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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 schoolrelated
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 fivepoint
difference at one end of the scale means the same thing as a fivepoint
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 Dminus, 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 byproducts of using the median to average student grades.
 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 testtaking skills are poor or whose recall of
facts is slower than required. Standardized tests show these students
to be of average ability. When teachermade 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 socalled C
students.
 Students with learning
disabilities are able to earn good grades without the special
accommodations that often single them out as "different."
 Highly motivated, gifted
students are more easily identified, and differentiated instruction is
more easily provided to them.
 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.
 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.
 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.
 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 byproducts 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 atrisk 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
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