Linear Grading – Why You Might Consider It
These descriptions represent my own thoughts and are
not official ASD policy. I entered teaching with significant statistical
training and have helped many teachers with their grades while teaching math
and computer classes for over twenty years.
Pete Tryon, SAHS Tech Coordinator
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Most
teachers use the traditional percentage based grading system: 90% - A, 80% - B, … 60% - D, below 60% is an F. If students miss work, they get a 0% for the
assignment. The ramifications of this
are not always what the teacher expects or wants.
Example: Student A is
a bright, not-very-motivated student who gets A’s (95%) on his homework when he
does it, but only turns in half of it.
What grade should he get?
Example: Student B ‘bombed’
your first test, not understanding what was wanted at all, getting a 26%. She then started studying and got a 71% on
the next one and a 77% on the third.
What grade should she get?
Using the
traditional scale, 95 averaged with 0 is 47.5% - student A would receive a ‘solid’
F . The average
of 26, 71, and 77 is 58, resulting in:
“Congratulations, I really like the way that you got to work on the last
two tests – oh by the way, your grade is an F!” I have talked with teachers about these
scenarios and some have told me that “well, in cases like those, I’d make an
exception and round up…” Some teachers
have a number of students in classes with grades between 25 and 40% where,
strictly on a mathematical basis, they have no chance of passing although it is
still many weeks from the end of the semester.
It can be hard to motivate these students.
Some
teachers wish to use a letter scale, assigning the letters A - F to all
assignments. This allows an A and an F to average to a C. Others switch to a 4, 3, 2, 1, 0 scale to
quantify this. The 4 (or 5) point scale works mathematically, but is hard to
apply to large tests, quizzes, and projects. In some situations, there really
is a difference between an 89 paper and an 81 paper and it is inappropriate to
give them the same grade. Many students
and parents are not used to the 4/5 point scale and it may take significant
effort to explain it.
It is
possible to use the same linear grading while still assigning percentage
grades. This has the advantage that the
grade that everyone sees is on the traditional percentage scale and that it is
also easily incorporated into Zangle. I used this method for many years, teaching
geometry and algebra. Use the
traditional percentages for grading assignments and simply set a bottom limit
for all F’s. I then set another value
for
‘missing’.
A – 95%
B – 85%
C – 75%
D – 65%
F – 55%
Missing – 45%
If you graph
these out (Figure 1), they illustrate that it is linear grading, with missing
work a one step penalty below Fs. An A and an F average to a middle C. An A and Missing average to
70%, a C-. Compare this with
counting missing as 0%, graphed in Figure 2.
Back to the
examples: Student A (missing homework)
would receive a 70% homework grade (average of 45 and 95). Student B (one bad
test) would receive a 67.7% for exams.
I used the
Linear Scale (Missing – 45%, F – 55%) for many years in my math classes. I also ran multiple comparisons, calculating
grades using both this scale and the traditional 0% scale. I found that I generally failed the same
students, but with the Linear Scale the students failed with higher
scores. This meant that
three weeks from the end of the semester, my failing students had grades in the
50s, not in the 20s and 30s. That put me
in the position of explaining to students and parents that if they wanted to
turn their lives around, turn in homework, retake quizzes, study, etc., they
stood a chance to raise their grade to a D.
Some of them would actually do it! Note that this scale has very little
effect on the grades of ‘good’ students.
I do not
recommend this for all situations – but if you have students with very low
grades, who give up early, if you find yourself wishing to ‘make adjustments’
or to ‘round up’, the linear scale may be appropriate. I would suggest that if you are interested in
this scale, try it with some test calculations. If you switch mid-term, no one is going to
complain! Instructions for one way to
implement this in Zangle are posted. Feel free to e-mail me with comments or
questions. (tryon_peter@asdk12.org)