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

Sometimes accessing mathematical ways of knowing and doing doesn’t start with the mathematics, it starts with the doing, making, creating and from that can comes an understanding of the mathematics, or a recognition of the mathematics and a desire to know more about the mathematics to deepen understanding of the making…the two way inspiration that Dr. Gerofsky talked about in the introduction.

Many of us grew up with the a combination of the worldview of capitalism - wealth as personal accumulation and as a goal in life, and the value of individuality and self-reliance. This is drastically different from Indigenous worldviews in which wealth is measured in the number of children and grandchildren that you have and in how much you give away. The colonial worldview, that many Canadian colonial children grew up, with is that human beings are on the top of the food chain, and in fact all chains, higher than animals and all things on the land. This is also in drastic contrast to Indigenous worldviews in which the interconnectedness of all things – human and more-than-human, elevate the value of each as a result of the interdependence of all things. In Indigenous worldviews the natural world is not a commodity, it is a relation (Indigenomics by Carol Anne Hilton).

The question, “how does an embodied, mindful AND conceptual way of living balance our lives differently from the mainstream traditions of consumer culture, and the industrial model of schooling that most of us grew up with?” is a big question. When I work with the FPPL and as I try to learn about and bring Indigenous ways of knowing into the classroom, I see connections between embodiment, mindfulness and conceptual ways of knowing. Learning is not only about acquiring knowledge, it is also about remembering. The article I read this week was a short APTN article, ‘The spirit of the medicine will lead us back’: How Avis O’Brien is guiding Elders to weave their first cedar hats. The article talks about how O’Brien used to feel shame about her identity, but when she started working with cedar, things began to change for her. “O’Brien says working with the healing power of cedar, the shame began to lift, and she became open to her cultural practices.” She is passing on her healing by teaching others from her community (particularly elders) to work with cedar as well. 

All cultures have traditional ways of creating and making. This week I was inspired by the Close at Hand video about the only rope walk in use in Norway today. My ancestors are from Norway and so I leaned in a little more to that video, watching the scenery and taking in the process of creating the rope. 

The many viewings and readings this week had me thinking about maker spaces in our schools. These spaces are often filled with lots of bright, shiny, plastic materials. I wonder how we can change the way students view these spaces – or activities, even in our own classrooms. How would our students learning/views change if instead of using collections of things found inside and purchased from a store, we bring natural materials into maker spaces, learning from the land, rather than all the shiny plastic materials. Even better, what if we had the maker spaces outside? If we do use human-made materials, can we present upcycling as a legitimate way of living and using materials, rather than a kind of ‘pretend thing’ we do at school? This has given me new thoughts on maker spaces and new possibilities for how to take math outdoors, using natural, foraged fibres from the land. 

I did the making rope activity this week. I cut down some tall plants and brought them home, only to realize that I had not brought the right kind of plants. They were strawy and brittle and broke as soon as I tried to twist them. So, after walking around unsuccessfully looking for appropriate natural fibres outside, I went to my junk drawer… you know the one that we all have. I was going to use some old ribbons that I had saved, and when I lifted the ribbons out, underneath, I found some straw-type material, I’m not exactly sure what it is, but I used that to make my rope. I followed along with the video, 'The art and geometry of rope making and yarn plying'. At first I started by following the directions as I was seeing them. When Susan said that she was using her right hand, I was using my left. I quickly realized that this was difficult for me, so I undid what I had started. I had to sit facing the same way as Susan was in the video (my screen beside me) to follow what she was doing (initially I tried to translate the movements without changing my position, but I was struggling with transforming the moves). I was also having trouble keeping up with the pace of the video. I slowed the speed of the video down to 50%, then I was able to keep up with the movements and I had a few good chuckles too, as Susan’s slowed down voice sounded… mesmerizing (you should check it out!).

Foraged Fibres

Junk Draw

Rope

As I was making the rope, I was thinking how much my students would love to do this, especially if we started by harvesting fibres from the land and then using them to create a real rope. We could start by looking for the proper type of grass or plant from the land around our school. I know that this activity would create a deeper connection for students with the land. I’m not totally sure about the mathematics we would pull out but for grade one students, we could definitely bring in measurement of our initial plant material (leaves or grass length) and compare it to the length of the final rope. We could consider the pattern of movements in making the rope(i.e. twist, twist, twist, twist, cross over – as Susan says in her video). We could test the weight that the ropes are able to hold (as in one of the ‘how to make a rope videos’), we can look at the curves in the rope, and count the numbers of turns, Doing these activities would broaden students understanding of what mathematics is and how connected mathematics is to everything we do. 

I found the viewings, activities and readings this week inspiring. I do wonder about Sharon Kallis’s ability to take the time to make her own clothing from plants. I admire her using her skills to combat fast fashion but it feels like she is coming from a privileged position to have the time, ability etc. to be able to do this. Although… she did say her nettle shirt was 12 years in the making! That’s perseverance! I was amazed by the video on Weaving the Bridge at Q’eswachaka – the history, practicality, craftsmanship, community connection and cyclical nature of making this bridge were inspiring. It is amazing what people can accomplish when we work together. 

