Week 3 Activity

This week in the Northern Quebec, temperature is on average around -40°C and the sun set around 3h30 (which is before I get home). Unfortunately, I was not able to draw outside, but there is a peaceful scenery I walk to so often I can recall a very detail image of the scenery.



Here is my drawing of it:



I noticed that human-made things are smooth; the road adjacent to the lake, the cover of my book or even the pages inside, the surface of the power line or the pylons, even my dog’s leash has very little texture or bumps to it. The lake in question is in the middle of the taiga, but a road was built nearby to facilitate the access of four-wheelers. Last year, workers made the road wider and stripped a big part of the vegetation on the sides of it. They even removed the big rocks and moved them to the side, which now creates holes in the road. I bet it drove them crazy to have to leave such an unsmooth irregularity on the road!

On the opposite, living things are more chaotic. The best example is the spruces. The spruces grow branches in fractal shape. They are not as furnished as they would be somewhere where the summer are longer. You can easily see through them. Some branches are more furnished than others, and some spruces are more furnished than others. Lichen grows everywhere in fractal shape as well, and in some places, it organizes itself in some chaotic arrangement of red, black, and white lichen. The rocks near the bed of the lake are arranged in a chaotic way, which you can hear while you walk on the lakebed. My dogs’ fur patterns are far from symmetrical, and so much more. But to me, this chaos is much more beautiful than the smoothness of human-made things. In Off the Grid, Doolittle (2018) stipulates that 2-dimensional grids could not represent this chaos well, thus the need to widen our perspectives to what Doolittle calls complexity theory and chaotic control. Which is a branch of geometry studying not just static shapes, but their dynamic and relationships with their environment.



How drawing can help my students:

Jefferys, C. W. (1942). Eastern Snowshoes. The Picture Gallery of Canadian History Volume 1, p.27 (Assisted by T.W. McLean)


Some shapes can be translated in Innu-aimun and Naskapi. Innu and Naskapi used to talk about shape, as we can see they were building them for tools. For example, the word kashkatishiu means something is square. The word, kashkatishiu is a verb. My students’ language is based on verbs. Observing and drawing can help my students learn about lines and angles by transforming those nouns into actions. In my classroom, most of the geometry has to be translated into actions. Parallel lines become ‘lines that do not meet each other’, right angles come with the hand gesture forming a T, a distance or a length becomes ‘going from here to here’, etc. Like Samuel mentioned in Dancing Euclidean Proof, drawing a landscape could them transform the math in their head into something more meaningful to them (Gerofsky, 2019). It could help them translate the noun-based odd language of mathematics into something they are more familiar with. Thus, creating metaphors they can build mathematics understanding upon. Other than developing deeper meaning, drawing the environment is a culturally relevant activity for my students. I can ask my students to use the environment to draw geometric concepts I teach, but also to widen their idea of geometry to include the shapes they see around them and constitute a part of their identity.



References

Doolittle, E. (2018). Off the grid. In Gerofsky, S. (Ed.), Geometries of liberation. Palgrave. https://doi.org/10.1007/978-3-319-72523-9_7

Gerofsky, S. (2019, April 12th). Dancing Euclidean proofs. [Video]. Vimeo. https://vimeo.com/330107264