Today, I heard two different children, independently of one another, use the same language to describe something. Hearing them use this descriptive language set my heart aflame in joy.  It was such a pleasure to hear them using this language — for them to capture, in similar phrases, an elegant, basic discovery about the nature of the world.

It was so normal.  It was so ordinary.  It was truly owned information. They knew what they were talking about.

It was the discovery that they were pointing out that drove me to madness.  Here’s the phrases they used.

“Mr. Watt, it looks like that x-axis motor is pulling the build platform too far to the south — along the negative side of the line, on pretty much every build line.”

And,

“Mr. Watt, it looks like the build-platform is pulling too far south into the negatives…  Either the motor or the drive train for the build platform has to be out of alignment or something.”

THESE ARE THIRD GRADERS.

And yet they have a very clear sense of the X, Y, and Z axis lines on the 3D printer.  It’s been messing up their models for the last three classes.  And, after printing a few calibration cubes, and other designs, they’re gradually discovering what I’ve known for some time. The build platform pulls ever so slightly to the south — along the negative end of the x-axis — on every rise in Z. That is to say, every time the extruder head goes up a layer in the build on the 3D printer… a shift occurs southward, toward the back wall of the Design Lab, and the object being printed is ruined after about thirty-five layers. Sometimes less.  Our fifth attempt at building, today, was ruined after a mere three layers of construction.

But Third Graders. Talking about X Y and Z axis and understanding what they mean.  Being able to analyze the movements of a robot and figure out — conceptually, and abstractly, and concretely — just what was going wrong with their designs.  Being able to look at the red,blue green lines on their SketchUp programs, and thus become able to see that objects reside in three dimensions, and that they can be described mathematically.

These are not typical Third Grader discoveries, I don’t think.  They’re barely used to the idea of number lines extending below zero, much less extending below zero, and being roughly drawn in three directions, all at right angles to one another. Set your coffee cup down (or your whiskey bottle, or whatever you happen to be drinking), and take a look at it.  It’s a physical object, right?  You could draw a line through the middle of it, through the exact center of it, top to bottom.  How many layers is it composed of?  On the one hand, it’s an infinite number of layers, mathematically.  A plane of mathematical precision has length and breadth but no depth.

As a 3-D object, though, your coffee cup (we’ll assume it only holds coffee for now), is made up of layers of atoms … and those atoms, however unbelieveably small they are, have mass. They have length, width and breadth.  And the plastic that the 3D printer, Moira, extrudes… well.  That has plenty of depth.  Enough to be visible to the naked eye on each layer.  The change is real to the kids who stand there and watch.  And they can see the X-Axis, the Y-Axis, and the Z-axis.  How many of those plastic pixels wide is your coffee cup?  How many deep?  How thick are the walls? The handle? And Can that handle be supported by its own weight as the printer builds it? Or does it need some sort of prop to hold it up? What is the right-sized prop? Where does it get put?

We’ve tested things that might throw off the printer.  Slamming doors. Running in the lab.  The air conditioner.  The most likely culprit remains the motor inside the 3D printer. Except that, we noticed, the models we’re printing from seem to have a lot of code errors in them.  Next week, we’re going to try to troubleshoot our models digitally, and empty them of some coding errors.  But truth be told, we’ve printed test cubes (think the weighted test cubes from the game, Portal) and they don’t turn out perfect — and we know that code is clean.  So we’re left with the problem that we may have a technical error inside the guts of our machine.  Are they disappointed?  YES.  Yes they are.

But part of me, as much as I hate the cause of their discovery, is thrilled.  These kids are learning to understand mathematics and geometry from a quite-different perspective than their classmates.  They understand that number lines can represent measurements from a central point.  They understand what X, Y and Z axes are, and that number lines can represent measurements from a value of  0 in three dimensions.  They understand that physical objects have measurements where width and depth are not zero, that they have to impart mass to objects.

Has every kid gotten it yet?  No. Probably not. Are they on their way?  Yes.  Yes I think they are.  Amazing how an annoying technical mistake can impart such important, and deep, abstract knowledge.

And sooner or later, these kids are going to fix the machine. Watch the learning then!

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