The results of the semester’s third test have just been
returned to the students. There are only three more lectures, a short break,
and then the final examination to go. Student Alan is on track for a B-plus
letter grade, and is out of range for an A-minus grade. After the lecture, Alan
speaks to the lecturer.
Alan: “Sir, I see that I am out of range for an A-minus
grade. Can I do something for extra credit?”
Lecturer: “Yes, you are out of range for an A-minus grade. You
can still aim for a B-plus grade.”
“I am worried about my GPA and graduate school. I need extra
credit.”
“How many marks would you like the extra credit to be worth?”
“Fifteen marks will be enough to get me into the A bracket.”
“Yes, I can set an extra test worth 15 marks. It will cover
all topics to date. We conduct the extra test during consultation time
immediately following the second lesson from today.”
“Sir, that’s not fair. It should cover only the topics in
Test Three.”
“You’ve been losing marks since Test One. That’s how you became
out of range of an A-minus grade. If the extra test covers only Test Three topics,
then you’re essentially re-taking Test Three. The new test would be only a
supplementary Test Three, and the score will replace (not add to) your Test
Three score.”
“That will not give me enough marks to get an A grade.”
“Well, you do your own calculations. Another thing: I must
offer the same extra test to all the other students – in fairness to them. Of
course, they can opt to stay with the marks they have, and not take the extra
test.”
“That’s for them to decide. I’m interested only in my extra
credit.”
“There’s one more thing. With the extra test, your letter grade
will be computed by taking your total marks (including from the final
examination) as a percentage of 115 marks, instead of as a percentage of 100
marks.”
“What? No! That’s not fair! I will likely be out of range of
A again! You add marks only to the numerator, not the denominator.”
“Alan, your misunderstanding is quite common. Grades are
awarded on the basis of the percentage of offered marks that you earn, not on
the basis of the number of marks you earn. This common misunderstanding is
caused by the common practice of using a 100-mark scale in assessment, when percentages
are calculated also on a 100-point scale. People (students, lecturers,
administrators) conflate the two. If grade computation uses only the numerator,
then a student who earns 100 out of 1,000 offered marks must be awarded an
A-plus letter grade, and be considered “High Distinction”. But this is clearly
absurd, since the student has mastered only ten percent of the course material.
Consequently, students who take the extra test will have their letter grades awarded
on the basis of their percentage of 115 marks, whilst students who do not take
the extra test will have their letter grades awarded on the basis of their
percentage of 100 marks, in the usual way.”
“None of our other lecturers does extra credit this way. I
will be speaking to the student union about this, and about you.”
“So do you want the extra test or not?”
“I want the extra test. And I want the denominator to remain
at 100 marks.”
END
