I took some time and sat by the green space outside my classroom and then some time by our school’s back parking lot. During this time, I noticed the trees, bushes, evergreens, and the design and layout of the crafted or architecture designs by those that were man-made.
I chose to use simple lined paper in my notebook and a black pen. As I was sketching, I noticed the flow of my lines and how much I required to use the lines on the paper. Here are some points that stood out to me as I completed my drawings.
Curves and Lines
The items that were natural (bushes, branches, leaves) all had curves; the flow of my wrist and pen constantly changed directions, or was jagged. Rarely did I follow the blue lines on my paper when I was drawing living or aspects that were natural to the environment.
The thinner the branches (or thinner my drawing lines) the more dense they became
The distance between the splits became smaller and smaller
I heavily relied on the blue lines of the paper when I drew items that were human-made or placed by humans.
The fencing was parallel to the ground, the lines were parallel and sequential
The lamp post was a perfecting perpendicular to the ground
The rocks are natural but shaped and used to create levels. I relied on the blue lines for guide
The fence was straight and even
Parking lot lines were perpendicular to the curb.
Angles
I was captivated by the bare branches and the forms they took to stem from the main trunk
Angles were larger towards branches lower down, they became smaller and smaller as they moved up the main trunk
There were various angles, never really two of the same, each degree was unique
Even items like pine needles or thorns can branch off a stem repeatedly, but they are not (or rarely) in perfect right angles.
Items human-made were often in right angles (90O) or straight angles. For example: Fencing
Application to students and the classroom
Taking a walk around the school campus would be a great practice for students to apply their understanding. Because it is based on observations, there are an infinite number of possibilities. For example, in Grade 6, we discuss types of angles, angles on a point, complementary and supplementary angles, etc. This would be a great practical skill for students to measure angles or even estimate. Perhaps not necessarily knowing the precise value, but seeing trends, and patterns.
When I introduce lines and angles to my Grade 6s, we often use bodies and sounds to create angles. For example, we channel our Grade 6 Spanish teacher who loves to say in a high pitch “aww, so cute!” when we describe acute angles. We widen our arms like sumo wrestlers and shout out in a low tone “obtuse” to show wider angles. We arch our backs or “stretch” backwards to emphasize “reflex”, going past the standard “straight angle”.
As a class, we also ask: which angles are easier to create or model? What limitations do we have on our bodies to make certain angles more difficult? We note the center point and how perspective can change, for example, whether an angle is acute or reflex, and how communicating this is important when conveying understanding. For my students, they tend to remember these angles because of sounds and actions in combination, because when they created the angles with their bodies, they had a certain sensation or multi-sensory experience.
I am blown away by your sketching ability—beautiful drawing with great geometry analysis. I see that this activity could provide our students to get a break from our "grided classroom" ( Gerofsky & Ostertag, 2018) for connecting math outdoors. This type of task also serves as a hook to learn more about the concept of geometry exploration, and it can significantly contribute to impactful learning when we provide students with the environment and opportunities to experience outdoor education. When meaningful opportunities are provided to learners with well-designed activities, appropriate tools, and teachers' support, students can explore math concepts like geometry meaningfully.
ReplyDeleteGerofsky, S. & Ostertag, J. (2018). Dancing teachers into being with a garden, or how to swing or parkour the strict grid of schooling. Australian Journal of Environmental Education, 34/2, 172-188.
Thanks for your engagement, Pushpa! I completed this activity before I read my article and I was shocked at their mention comparing the shapes in nature and the grids formed by man. It is amazing how much we can notice and observe when we take the time... As cited in Doolittle (2018) article, '[t]o paraphrase Leopold Kronecker, the Creator gave us shapes; straight lines are the work of man" (p. 104).
ReplyDeleteThank you Christina for the beautiful drawings and reflections. Great observations on how you used the lines in your notebook. It's wonderful how you already apply embodied learning when teaching angles to your grade 6's. I agree that a walk outside provides students an opportunity to apply their understanding further. As Pushpa said, it's indeed a break from our grid-like classroom. I also really like how you include sound as part of the multi-sensory experience!
ReplyDeleteChristina, I enjoyed this quiet moment you managed to capture with your drawing!!
ReplyDeleteI sincerely appreciated the reflection you provided with how you noticed that your drawing changed with what you were capturing!
Secondly: the way you were able to incorporate geometric terminology into the description of your drawing gave me ɑ pleasant feeling inside and contributed to the peaceful feeling I had while looking at and reading this activity post!
I find it interesting that when I was reading the directions for this activity, I thought of the same thing that you suggested; by inviting students to find shapes in the natural elements they find outside, and then in the man made structures also, and whether there would be more or less in either of the elements (man made or natural)