Norm-Referenced Grading

Assessment of student performance is essentially knowing how the student is progressing in a course (and, incidentally, how a teacher is also performing with respect to the teaching process). The first step in assessment is, of course, testing (either by some pencil-paper objective test or by some performance-based testing procedure) followed by a decision to grade the performance of the student. Grading, therefore, is the next step after testing. Over the course of several years, grading systems had been evolved in different schools systems all over the world. In the American system, for instance, grades are expressed in terms of letters, A, B, B+, B-, C, C-, D or what is referred to as a seven-point system. In Philippine colleges and universities, the letters are replaced with numerical values: 1.0, 1.25,1.50, 1.75, 2.0, 2.5, 3.0 and 4.0 or an eight-point system. In basic education, grades are expressed as percentages (of accomplishment) such as 80% or 75%. With the implementation of the K to 12 Basic Education curriculum, however, student’s performance is expressed in terms of level of proficiency. Whatever be the system of grading adopted, it is clear that there appears to be a need to convert raw score values into the corresponding standard grading system. 

Norm-Referenced Grading

The most commonly used grading system falls under the category of norm-referenced grading. Norm-referenced grading refers to a grading system wherein a student’s grade is placed in relation to the performance of a group. Thus, in this system, a grade of 80 means that the student performed better than or same as 80% of the class (or group). At first glance, there appears to be no problem with this type of grading system as it simply describes the performance of a student with reference to a particular group of learners. The following example shows some of the difficulties associated with norm-referenced grading: 

Example: Consider the following two sets of scores in an English 1 class for two sections of ten students each:

A = { 30, 40,50, 55, 60, 65,70,75,80, 85}
B = { 60, 65, 70, 75, 80, 85, 90, 90, 95, 100}

In the first class, the student who got a raw score of 75 would get a grade of 80% while in the second class, the same grade of 80% would correspond to a raw score of 90. Indeed, if the test used for the two classes are the same, it would be a rather “unfair” system of grading. A wise student would opt to enroll in class A since it is easier to get higher grades in that class than in the other class (class B).

The previous example illustrates one difficulty with using a norm-referenced grading system. This problem is called the problem of equivalency. Does a grade of 80 in one class represent the same achievement level as a grade of 80 in another class of the same subject? This problem is similar to the problem of trying to compare a Valedictorian from some remote rural high school with a Valedictorian from some very popular University in the urban area. Does one expect the same level of competence for these two valedictorians?

As we have seen, norm-referenced grading systems are based on a pre-established formula regarding the percentage or ratio of students within a whole class who will be assigned each grade or mark. It is therefore known in advance what percent of the students would pass or fail a given course. For this reason, many opponents to norm-referenced grading aver that such a grading system does not advance the cause of education and contradicts the principle of individual differences.

In norm-referenced grading, the students, while they may work individually, are actually in competition to achieve a standard of performance that will classify them into the desired grade range. It essentially promotes competition among students or pupils in the same class. A student or pupil who happens to enroll in a class of gifted students in Mathematics will find that the norm-referenced grading system is rather worrisome. For example, a teacher may establish a grading policy whereby the top 15 percent of students will receive a mark of excellent or outstanding, which in a class of 100 enrolled students will be 15 persons. Such a grading policy is illustrated below: 

1.0 (Excellent) = Top 15 % of Class
1.50 (Good) = Next 15 % of Class
2.0 (Average, Fair) = Next 45 % of Class
3.0 (Poor, Pass) = Next 15 % of Class
5.0 (Failure) = Bottom 10 % of Class

The underlying assumption in norm-referenced grading is that the students have abilities (as reflected in their raw scores) that obey the normal distribution. The objective is to find out the best performers in this group. Norm-referenced systems are most often used for screening selected student populations in conditions where it is known that not all students can advance due to limitations such as available places, jobs, or other controlling factors. For example, in the Philippine setting, since not all high school students can actually advance to college or university level because of financial constraints, the norm-referenced grading system can be applied.

Example: In a class of 100 students, the mean score in a test is 70 with a standard deviation of 5. Construct a norm-referenced grading table that would have seven-grade scales and such that students scoring between plus or minus one standard deviation from the mean receives an average grade.

Solution: The following intervals of raw scores to grade equivalents are computed:

Only a few of the teachers who use norm-referenced grading apply it with complete consistency. When a teacher is faced with a particularly bright class, most of the time, he does not penalize good students for having the bad luck to enroll in a class with a cohort of other very capable students even if the grading system says he should fail a certain percentage of the class. On the other hand, it is also unlikely that a teacher would reduce the mean grade for a class when he observes a large proportion of poor-performing students just to save them from failure. A serious problem with norm-referenced grading is that, no matter what the class level of knowledge and ability, and no matter how much they learn, a predictable proportion of students will receive each grade. Since its essential purpose is to sort students into categories based on relative performance, norm-referenced grading and evaluation is often used to weed out students for limited places in selective educational programs.

Norm-referenced grading indeed promotes competition to the extent that students would rather not help fellow students because by doing so, the mean of the class would be raised and consequently it would be more difficult to get higher grades. Similarly, students would do everything (legal) to pull down the scores of everyone else in order to lower the mean and thus assure him/her of higher grades on the curve.

A more subtle problem with norm-referenced grading is that a strict correspondence between the evaluation methods used and the course instructional goals is not necessary to yield the required grade distribution. The specific learning objectives of norm-referenced classes are often kept hidden, in part out of concern that instruction not “give away” the test or the teacher’s priorities, since this might tend to skew the curve. Since norm-referenced grading is replete with problems, what alternatives have been devised for grading the students?