Week 3: Playing the Grid with Courage, Mischief, and Joy

 I love the quote from Gerofsky & Ostertag (2018) I used for the title of this reflection. I am not certain whether I teach with courage, but I occasionally try to when courage is warranted. More often than not, I am guided by mischief and joy. Please keep that in mind as you wonder why I took the direction I did with this assignment.

Gerofsky & Ostertag (2018) pose metaphors, ask big questions, and provide examples of experiences with student teachers relating to the notion that perhaps it might be important in these days of climate change and uncertain futures to consider approaches in teaching that move beyond the static Euro-centric fetish with grids and recognize the limitations of our power to predict, control, and own the world. 

Education is filled with grids, from schedules, to delineated subjects, to mark books, to classroom layout. Gerofsky & Ostertag wonder whether it might be helpful to acknowledge the benefits of the grid and to also value "playful, artistic approach(es)" to schooling that allow us to dance and parkour within the boundaries of the grid in creative, flexible, and unexpected ways. By doing so, teachers might help students practice navigating uncertainty and responding to the human and non-human world with joy and creativity.

While I was drawing and digesting the article by Gerofsky & Ostertag (2018), I must admit that I was not thinking of math. I am a generalist elementary teacher by trade and very much used to letting activities bloom in a wide space. Schedules and subject areas are always blurry, soft, and malleable to the likes of me. 

I'm going to start by describing my experience with drawing. I launched into the activity a few days after initially reading the directions. My mind recalled that we should sketch living and human-made things. I started with human-made things, going for the types of things that interest me: bread and pastry. I make my own bread from a sourdough culture that is now over two years old. I'm fascinated by the structure I provide the loaf and the gasses produced by the little critters that make it puff up and taste good. I'm constantly trying to use heavier and sharper grains, attempting to give it enough of a workout, enough time, and the perfect temperature to create a loaf with a pleasing shape (balance of height and width) and beautiful pockets of bread breath. I realize that bread walks the line between human made and natural, but that's what I like about it.

I decided that I wanted to find a living (or at least once alive) thing that reminded me of bread and chose a piece of coral that my parents brought back from their travels. I was curious to really study and compare the structure of the bread with the structure of the coral. What I found was that the little holes all over the coral are more perfectly round than the pockets of breath captured in the gluten of my bread. They are formed by little creatures called polyps.  The coral is a like a massive housing structure that thousands and thousands of polyps create by secreting calcium carbonate. It hardens as it forms around them. By contrast, the pockets of breath in bread are delicate and elastic. I have noticed generally that these are like balloons squeezed flatter the deeper into the bread you go. They also seemed shaped by the pattern of my kneading and rolling of the final loaf. The coral was obviously part of a much larger structure, with hints of what it originally looked like. I noticed these finger-like folds in the piece I have, perhaps providing more surface area for the creatures that inhabited it or space for ocean water to move all throughout it. 

The next human-made structure I decided to feature is the beautiful, roughly triangular, and delicious sfogliatella pasty. I bought this one from my local Italian bakery and have yet to eat it. I do not know how the pastry chefs shape the dough, although I know that all of the crispy layers are formed by very thin dough and that they can be unravelled a little like a ribbon. In fact, it is almost exactly like a roll of thin ribbon with the centre pushed out to create a cone-shape. My hypothesis is that the cone is then filled with ricotta and candied citrus rind and flattened.  Personally, I think that they are the most pleasing and pretty pasty you can find. It was difficult sketching without nibbling, I can assure you.

I decided that the sfogliatella reminded me of a seashell. The one I chose is from a local beach. The lines of this particular shell run into two directions: parallel, gently curving lines from hinge to mouth and growing semicircular lines from side to side. The latter curving lines are growth lines and form over time. The former hinge-to-mouth lines are not related by growth, but emerge as part of the pattern of the growing shell. I'm not sure why. Even though they resemble one another on the surface, the formation of the sfogliatella and shell are not deeply analogous. 

I realize there was no requirement to find living and human-made shapes that reminded me of one another, but I have a science background and I like to write poetry. I find that testing analogies is a way of really wrapping my head around a subject or idea. If I can find a good analogy, I feel like I have insight or even maybe discovered something hitherto unnoticed about it. I did some work on this in the summer: using analogous thinking to help in mathematical problem solving. "This reminds me of..." helps to make sense of shapes, graphs, word problems...you name it. Asking "what does this remind me of" might be a useful way for kids to first start tackling problems when they are stuck.

At first glance, the subjects I chose do not cry "lines and angles". They are very organic, all of them. No human-made grids with 90 degree angles and straight lines. Lots of curves. I like curves, don't you? Winding trails, soft folds of a skirt, tree rings, Hobbit houses. Curves show up often in the natural world, but perhaps they are hard for us Westerners to engineer? Perhaps we like our paintings to sit flat and our doors to close tightly. Or perhaps curvy load-bearing walls are too expensive. The geometry of curves is more complex than that of straight lines meeting at angles, for sure. It is also easier to to manufacture furniture and appliances if you know exactly what lines and angles to expect.

Dancing Euclidean Proofs is also full of curves. Even though arms and legs are lines and position themselves by anchoring to a point, they come alive in curves. As soon as you swing a leg or an arm, you make an arc. I have been exploring contemporary dance lately (as a beginner) and I often have to flex and bend in ways that seem angular and stark compared to classical ballet. However, the fluid movement still happens in curves. Many of the turns have a logic dictated by the unfolding and straightening of my legs. My arms flow in relation, although hold a position that keeps me from over-spinning and losing my balance. 

Anyway, I continue to enjoy our explorations. I am aware that I owe two more sketches. I'll have them soon :)