I've been wrestling with the question of whether or not to include a 3.5 in my 4-point rubric, but the problem is, I keep coming up with one big reason against it:
Nothing seems to motivate a student on the brink of insight like a score of "3 out of 4."
Nothing breathes life into a student's determination like that *forehead smack* they get when they realize what a careless, boneheaded, nearly unforgiveable error has kept them from achieving a perfect score on a skills quiz.
Their mistake is usually something pretty witless -- a negative sign, say, that got dropped during a hurried calculation, or an inability to decipher their own messy chicken-scratch work. Wait, that's not really fair to chickens. Their scratching is much more deliberate.
I've heard all the begging for an extra half-point, all the groveling, cajoling, sullen threats of self-punishment. And I'm not buying it. Nope, sorry. Not convinced.*
Seeing how they suffer reminds me of something I've learned through years of meditation practice -- namely, that as a teacher, it would be uncompassionate of me to take their struggle away from them.
That struggle is the sign of their genuine engagement with the mathematics. When they are suffering the loudest is the exact moment when they are most involved in the process of doing mathematics.
That heart-piercing moment of angst at their own careless error -- and the lengthy, painful, and often howling soliloquy that follows shortly thereafter -- is a critical part of their learning process. And -- speaking only for myself -- I've come to realize that I do them a disservice when I lessen the sting of that 3 out of 4 score.
How the heck can half a point make such a difference?
The best answer I can come up with is, I don't know. I only know that it does.
All I know is that for some reason, that 3 out of 4 pricks at their ego, it pokes at them, it makes them a little crazy. It jump-starts a hunger for the kind of focus and determination they will need to get themselves to the next level.
And I should probably be honest with you about something.
I like that kind of clarity in a student.
This is the point that most of my students usually never get pushed past. It's the same place where I myself -- as a once-discouraged math learner -- almost allowed myself to get left behind.
The teacher tends to move on, driven by an overburdened curriculum, while the bulk of the class trudges along behind him or her, dragging their sorry butts and their overstuffed backpacks that are filled with the kind of crumpled and torn papers that could only result from a person rolling with them in the dirt or using them as padding on a bed of nails.
For whatever reason, a 3.5 out of 4 just doesn't seem to have the same sting. In fact, it seems to take the sting out of marginal failure, reducing the urgency to give that last little oomph of a push that gets a person to the next level.
I think that, in a weird way, that little affront is kind of good for them. It has nutrition in it -- nutrition that they need.
* Now, if a student were to threaten to smash her iPhone to smithereens, that is a mental health threat that I would take very seriously. But this is basically the adolescent equivalent of threatening to hold their breath until they pass out.