Friday, December 07, 2007

Apples, oranges, and zeros

This isn't from Hugh's original post, but from his response to one of the comments.

Your insistence that a zero is valid in a percentile frame of reference is to say that you can add an orange to a collection of apples, and still arrive at an apple that is a pure indicator of the collection of apples. ("Orange" being a zero given for late or missing work.) How do you do that?

Come to the grocery store with me...

In the produce section of most grocery stores, you can buy apples by the bag. Let's say you see a bag of apples that are particularly nice. They don't have any that are puny or look green and you don't spot any bruises. So you pick up that bag and as you do, you notice that it seems kind of loose. You pick up another bag and it is heavier! Factory error, naughty shopper, whatever the reason, the first bag is short an apple. Doesn't that matter?!

Zeros are not oranges. They're apples that are missing.

if they actually do score a zero on a test (not because they are absent) but because their answers are not correct, or they don’t provide any answers at all, that should not be represented in the mean score over the term?

With regard to your hypothetical case of the student actually scoring zero…you cannot escape the fact that the mean is ruined by extreme scores. You might consider using the median average, which is less affected by outliers.

In this case, the apple isn't missing. It's just... squishy. The question: how much does that one squishy apple affect the value of the bag?

My answer: a stinkin' LOT!

About five percent of my undergrad and graduate profs practiced their craft in the same way, and they were revered by their students. The others “profs” who practiced “real world” grading and lectured to sleeping students were merely tolerated as a means to an end…the sheepskin.

Well... YEAH! I mean, I'd love it too if I could focus just on doing a bang-up job on my lesson planning, grade nothing, and earn merit pay for being a wonderful teacher because all I submit are my wonderful lesson plans!

But that's not how it works. Students who don't turn in major assignments have big gaping holes in their overall grade that reflect the big gaping holes in their proof of competence. Maybe they understand the material - but I have no proof.

The more I read about this issue and ponder it, the more I am in favor of giving a zero when there is zero work done, but allowing students as much opportunity as they need to demonstrate competence, until the decision is no longer mine to make after the term ends.


Hugh O'Donnell said...

Clix, I appreciate your participation in this discussion. None of what I've said about grading (including the use of zeros) is meant to skewer any teacher out there who is trying get the job done, and I appreciate your willingness to give the matter your attention and more than a declaration of disagreement (as did the blogger to whom I responded about the apples and oranges).

One of the shortcomings of blogging about the effect of zeros on grades is that the bigger picture is incomplete, and most teachers (including myself not too long ago) are left wondering, "What the heck do we do without THAT option?"

There' s more to the grading story, and I didn't give you much for a reply today, because I hadn't realized the amount of time and energy you'd invested in thinking about what to do. My apologies for that.

BTW, I never meant to convey the idea that, hypothetically, the student who misses half their summative assessments should pass the course. Your professional judgment correctly determines that that would be ridiculous, and it would be, whether you jotted down "Inc" or zero to indicate the absence of evidence.

Don't believe the claim that grades have to be 100% "objective." Grades need to be the result of professional judgment backed by sufficient evidence.

My objection to zeros is not meant to contradict genuine professional judgment, but to highlight the fact that zeros are, in general, disproportionately damaging to grades.

If you allow students the opportunity to make up work, to raise their scores if they present evidence of additional preparation, and put the emphasis on learning rather than task completion (i.e., looking for other evidence of learning, as you mentioned in your further thoughts below), then, I suppose, a zero would be just as useful as an incomplete, as long as you don't treat it as an actual value that belongs in a mean average.

Students who see no hope of improving their grade (the zero) turn off to learning. If they see an opportunity for success, they're more likely to engage.

Successful students are students who believe they can be successful, wouldn't you agree?

Thanks again for taking the time to put your thoughts "on paper."

Clix said...


Thank you so much for responding in such depth! It's very kind of you, and the conversation has been absolutely fascinating all around. Even from rightwingprof, who, as you mentioned, is a bit more... set. I dunno, maybe I'm pudding and he's custard? *g*

It's so nice to be challenged and made to think ... but without having to respond right away! Challenges from my students are ever so much more stressful, because naturally I don't want to just let things slide, but even though (I think) I do a fairly good job of responding firmly and fairly (most times), you know, there's always an every now and then where later on I think, "yanno, I really should've XYZ instead of ABC." And if I'd had time to THINK about it, maybe I would've. Ah well.

So. You're right - to an extent - that grades don't have to be 100% objective. Truth of the matter is, I think we both agree that no matter how hard we try, they won't ever be! The problem I face is... well, to put it bluntly, parents are allowed to yell and fuss and I'm not. And I'm not entirely convinced that my current administration has got my back. When dealing with a Monstrous Parent, I want to be able to wield the Illusion of Objectivity as a backup, in case their Logic Refusal Powers are too much for my Piercing Evidence.

In addition, what I have experienced with zeros goes the opposite way from what you describe. When I point out to a student that the work they HAVE turned in has been good, and I show them how much replacing a zero with even a barely-passing grade helps their overall average, something seems to click inside that thick skull. Look: You CAN do this. (See? You did it before, didn't you?) And also look: it DOES matter.

In fairness? This is going to take some struggling-through for me. My assessments are fairly well aligned with the standards, but I don't do a good job of showing the connection (or how it affects them) to the students. Maybe when I am better able to inspire students to learn in other ways, I can erase "Replacing A Zero" from my spellbook. :D

Hugh O'Donnell said...

Clix, you're using zeros constructively, for the same ends I'd use an "INC."

I enjoyed your comment above, "yanno, I really should've XYZ instead of ABC." Wouldn't we all like to be perfect? I teach my students that "the only people who don't make mistakes are people who never DO anything." (We're all walking arguments for formative assessment.)

The whole grading game is truly a mess and my mission is to mitigate the destruction of student motivation. I would truly like to see a report card become a strip (the one for your child, Mrs. Jones) out of a teachers standards-based gradebook. Then there's no question about what's what.

It seems that all the arguments are about the math! But ironically, that's what parents want, the number or symbol that tells all. The real irony is that it doesn't tell much at all. Parents complain about grading, but won't move away from it. What's a poor teacher to do? ;)

Glad we had a chance to talk. I really don't think we're that far apart in our views.

Hugh aka Repairman

Clix said...

Hee! :D

I have a similar statement to students - "the only people who don't have to do things they don't want to do are people who are already dead."

Hugh O'Donnell said...

I'm gonna steal that one!

Seriously, I also teach kids that the most successful people are those who make a HABIT out of doing the things most other people don't want to excel and be accountable.

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