”Philosophy is written in this grand book – I mean the universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth.– Galileo, 1611
A humanities slant to a traditional math subject…
“Mama, I REALLY love geometry.”
Since we started the block at the beginning of the month, she has been drawing and practicing her lessons even in her spare time.
“What do you love about it?” I ask.
“I love the straight lines. I love how precise and exact it is. You know, like baking. I don’t like cooking when you add a pinch or splash. I like measuring.”
She tells me this as I watch her swing her compass to make another circle or glide her pencil across the straightedge of her triangle. I don’t notice her words as much as I notice her body language. She is relaxed, almost relieved at having to do this task. There is order and certainty in a straight line or a circle with the flick of the wrist.
GEOMETRY. The root of the word is “earth measure.” Measuring the earth can be a poetic endeavor even if it is exact and precise.
Our geometry block was planned for a little later but I shifted gears and introduced it this month. Unfortunately, compasses are hard to find in our little town so it was a mad dash for parents and kids to try to find a compass, let alone an open store to buy one.
Another challenge was teaching a very physical and coordinated activity over Zoom with poor Internet. It’s easier to teach this when I am sitting next to the child. It can be frustrating to follow along with my exact instructions and when the audio cuts out or the screen freezes.
So why am I introducing this now? Why not wait until I have the students all together back in our little classroom?
Because they need this block right now. Three weeks of being at home with no end date in sight means there is a lot things that are up in the air. There is a lot of information and life just isn’t as black and white as we would like. I often answer questions with: “Vamos a ver.”
Geometry, on the other hand, at least the way we are diving into it, is known. We are using straight edges, compasses, and triangles. There is no ambiguity when I say “draw a circle with a 5cm radius.” It’s either a circle with a 5cm radius or it isn’t.
But still, it’s not just about angles and proofs. We spend most of the time building and playing with the forms to create patterns. We use these patterns to match what we find in nature.
As my husband watched me help #4 with one of the geometric constructions, he remarked that he would have enjoyed geometry more had he learned it the way she is learning it.
The first geometric construction I introduced was the 6-division of a circle and “the seed of life.” But first, I showed them a picture from Da Vinci’s Journal:
And then they made their own:
The seed of life is the pattern of creation. When we eventually look at embryology in the high school years, they will see these patterns again in the beginning of life.
Once she did the seed, as you can see, she continued to create the flower of life.
The circle itself is a powerful symbol. We work at inscribing shapes within the circle: the triangle, the square, the hexagon, the pentagon, etc. The children start to see the power of the circle to house all the shapes. I tell them the story of “Giotto and The Perfect Circle” and we try to make the perfect circle freehand like Giotto did.
The constructions get increasiningly difficult and need practice. Without the precision of measurement, the pattern won’t “look” right or by the end of the steps, it falls apart. A care in measuring that “90 degree angle” or that “5cm radius” is required. Patience is required to achieve on paper what nature and the universe itself does effortlessly.
Some get it on the first try and others need the instructions repeated. The onus is on me to communicate each step precisely and with clarity. We may have different definitions of a “point of intersection” or “dropping a vertical line” or even “centre.”
“Which centre?” I was asked. I stop to weigh my words because I assumed everyone understands that there is only once centre in a circle but then I realize that we have twelve points that could possibly be the center of the next circle:
It is a practice in communication, verbally and visually. How do I show what I mean without assuming that everyone knows what I mean? Am I clear? I also have to do this in Spanish and English.
I am grateful when they say “I don’t understand” or “Can you repeat that part please?” It forces me to take a step back and make things simpler. It is frustrating for them but it’s a test of perseverance and discipline for all of us. There is nothing more satisfying when they finally understand that particular “arc” that is supposed to cross the circle exactly where the next point should be.
I tell my group that we are learning the language of the universe as Galileo so aptly said. (They also had to write that quote in English and in Spanish.)
We also have gone back to basics to understanding what these terms mean. We take for granted that our kids know what this means. A point is a coordinate – a position without size. Even when I make a pencil point on the page, it has dimension.
How many straight lines can go through two points?
Only one. If you want to curve it, there are many ways to get there. But in this three dimensional reality, there is only one straight line that can be determined by two points.
This is a lesson for me too. There is one straight line to get from today to a day when we can all gather again, when I can go visit my parents, when there is no curfew or certain days we can drive. That line for me consists of moving through each moment doing the next right thing for me, my family, and the kids I show up for. Maybe I can’t see that next point but I know it’s there. It exists. I just have to choose how to walk this line until I can see it.
I am grateful for being to walk this line with these amazing kids.