaps the most sophisticated kind of absolute grading because the method attempts to equate grades with different kinds of performance. In all the grading systems reviewed above, the teacher assumes that students who receive good final grades have learned the more important material and mastered the more complex levels of thinking, but this assumption may not be valid. For example, students who do very well on objective exams and poorly on written assignments may earn a respectable final grade, but may not have mastered important intellectual skills that the teacher had in mind. The objective-based grading method takes into account both the amount of material students learn and the level of cognitive complexity they achieve.
To use objective-based grading, the teacher must first review the kinds of knowledge and skills that are implicit in the course and make them explicit as course objectives. You must identify two kinds of outcomes: minimal objectives and developmental objectives. Minimal objectives are statements of essential course outcomes and basic skills; developmental objectives reflect higher-order cognitive processes such as critical thinking, decision-making, and complex problem solving. Examples:
Minimum Essential Objectives
The student will be able to:
Developmental Objectives
The student will be able to:
It may be easier, at least initially, to measure achievement of minimal and developmental objectives using completely separate exams and assignments for each type of objective. This technique will simplify record-keeping and help you focus more sharply on the different kinds of tasks that are appropriate for assessing the two types of objectives. Test questions and exercises for minimal objectives are relatively easy to create because they assess basic knowledge and well-rehearsed skills. Measuring developmental outcomes is more difficult, for you must not only master the classification systems for complex thinking and reasoning skills but also must be able to devise assignments that measure these skills. Some writers suggest that "novelty" is one element common to higher-order learning tasks and therefore assignments that require students to apply their thinking skills in new ways or in new situations will test complex reasoning.
If you develop tests and exercises
that accurately assess both kinds of objectives, you can set performance standards
and grade equivalents on a scale like this one:
|
Grade
|
Performance
Standard
|
|
|---|---|---|
|
Essential
Objectives
|
Developmental
Objectives
|
|
|
A
|
90% or more
|
85% or more
|
|
B
|
90% or more
|
75 to 84%
|
|
C
|
80% or more
|
60 to 74%
|
|
D
|
80% or more
|
50 to 59%
|
|
F
|
less than
80%
|
less than
50%
|
In this example, in order for students to pass the course they must master at least 80% of the minimum essential objectives and 50% of the developmental objectives. Obviously, setting these cutoff points must be done carefully, taking into account the difficulty of the tests and assignments and student performance in previous classes or other sections of the same course. If using this kind of scale seems too difficult, you could use the "total points possible" system instead. By awarding more points for tests and assignments on higher-level objectives and fewer points for tasks on less important objectives, you would still reap some of the advantages of the objective-based method.
No single grading system will be
appropriate for all courses at all times, and teachers must be sensitive to
differences in students and subject matter when choosing a grading system. It
takes time to develop realistic expectations about student performance, and
the best teachers constantly reexamine their grading assumptions to verify that
their systems are valid. Finally, the accuracy of any grading system is dependent
upon the validity and reliability of the measures we use to assess student performance,
so improving the quality of exams and course assignments will improve the accuracy
of the final grades.
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