Since this is our last post for this class, the question I have is, "what are one or two things that you have learned or experienced in this course that you will explore more deeply and/or apply in your current practice?"

Week 8 Reflection - Mathematics & fibre arts, fashion arts and culinary arts

This week I attended the last session of the Re-Imagining Mathematics Seminar put on by the E. Lando Virtual Learning Centre (Cynthia was organizing along with Jo-ann Archibald, Joanne Yovanovich and Leyton Schnellert). They discussed Kagann Jad, “The mouse Woman” who is the symbol of the Indigenous Math Network. Mouse woman is like math - helpful and ever present. She always finds a way to help us out. This connected for me with the activities this week. The activities – which were maybe not clearly connected to what we traditionally consider mathematics – had a way of sneaking math in. The math was helpful, if not front and centre.

I had an interesting conversation with a colleague this week regarding how to fit Indigenous “content” into mathematics. My colleague is struggling to see: how to ‘fit it in’, the value of taking time away from learning math skills to ‘play’ with cultural aspects of mathematics, how this all relates to student success – both in math classes at school but also in life after school that requires the pre-requisite math skills/courses etc. I tried (somewhat successfully I think) to bring a different perspective into the conversation. I pushed back on the idea that it is enough to teach Indigenous ‘content’, but suggested we need to rethink the way we teach mathematics, asking how we can bring Indigenous knowledge and pedagogy to the classroom, so that Indigenous (and in fact, all students, ethnomathematically) see themselves reflected in our mathematics classrooms. We also discussed a few ways of doing this that necessitate a shift, not a complete overhaul, of our programs. Saying all of this connected for me with Dr. Gerofsky’s statement in the introduction, “It takes a change of attitude to start noticing the mathematics inherent in all these skills, crafts, and practices, and to connect these physical ways of making with the concept and patterns of mathematical relationships.” Thinking differently about what counts and does not count as mathematics is part of this process of shifting attitudes. Sometimes, like Kagann Jad, the mathematics sneaks in!

The reading I am reflecting on this week is b) Uyen Nguyen (Bridges 2020) Folding fabric: Fashion from origami

The following two quotes from Nguyen, give some insight into the article.

“Fashion loves the juxtaposition of extremes.” (p. 93)

“I wanted to give my artwork functionality.” (p.93)

This paper explores Nguyen’s exploration with folding fabric, origami style, and using rigid paneling and heat settings to maintain the folds. The paper explains the techniques Nguyen uses and the types of designs. 

The techniques used include the following:

• Adhesion of semirigid panels to all regions meant to remain planar and unfolded
• Panels constrained in a way that forces them into the desired configuration
• Adding snap buttons to force some vertices to connect
• Heat setting fabric while in folded configuration
• Sewing vertices together to counteract gravity

Where’s the math?

• Patterns, Geometry – understanding the variable stability of geometries, Fibonacci sequence (Nguyen created a series of Fibonacci skirts), measurement – fabric, weight, temperature, effects of gravity, impact of the distance between folds, dihedral angles, all of the mathematics involved in sewing (I’m sure there are more mathematical connections I have missed)

Here are a few images from the article.

Nguyen ends the article with the following quote. I am including it because in it she states the value of the mathematics behind her design and also expresses the desire for deeper mathematical understanding to improve her designs. It’s a long quote but it sums up the article nicely.

I’ve used fashion and origami to represent various concepts in mathematics. While I use a lot of mathematics in my origami design process, having a more rigorous understanding of the mathematical constraints behind the construction of a fitted garment would enable me to improve my designs moving forwards, both with and without origami elements. I plan to design both clothing that can be fitted and practical as well as garments that are more conceptual and artistic. (Nguyen, 2020, p. 102)

Both this article and the viewing, “How Orbifolds Inform Shibori Dyeing” by Carolyn Yackel talked about the idea of constraints. Learning to work within constraints or using constraints to create something mathematically beautiful. I wonder how often we feel that constraints are negative, rather than embracing how constraints can add to the beauty? 

I experienced working with constraints as I (continuing on with my theme this week of folding) chose to do the activity on Miura Ora Origami (the technique Nguyen uses in her fashion design). 

Here is a bit of the process and the final result:

The first two rows were mind- bending and required resilience. But as I continued to repeat the steps to add more rows, I began to understand what I was doing. Eureka!!! It reminded me how exciting it is to successfully make your way through the struggle! The final two rows I was able to complete without following the steps. I got so much satisfaction in completing this folding activity. I showed everyone my final product. It was only by working within the constraints of the necessary folds that I was able to produce this beautiful product, within the constraints came the freedom of the design. (A binary statement?)

Although this type of origami would be outside the capabilities of young students, there are many simpler types of origami that young students are capable of creating. 

What are the benefits of students learning to creatively work within constraints? 

This week, I’m considering how to bridge the dichotomy between the physical world and  the abstract, conceptual world. Folding paper, spatial reasoning, geometry… when we work with the physical, it strengthens our understanding of the abstract. I’d love to hear your thoughts on this. Many of the activities in this course are doing just that, bringing the physical world and the conceptual world of mathematics together – embodying mathematics! Through movement, drama, film, various kinds of art, poetry, novels the mathematics sneaks in, just like Kagann Jad, helping us out!