From the ERIC database
Grading Students. ERIC/AE Digest.
Some instructors record letter grades for tests and assignments, and others record numerical values, often the percent correct on tests. Later, under either method, the grades are averaged, often employing a weighting process designed to make some grades count more heavily than others. Discussion of the merits of different approaches usually centers around the question of whether it is better to average letter or numerical grades or around some feature of the weighting process.
This Digest discusses several aspects of assigning grades. First, an issue that underlies for both approaches, variability of test scores, is discussed. The use of standardized scores is presented as a solution to the variability problem, ideas on assigning letter grades, and recommendations are then presented.
To see how this outcome could occur, consider a course in which the midterm examination was much more difficult than the instructor intended; scores ranged from 35% to 95% with an average of 65%. Further assume the instructor did not view this outcome as desirable and, with the intention of being fair to the students, included a large proportion of easy questions on the final examination. Their presence caused a great reduction in score variation. Final examination scores ranged only from 88% to 100% with and average of 94%. Only a small number of harder questions kept everyone from earning very high scores in a narrow range. The result was that differences from one student to another in final course averages were largely attributable to scores on the midterm. Thus, a student's achievement in the latter part of the course was effectively devalued, which was hardly fair or in keeping with the presumed intention that grades reflect achievement across the entire course.
It may be difficult to work with z-scores, because half of them will be negative and all will probably lie between -3 and 3. Therefore, it is convenient to transform the z-scores into T-scores as follows: T = 50 + 10z. T-scores will have a mean (average) of 50 and a standard deviation of 10. Thus, a T-score of 60 represents a number-right score one standard deviation above the average. If the distribution of scores approximates the shape of the normal curve, about 16% of the T-scores will be above 60 and about 10% above 63. Similarly, about 16% of T- scores will be below 40 and about 10% below 37.
If T-scores are computed for every test, averaging them will provide a composite score from which the influence of the variability of the scores has been eliminated. (Strictly speaking, if more than two scores are to be averaged, the intercorrelations among the scores should be taken into consideration in order to control for the degree of "overlap." However, simple averaging of T- scores should produce a good approximation of the more precise result.) T-scores are typically provided for multiple-choice tests processed by measurement services offices at universities. Moreover, T-scores can be calculated for any numerically evaluated non-test assignments you may wish to include in the course composite. Like other scores, T-scores may be weighted differentially. For example, if you wish to weight the final exam twice as much as the midterm, multiply the T-scores from the final by 2, add the midterm T-scores and divide by 3.
It should be noted at this point that T-scores report only a student's relative position in the class and not an absolute measure of achievement. However, we contend that the difficulty level of nearly all academic tests is arbitrary and that, regardless of the scoring method, they provide nothing more than ranking information. The concern of this Digest is that the scores be averaged in a manner consistent with the instructor's intention.
ASSIGNING LETTER GRADES
- What is a typical letter grade distribution for a
course of this type with this kind of student?
- Are there any circumstances which might warrant
altering this "typical" distribution, e.g., did the
course progress especially well or poorly?
- Where in the distribution are key students whose work
you know especially well, students you believe might
deserve especially good or poor grades for reasons
other than test performance?
- Where are naturally occurring "breaks" in the
distribution of average T-scores? (There is no
"scientific" reason for letting these points determine
letter grades, but if their use is not inconsistent
with other considerations, it will help to prevent
hard feelings on the part of students who otherwise
might miss a better grade by one T-score point.)
Two ideas to be avoided or at least questioned in determining letter grades are:
- That the T-score spread should be the same for each letter grade.
- That an equal number of As and Fs, Bs and Ds, should
necessarily be awarded.
Finally, it must be remembered that assignment of letter grades across a range of average scores is essentially arbitrary and a matter of professional judgment.
2. When testing higher level cognitive skills, vary the difficulty of the questions so as to discriminate among all skill levels. Include items sufficiently difficult to challenge even the most talented students and a few items sufficiently easy that most will answer correctly. The latter may include a disproportionate number of lower level cognitive skills. The average percent- correct score should be somewhere in the range between 50% and 70% in order to maximize discrimination among achievement levels.
3. Alert students to the fact that the test may be more difficult than what they are accustomed to, but that the percent-correct scores will be interpreted in a relative, rather than an absolute sense.
4. Determine the minimum passing score on each test by identifying items that you (and/or your colleagues) judge to represent essential knowledge, or that you (or they) believe should be correctly answered by any student deserving of a passing grade. Base the passing score on the percentage of the total points these questions contribute. You may wish to compute a separate score for items so identified, but it is probably sufficient to use this percentage regardless of which items are answered correctly.
5. Use your professional judgment to determine cut points between grades. You might consider the test performance of students about whom you have independent knowledge of achievement via other assignments or previous courses. Naturally occurring breaks in the score distribution can suggest cut points between letter grades that might minimize the number of students clamoring at your door for the extra point or two needed for the next higher grade. Ultimately, judgments in this area are subjective and should be acknowledged as such when implemented.
6. Do not feel obliged to "grade on the curve" whereby a specified percentage of students will receive each letter grade. To do so can be as arbitrary and capricious as to adopt prescribed percentage ranges for assigning scores, especially in smaller classes.
This Digest was adapted with permission from "Testing Memo 6: What kinds of grades should be averaged," and "Testing Memo 11: Absolute versus relative grading standards: What does a percentage mean," Office of Measurement and Research Services, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060.
Lysne, A. (1984) Grading of Student's Attainment: Purposes and Functions. "Scandinavian Journal of Educational Research," 28(3), 149-65.
Nottingham, M. (April, 1988) Grading Practices--Watching Out for Land Mines. "NASSP Bulletin," 72 (507), 24-28.
Ornstein, A.C. (April, 1989) The Nature of Grading. "Clearing House," 62 (8), 365-69.
Terwilliger, J.S (1989) Classroom Standard Setting and Grading Practices. "Educational Measurement: Issues and Practice," 8(2), 15-19.
This publication was prepared with funding from the Office of Educational Research and Improvement, U.S. Department of Education, under contract RR93002002. The opinions expressed in this report do not necessarily reflect the positions or policies of OERI or the U.S. Department of Education. Permission is granted to copy and distribute this ERIC/AE Digest
Title: Grading Students. ERIC/AE Digest.
Descriptors: * Academic Achievement; Elementary Secondary Education; * Grades [Scholastic]; * Grading; Scores; * Scoring; * Student Evaluation
Identifiers: Composite Scores; *Standardized Scores; T Values; Variability; *Z Scores
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