Words and Shapes and Numbers and Spiders: A Web of Ideas Loosely Spun

Dear Readers,

Hello from Beacon, New York.  I’m working in a café this morning, about 30 minutes south of where we’re staying in Milton. I’m taking a much-needed break from thinking and reading and writing about elementary school math.

I’m creating a math assessment for my school based on the new “Common Core” standards. The way I’ve been working has been to read and reread the standards from Kindergarten to fifth grade, looking for overarching themes, any sort of big, inclusive ideas that could tie the disparate topics together. The way these new standards are written is kind of conducive to that, and kind of not. Inevitably, I find, what happens in these lists of mental feats “all children” are meant to be performing by X years of age is that yet another layer of translation is necessary to go from materials to teacher’s brain to child’s brain and back again. I mean, no matter how you slice it, it’s still a lot of words words words about a discipline that was evolved over many generations by humans interested in developing more efficient ways to solve real problems.

Here’s how any given day of work usually goes: I sit down at my laptop and open the grade level assessment I’m working on (right now it’s fourth) and the pdf with that grade’s standards. I review what I’ve already done and then start making “test items,” or small discrete tasks that ask a child to work with a certain skill or bit of math knowledge, such as apply the area formula to a story about measuring a floor for carpeting.  In the middle of just about every item, Doubt creeps in. Isn’t there some less abstract way to make the idea of “area” clear? How many experiences of covering surfaces with cloth or paper did I need to have before area actually made sense to me? (Answer: a lot. I have ruined a lot of paper and fabric in my life.)

As I sit here and puzzle about this, I’m just baffled why educational standards continue to be conveyed in language alone. With all that we have available now in the realm of media and visual models for complex systems, why this reliance on language? I also feel myself getting subtly brainwashed in this idea of standardization….I can’t really articulate that well, but it’s a horribly oppressive feeling.

 

I’m immensely grateful for the fact that during this last push to finish the math standards-aligned assessments, I’m not in New York City. I’m in the Hudson Valley in upstate New York. So I spend a chunk of time each week immersed in dense language disconnected from imagery, and the rest of the time in lushly green surroundings with woodchucks, chipmunks, rabbits and deer popping out of the brush from time to time. Last night on the porch I saw a huge spider crouching at the center of the most intact spider web I’d ever seen. A gnat flew into the corner of the web and the spider raced over and wrapped it up in silk, then scrambled back to the center. I blew gently on the web to see what would happen and the spider clenched its legs tighter and held on. Then I saw a cricket under one of the porch chairs, right before he boinged away. At dusk the fireflies came out.

The other night there was a magnificent lightning storm. We sat on the porch and watched the flashes of electricity touching down on the Hudson. The booms were everywhere; Charlotte startled at the biggest one, but soon thereafter was laughing and clapping her hands and saying BOOM! 

 

The driveway here is like an enormous blackboard.  Charlotte and I take the sidewalk chalk out there. She makes lines and squiggles and says, “I draw. Chalk. Nudder one.” I take the chalk and draw geometric shapes, working out some of the visual ideas I get while working on dry geometry and number standards. Early in my teaching career I read a chapter of a book about Greek mathematicians, on Pythagorus. I don’t have the chapter anymore. It was about how Greeks saw numbers as having shapes, and how triangular numbers and square numbers were seen as especially magical. The kids and I used beads to test out these ideas and I was astounded, delighted and intrigued by this connection I’d never heard of. Ben saw my drawings and made his own numerical dot drawings, aligning the dots differently, saying, “This is why the Sumerians’ system got unwieldy!”

 

I have to get back to work now.