A bunch of people have been mailing me links to an article from USA today
about schools and grading systems. I think that most of the people who’ve
been sending it to me want me to flame it as a silly idea; but I’m not going to do that. Instead, I’m going to focus on an issue of presentation. What they’re talking about could be a good idea, or it could be a bad idea – but because the
way that they present it leaves out crucial information, it’s not possible to meaningfully judge the soundness of the concept.
This is very typical of the kind of rubbish we constantly see in
the popular press. They’re so clueless about the math underlying what they’re
talking about that they don’t even know when they’re leaving something crucial out.
The article focuses on how you record failing grades in a percentage-based
system: If 91-100 is an A, 81-90 is a B, etc. – then what should you record for an F? The article talks about a movement in schools to record Fs as 50s, rather than 0s.
What they left out is: what is it that’s actually being recorded?
When you take a test, what’s generally recorded is your actual score on
the test. So if you got 74% on a test, what would be recorded is the “74”, not
“C”. On the other hand, many things are graded not on a percentage basis, but on
a judgement of the appropriate grade on a 5-point letter-grade scale, so that the full information about how you did on an assignment or test is “C”.
In the former case, changing peoples scores is thoroughly unfair. If student
1 failed – but failed by just a hair, with a 50%, and student 2 failed terribly
with an 18% score, then student 1 should have an easier time raising his/her grade by doing well on other work than student 2.
In the latter case – that is, the case where you were given a grade
based on a five-point letter system, where a “D” was recorded as 60, and an F was recorded as 0 – that’s very unfair – because the scale is profoundly unbalanced. What corresponds to a one percentage point difference in a percentage-based score is translated into a 60 point difference by the conversion from letter to percentage.
Look at a simple example. Suppose you have a student who turns in five
writing assignments, which are graded on a 5 point scale. The student gets
F, B, B, B, C. If you score those as 50, 90, 90, 90, 80, then the average is
80, which would convert back to a C. If you score them as
0, 90, 90, 90, 80, then the average is 70, which converts back to a D.
It’s really not fair – because what you’ve done is created a tight cluster of
scores for passing grades, and then a comparatively huge gap between a minimum passing grade, and a maximum failing grade. Expressed that way, you can see what the real problem is. If you use a bad conversion from five-point scoring to percentage, you get unfair results. The real root cause of the problem is that
the way that the grades are produced, and the way that they’re recorded or averaged are very different.
If that’s what people are talking about, then I’m absolutely on the side of
the people who want to change the grading system.
On the other hand, some of the text in the article makes it sound like
they’re not going to distinguish between real percentage grades, and converted
letter-grades. The correct solution is to pick a consistent grading system. If you want to use percentages as the fundamental grading system, then use percentage-based grading – and have the teachers assign the full ranges of scores
when they’re doing a subjective grading, so that a percentage score from a test
graded by right/wrong answers, and a subjective score from an essay test are
Just bumping failing scores on subjective grading to a 50% is a lousy
solution. But it’s a less lousy solution than using 0.
But as I said, the article does a totally lousy job of talking about
this. It keeps talking about the difference in difficulty of raising a
failing grade when it’s scored as a 0 – without ever getting into the real
issue, which is the lousiness of the conversion system. For example, they
include the following from an opponent of the change:
But opponents say the larger gap between D and F exists because passing requires a minimum competency of understanding at least 60% of the material. Handing out more credit than a student has earned is grade inflation, says Ed Fields, founder of HotChalk.com, a site for teachers and parents: “I certainly don’t want to teach my children that no effort is going to get them half the way there.”
If a student really got a 0, then I’d agree with Mr. Fields. It shouldn’t be artificially boosted to 50%. On the other hand, what the story never
addresses is the fact that a student who really got 50% could be
treated by the grading system as if they got 0%.
They do briefly mention the fact that A, B, C, and D are broken
down in 10-point increments from 60 to 100, but F is separated by a much wider gap. But there are two problems with the way that they refer to that. First,
if you’ve got 4 letter grades separated by 10-point increments, they can’t cover the range from 60 to 100. There are 5 10-point
increments in that range: 60, 70, 80, 90, 100. And second, the issue isn’t really
that there’s a wide gap between 60 and 0; the fundamental problem is that the
process of converting from 5-point scores to percentages is broken because it
artificially creates that 59 point gap. The gap is an artifact of the
conversion process – and it can unfairly penalize students.
I think it would be a thoroughly unfair, foolish, even disgraceful exercise in
grade inflation to turn all Fs into 50%s – ignoring the distinction between 10%
quality work and 50% quality work. But I also think it’s an unfair, foolish
idea to round it the other way, and turn all Fs into 0%s, ignoring the distinction
between 10% quality work and 50% quality work. Why is the idea of grading everything the same way – all percentage based – so unacceptable?