Week 9 - Critical Reflection - Mathematics & traditional and contemporary practices of making and doing

    Over the past several days I found I was not only reflecting and making connections between the introduction, viewings, activities, and readings for this week but also thinking back over the experiences we have had over the whole course. Themes that emerged from my stops/pauses could be connected backward through the course.

Intergenerational Teaching and Learning

    The idea of intergenerational teaching first came up to me this week in the reading “’The spirit of the medicine will lead us back’: How Avis O’Brien is guiding Elders to weave their first cedar hats”, an article by APTN, and has been a theme over the course for me. So many of the activities we have undertaken have given me the option to engage with crafts that I have previously explored and have been taught to me by mom or grandmother (or both), specifically knitting and quilting. Even in the first week, I went to my little garden which connects me to my mom and my dad as gardening and growing food was (and is) something we do as a family. I explored art through quilting, learned about some of the mathematics of knitting, learned about mathematical ways of seeing and describing patterns in quilts, and realized that I had previously knit a mathematical object! When we were braiding this week, I thought of how my dad gave my sister and I string and a pile of harvested onions and asked us to figure out how to braid the onion tops together with string for support so the onions could be hung for storage.

Throw-back to Week 4 -
bringing in quilting to mathematical art endeavors

    Often we think of intergenerational learning going in one direction, from older generations to younger generations. One of the spinners in the film “The art and geometry of rope making and yarn plying” noted that when she spins, she feels connected to all the spinners that came before her. However, in the APTN article, it is noted that weaving (with cedar, specifically) has been a cultural practice that “went to sleep” due to colonial laws imposed on Indigenous peoples and the people who are now Elders did not have experience learning and practicing weaving. Now it is people in younger generations, such as Avis O’Brien, who have learned to weave and are bringing the cultural practice to the Elders.  For me, this connected to being able to virtually meet and learn from Evelyn Vanderhoop, a Haida weaver and artist, in my elective course HGSE 371 last summer. Even though she comes from a line of weavers, having learned from her grandmother and mother, she also travels to museums where woven pieces that were taken from the Haida are located to study the designs and patterns that may not have been seen in Haida Gwaii in recent times and brings the designs back to her woven robes, reintroducing them to the Haida of all generations.  (Evelyn has a really wonderful Youtube channel where she posts videos of her simultaneously weaving and telling stories or teaching history from a Haida perspective – check it out here).

So, how do I relate this to the teaching of mathematics and bringing “ancient and ancestral technologies” into mathematics classes? By giving our students the opportunity to play with and explore traditional ways of making things while exploring the mathematics, we are connecting them to generations before and an aspect of being human and providing for ourselves. Susan notes in this week’s introduction, by making we can “really appreciate how lovely and skilled these technologies are, and how important they have been for human thriving throughout the ages.” By making sure we explore ancient techonlogies that are common across cultures but also from individual cultures (especially those represented in our students), perhaps we might give students an avenue to re-awaken some cultural practices and knowledge in their own families. I imagine students going home and talking about their learning and families perhaps taking time to explore connections to family history of making. The fact that we explore mathematics in it might be a side benefit to connecting to culture.

Question: What do you find are the benefits of exploring ancient technologies through mathematics classes? What about modern technologies?

(Aside: I have been struggling throughout the course with the privilege that is embodied in some of the activities and this came up again this week. It almost seems contradictory to speak of privilege in relation to making culture, especially when it is based in ancient technologies. Usually I am connecting the concept of privilege to time. This week it came up for me in the video Vested Interest. Following Sharon Kallis through the process of making her vest, right from visiting the farm to collect fleece to adding pockets and the final stitches, showed what a time-consuming process it is. Kallis has this time because she is being paid as an artist-in-residence. Maybe this vest project is an extreme example of creating without being consumers first, but I think of single parents who are working multiple jobs to feed and cloth multiple children and maybe also be taking care of aging parents or other family members. It’s nice to say we need to connect to the land in order to take care of the land, but in a system that oppresses large groups of the population in many different ways, who are the people that can embrace the way of being of foraging and upcycling and creating and making or even writing mathematical dances, art, or poetry? I tied this back to the classroom because it is here where we can provide that time to connect with the land and connect with traditional practices of making and technology and give students those experiences as a way to decolonize education and a small part of society.)

Mathematics as Inherent to and Inseparable from Artistic Endeavours

The idea of mathematics being inherent to and inseparable from various human endeavours really came to the forefront to me in the week about dance and I really connected with Karl Schaffer’s idea of the third space where math and dance combine in a way that each supports the other and where it is hard to distinguish between the two ways of knowing. I can see this in visual art, paper folding and sculpture, music, knitting, quilting, drawing, and everything with which we experimented over the course. Last week Joy and I had an exchange of how the Indigenous Math Network has Kaagan Jaad (Haida Supernatural Mouse Woman) as a symbol for the network and the connections Billy Yovanovich, a Haida carver and artist, makes the connection of how mathematics is like Mouse Woman, sneaking in to help us out. I see how mathematics is inside all of the activities we have done, helping us out but also how the craft/art/activity helps, in turn, in supporting our mathematical understanding. They work together in an interwoven way that squishes both together so they can’t be separated.

Kaagan Jaad as photographed for
Out of Concealment: Female Supernatural Beings of Haida Gwaii
 by Terri-Lynn Williams-Davidson
(Image from: https://thelasource.com/en/2019/10/21/out-of-concealment-the-interconnectedness-of-femininity-the-supernatural-and-the-environment/)

I, along with Joy, was in a meeting with the Lower Mainland Math Contacts yesterday and we got into an interesting discussion about Indigenous ways of knowing and Indigenous cultural practices and mathematics. One of the members shared a beading project she did with students alongside and Indigenous Education teacher. Even though there were specific mathematical outcomes to the activity related to patterns, she noticed so much more mathematics coming to life in how students were creating their projects – counting, measuring, comparing, and much more. Her take-away from the project was that we can start with an activity or project and then look for the mathematics, rather than starting with a math concept and developing projects from there.

Question: In planning activities with your students, are you finding that you start with an activity and find the mathematics or start with the mathematics and develop/find an activity that supports the math or a bit of both? What do you prefer?

I connected with that idea of starting with the activity and letting the mathematics support it because of how I have experienced mathematics as an inherent part of the activities we have done. I could feel the mathematics. I noticed this in the video about the rope making in Norway and how the ropemaker seemed to feel the tension in the materials as she was pulling the rope. I know when I played with the raw fleece to ply it, I was feeling (sometimes more successfully than others) for how fast and hard I could tug on it to pull the fibres without them disconnecting from one another and then getting a feel for how tightly I needed to twist and ply to get a stable piece of plied yarn. I know I feel the patterns when I dance, too, and hear and feel patterns of notes when I play music. I have discovered and learned that feelings of having mathematics inside my body, right down in my core, when I engage in different human activities is what is meant by embodied mathematics.