Tuesday, November 20, 2007
Here’s the first in a miniseries about the folly of awarding a grade of zero for late work or work not turned in.
Part 1: The Math of Zero in a Percentage Scale
I was talking to a colleague recently about how although there is no one “right” way to grade, there certainly are justifiable and unjustifiable grades.
Then I said, innocently as I could manage,”…and giving kids zeros as a penalty for late work or for work not turned in is a perfect example of unjustifiable grading.”
He immediately went on the attack. “I’ve heard that the school board is about to require us to not give zeros! That’s outrageous! No work, no grade! We have to teach kids to be responsible!”
I didn’t know which of the four positions he took to reply to first, so I chose the easiest.
“Nope,” I said, “the school board is not about to require the high school to quit giving zeros. We’re in a conversational mode, and I hope people are willing to think about standards-based grading and talk it over.”
“However,” I followed up with, “have you given any thought to the math of zero?”
“What do you mean, the math? Zero is zero. Nothing is nothing. No work, zip. End of story.”
Realizing that I had no graceful exit strategy from this conversation if my colleague proved resistant to my charm and logic, I set up a problem for him to analyze.
“Think about this,” I suggested. “Everyone is familiar with a 4.0 GPA scale, right? What if the F (a zero, right?), in a 4.0 scale had the same weight as a zero in a scale of 0-100, the percent scale we use almost universally for grading?”
“What are you getting at?” he asked.
“Just this,” I said. “In a 4.0 scale, A=4, B=3, C=2, D=1, and F=0. The difference between a D and an F is just one point. On the percentage scale, the difference between a D and a zero is 60 points. Does that seem proportionate to you?”
“No,” he said, as the math began to register. “On a 4.0 scale, if it were equivalent to a percentage scale, the F would be, what, negative 6?!”
“That’s in the ball park,” I said. “Isn’t it amazing that we teachers don’t ask these kinds of questions more often when we talk about grading?”
“Yeah,” he said thoughtfully.
“Look,” I said, “here’s a two-page article from the Phi Beta Kappan entitled “The Case Against Zero” written by Doug Reeves, an international education consultant from in Colorado. He explains it far more eloquently than I can. Check it out.”
The following week, I asked him if he liked the article. “Man,” he said, “I am DONE with zeros!”
“Pass it on,” I said, “because there’s more…”
(Next up: Why Zero Isn’t A Grade At All)
- Lisa said…
- Okay, I am definitely sneaking this in to our Monday Meeting Madness discussion at school!
- Clix said…
- What about a student who does the assignment and flubs it – say, earns a 40? Have they earned the same grade as someone who turned in complete gibberish?Secondly, could this not be resolved equally well by going to a 4.0 scale instead of percentiles? I think a lot of it is a difference in understanding what “zero” means.
- roller coaster teacher said…
- Our district have gone DuFours and PLC on us (lame wording, but does it make sense? Rick and Becky DuFours and their professional learning communities) for the past year or so. Anyway, at one training, Mr. DuFour explained the “math of zero” just like you did here, and a massive light bulb turned on in my head.I definitely vote for switching to 4.0 grading scale/system.
- Hugh O’Donnell said…
- Good luck, Lisa! Buy-in is essential (not 100%, but “significant”).Clix, I think you answered your own question. What’s the difference between a 40 and a genuine zero? Treat them both like Fs, which is what a 50-60 would be in the percentile scale.Fortunately, these hypothetical objections rarely pop up in real life. But no system is bullet-proof. ;)Both kids need the opportunity for remediation if they demonstrate the willingness to engage in further learning, and the inclusion of their more recent, and, we hope, higher score in their grade.RCT, glad to see you here!The DuFours are on track. Our district went with the Doug Reeves program because we were presented the opportunity to get the whole enchilada free, courtesy of our Educational Service District.
We’ve also been heavily influenced by Stiggins on classroom assessment, and O’Connor on standards-based grading, and Marzano’s work in several areas, including the “nine categories of instructional strategies.”
- ms-teacher said…
- Thanks for this. My assumption then is if I assign 20 points to an assignment, then the lowest score a student could receive is 10 points. This makes sense to me. However, what do you did with a student who is rarely, if ever, in class and so misses out on most of the instruction and no learning takes place?
- Hugh O’Donnell said…
- Ms-Teacher, if you have plenty of INCs in your gradebook that were never made up, and the attendance is really poor, you have enough evidence to flunk the kid without worrying about the math. An F is an F.Your question really highlights why we shouldn’t just use numbers to assess learning. We have to make authentic judgments backed by sufficient valid and reliable evidence.Do what works for most of the kids. The exceptions to the rule will work out intuitively, i.e., with common sense.
- The Science Goddess said…
- I think we also need to be forgiving of ourselves as professionals—and remember that we are humans evaluating other humans. Subjectivity is a fact of the matter. The percentage system gives a false sense of security that we’re being wholly objective about achievement.