September 17 Exit Slip

 My family (me, my wife, and three children) have a practice of connecting with my and my wife's parents each weekend, usually through a FaceTime or Zoom "call" (they all live far away in the U.S.). In describing for them this past weekend my experience of being in the Orchard Garden for my math cohort-based education courses, I have been amused by their reactions. Some questions are: "How can you focus outside?", "Why be in a garden to learn about math education? - math is about numbers, not plants", and even "You're spending all this money to go sit in a garden" (as if nothing else could be happening there but sitting).

So it is most instructive for me to reflect on our September 17 class in the Orchard Garden in light of these questions. What are we doing there? What lessons is the garden teaching us that will be useful as math educators?

The first part of our class involved being in a "sit spot." In this exercise, we were asked to find a place that "calls to us" in some way and to sit quietly there for a length of time as we noticed the world around us. We were asked to sketch two things that were alive and growing and two which were human-made, with attention to the lines and angles of what we were observing. There were a number of ways in which this activity informed my own thinking about teaching - and teaching math in particular.

First, what a pleasure it was simply to "settle in" somewhere quietly in a natural setting. Math people are perhaps known for being analytical sorts. The development of the ability to observe and the chance to get into an observational state was helpful. In math education, we want our students to cultivate the ability to make observations of what they notice as their mathematical knowledge increases; the "sit spot" activity is perhaps way to help develop that skill.

Second, there was for me a fascination in thinking about how both the natural and man-made objects I observed reflected mathematical concepts. As I was sketching my objects, I couldn't help but wonder: what mathematical concept might be illustrated in these objects? Obviously the man-made objects brought to mind the mathematical use of angles and tools and precision equipment and fractions and so on. But I began to see math in the natural world as well. For example, the arc of the grape vines I was observing formed what was essentially a beautiful paraboloid (I enjoyed looking directly up to the high point of the paraboloid from underneath it). There was also a lovely symmetry in the shape of a grape leaf. Math is found everywhere.

Third, I thought about how moving myself to a new place in the garden meant I was able to see things from a different perspective. This is another skill I hope to cultivate in my math students. 

Fourth, a comment was made that has stuck with me: we ourselves are part of the natural world. When we observe man-made objects (and math often seems to be taught with reference to such "real-life" applications), with all their precision and right angles and structure, how much more interesting and satisfying these objects are when situated in a natural setting. There is a sense in which the "natural" and "man-made" worlds are meant to complement one another. I'm not sure I had ever thought of things in that way before and I was grateful for the insight. How is the beauty of the math we study and teach enhanced by simultaneously considering the natural world around us.

After the "sit spot" we had a time of discussion about being a reflective teacher (one who is wholehearted and openminded and responsible). The discussion itself contained a number of helpful insights for me, but what has stuck with me is how it felt to have that discussion in the setting of the Orchard Garden. In the indoor classroom, I tend to feel "constrained" and "uptight" a lot. I find having genuine conversation and penetrating discussion to be challenging. Something about being in the garden impacted me differently: in the open outdoor space with my senses engaged by the natural surroundings, I felt myself also open up in my mind and heart. I seemed better able to listen and more willing to contribute. Perhaps "garden-based learning" sometimes just means that we simply learn better because we are there in the garden. It made me want to get my own blackboard and take my future high school math classes outside! (My daughter told me that means we should move somewhere like southern California, where the weather would allow for such instruction on a regular basis!)