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Success for All: The Median is the Key

by Russell G. Wright

May,1994, Phi Delta Kappan, Reprinted with Permission

You are probably good at what you do. Most of us gravitate to jobs and careers that closely match our likes and strengths. Once in those jobs, we make choices that reflect our desire to emphasize our strengths and hide our weaknesses. We are human, after all.

In the best secondary classrooms in America, students are asked to perform a wide variety of tasks. Some students are good at all these tasks, most are good at some of them, and some are good at none. When students are good at all school-related tasks, we reward them with good grades. Those who are good at only some tasks receive mediocre grades that result from averaging the good with the bad. And, of course, the students who are good at nothing -- or who long ago quit trying -- receive failing grades.

Did you notice the difference between the adult work experience and the child's school experience? In science -- I speak as a science teacher, but my message is for all -- we have students who measure accurately, make careful observations, and are meticulous in following laboratory procedures but receive a C or D on their report cards because they can't or won't memorize the vocabulary, formulas, and metabolic pathways common to science courses. These students may like "doing" science, but they understandably refuse to take more than the minimum number of science courses needed for graduation. By not recognizing the strengths of our students, we are turning them away. We are telling them that they don't belong -- that science, mathematics, foreign languages, English, physical education, art, music, and so on are only for those who can do it all.

How can we make the classroom experience more like the work experience? How can we expose our students to the variety of tasks and activities that make up the disciplines we know and love and still allow them to succeed even if they are not good at everything? The answer lies in the way we average student grades and determine report card grades; after all, the word "average" does not require the use of the arithmetic mean. The mean is only one of three common measures of central tendency. In addition, there are the median and mode, and each has a specific application in statistical analysis that should be considered for use in grade averaging.

In determining a median grade, one arranges all of a student's grade in descending order. The median grade is the grade in the center, with an equal number of grades (or proportion of grades) above and below it. If there are an even number of grades with no central grade, the two grades that straddle the central position are added together and divided by two. The median in this case is the mean of the two central grades. Using the median, a student with grades of A, A, B, B, B, C, F, F would receive a B rather than the C that results from calculating the mean.

The median is actually the statistically correct measure of central tendency for ordinal data. Ordinal data consist of numbers on a scale whose intervals are uncertain or inconsistent. The numbers on such a scale carry information only about order. That is, we know that an A is better than a B, but is it always the same amount better? We also know that an 85 is better than an 80. But does an 85 on one test mean the same thing as an 85 on another? Are your tests so precise that a five-point difference at one end of the scale means the same thing as a five-point difference at the other end?

Because of the imprecision of grading and the absence of uniform intervals between grades, grades are not interval data. Grades are ordinal! And, since grades are ordinal, the best summary of grades -- and therefore the grade that should appear on the report card -- is the median, not the mean.

How do students react when their report card grades are calculated in this way? Well, my biggest fear never materialized. In the 12 years since I began using the median, none of my students has ever stopped working after being assured of getting an A. Straight A students have continued to get A's on most things.

When I started using the median in the middle of a school year, I did notice that a few of my straight C students began to get A's and B's on some work. When I asked them why they were working harder this semester, I got such answers as "My hard work is going to count more the way you're grading us now." No longer would one area of weakness pull their grades down. Some D students who were not interested in working toward a C were forced to work harder just to keep their D's. Some failing students began to pass, and my relationship with my students began to change. I became an advisor on how best to use available skills and strengths. I found myself telling individual students which upcoming activities they should spend their time on and which they should ignore.

Imagine a teacher telling a student not to study for an upcoming test! If the best a student had ever done on tests was a D-minus, I actually advised him or her to use the time that would normally be spent studying for a test to write a better research paper. This tactic was especially effective with students whose grades on previous papers were close to a B or A.

There are at least seven beneficial by-products of using the median to average student grades.

  1. Many C students are motivated to work harder. It is primarily students of average ability who suffer in classrooms in which grades are averaged using the mean. These are often students whose test-taking skills are poor or whose recall of facts is slower than required. Standardized tests show these students to be of average ability. When teacher-made tests merely confirm this, there is no problem for anyone but the student. However, when the median is used in combination with a wide variety of graded activities, tests recede in importance, and the report card grade for the student of average ability may turn out to be an A or a B, thus rewarding successful efforts in some areas without dwelling on failures in others. Imagine the motivating effect that this can have on so-called C students.
  2. Students with learning disabilities are able to earn good grades without the special accommodations that often single them out as "different."
  3. Highly motivated, gifted students are more easily identified, and differentiated instruction is more easily provided to them.
  4. The teacher can hold higher expectations without hurting student grades. I have seen this effect in my own classes: all who are willing to work are able to meet the higher standards on enough of the activities to achieve a C average or better. Most of my students have achieved better than a C.
  5. Poorly motivated students are forced to work harder to receive a passing grade. To pass a course when the median is used, the student must pass half the work.
  6. Students show a lower level of anxiety and an improved attitude. Anxiety is definitely lessened when, with 60% of the work remaining in a marking period, all students are still able to earn A's on their report cards.
  7. It's easier to average grades by picking the middle grade. Not only is the median a time saver at the end of the marking period, but it also allows students to keep constantly updated on their average throughout a marking period.

When I conducted a study of the effect of grading on students' attitudes toward science in grades 7 through 10, I found that 39% of the variance in science attitude can be explained by grading factors (last report card grade, perceived fairness of the grade, range of grades earned by an individual on a variety of course activities, and grading awareness). The grade itself had a high correlation (+ .49) with attitude, as expected, but the grade alone accounted for only 24% of the variance.

The other grading factors accounted for the additional 15% of the variance in attitude. Grade range contributed about half of that additional variance. Or, put another way, with a correlation of -- .53, grade range alone accounts for 28% of the variance in attitude toward science. (Grade range was defined as the difference between the typical grade for activities on which a student does best and the typical grade for activities on which a student does worst.) This finding indicates that students are frustrated when they do much better on some activities than they do on others. The median is one method for addressing both of these factors. It is easier for students to receive at least a C when the median is used, because bad grades need not destroy an otherwise good record. (The median is also very easy for all students to understand, and constant updating requires little extra time. Grading awareness was also an independent contributor to the variance in science attitude.)

The beneficial by-products that I have observed may have resulted from the fact that under this system it is the student, not the teacher, who decides what activities are important. If a teacher is skillful in designing options, the student will learn and "do well" in the course at the same time.

We are often admonished to hold high expectations for all students. On the other hand, we are warned that, unless we provide success to these same students, they will soon feel that they don't belong in a particular subject or even in school at all. Mary Budd Rowe tells us of the lack of "fate control" typical of the at-risk youngster. How can we possibly make sense of these conflicting demands?

I believe that the median is the key. It allows a teacher to raise expectations. It provides more opportunities for success by diminishing the impact of a few stumbles and by rewarding hard work. In a median classroom, no student who is working hard should get less than a C, and the majority should be getting A's and B's. By providing choices and by using the median to reward success, we can make "success for all" a reality.

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Last updated on Friday, February 16, 2018