{"id":641,"date":"2008-05-20T12:52:22","date_gmt":"2008-05-20T12:52:22","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2008\/05\/20\/stupid-grading-tricks\/"},"modified":"2008-05-20T12:52:22","modified_gmt":"2008-05-20T12:52:22","slug":"stupid-grading-tricks","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2008\/05\/20\/stupid-grading-tricks\/","title":{"rendered":"Stupid Grading Tricks"},"content":{"rendered":"

A bunch of people have been mailing me links to an article from USA today<\/a>
\nabout schools and grading systems. I think that most of the people who’ve
\nbeen 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
\nway that they present it leaves out crucial information, it’s not possible to meaningfully judge the soundness of the concept.<\/p>\n

<\/p>\n

This is very typical of the kind of rubbish we constantly see in
\nthe popular press. They’re so clueless about the math underlying what they’re
\ntalking about that they don’t even know when they’re leaving something crucial out.<\/p>\n

The article focuses on how you record failing grades in a percentage-based
\nsystem: 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.<\/p>\n

What they left out is: what is it that’s actually being recorded?<\/p>\n

When you take a test, what’s generally recorded is your actual score on
\nthe test. So if you got 74% on a test, what would be recorded is the “74”, not
\n“C”. On the other hand, many things are graded not on a percentage basis, but on
\na 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”.<\/p>\n

In the former case, changing peoples scores is thoroughly unfair. If student
\n1 failed – but failed by just a hair, with a 50%, and student 2 failed terribly
\nwith an 18% score, then student 1 should have an easier time raising his\/her grade by doing well on other work than student 2.<\/p>\n

In the latter case – that is, the case where you were given a grade
\nbased 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.<\/p>\n

Look at a simple example. Suppose you have a student who turns in five
\nwriting assignments, which are graded on a 5 point scale. The student gets
\nF, B, B, B, C. If you score those as 50, 90, 90, 90, 80, then the average is
\n80, which would convert back to a C. If you score them as
\n0, 90, 90, 90, 80, then the average is 70, which converts back to a D. <\/p>\n

It’s really not fair – because what you’ve done is created a tight cluster of
\nscores 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
\nthe way that the grades are produced, and the way that they’re recorded or averaged are very different.<\/p>\n

If that’s what people are talking about, then I’m absolutely on the side of
\nthe people who want to change the grading system. <\/p>\n

On the other hand, some of the text in the article makes it sound like
\nthey’re not going to distinguish between real percentage grades, and converted
\nletter-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
\nwhen they’re doing a subjective grading, so that a percentage score from a test
\ngraded by right\/wrong answers, and a subjective score from an essay test are
\nequivalent.<\/p>\n

Just bumping failing scores on subjective grading to a 50% is a lousy
\nsolution. But it’s a less<\/em> lousy solution than using 0.<\/p>\n

But as I said, the article does a totally lousy job of talking about
\nthis. It keeps talking about the difference in difficulty of raising a
\nfailing grade when it’s scored as a 0 – without ever getting into the real
\nissue, which is the lousiness of the conversion system. For example, they
\ninclude the following from an opponent of the change:<\/p>\n

\nBut 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.”\n<\/p><\/blockquote>\n

If a student really<\/em> 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
\naddresses is the fact that a student who really<\/em> got 50% could be
\ntreated by the grading system as if<\/em> they got 0%.<\/p>\n

They do<\/em> briefly mention the fact that A, B, C, and D are broken
\ndown 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,
\nif you’ve got 4 letter grades separated by 10-point increments, they can’t<\/em> cover the range from 60 to 100. There are 5<\/em> 10-point
\nincrements in that range: 60, 70, 80, 90, 100. And second, the issue isn’t really
\nthat there’s a wide gap between 60 and 0; the fundamental problem is that the
\nprocess of converting from 5-point scores to percentages is broken because it
\nartificially creates<\/em> that 59 point gap. The gap is an artifact of the
\nconversion process – and it can<\/em> unfairly penalize students.<\/p>\n

I think it would be a thoroughly unfair, foolish, even disgraceful exercise in
\ngrade inflation to turn all Fs into 50%s – ignoring the distinction between 10%
\nquality work and 50% quality work. But I also think it’s an unfair, foolish
\nidea to round it the other way, and turn all Fs into 0%s, ignoring the distinction
\nbetween 10% quality work and 50% quality work. Why is the idea of grading everything the same way – all percentage based – so unacceptable?<\/p>\n","protected":false},"excerpt":{"rendered":"

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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[3],"tags":[],"class_list":["post-641","post","type-post","status-publish","format-standard","hentry","category-bad-math-education"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-al","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/641","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=641"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/641\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=641"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=641"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}