Final Project: Printmaking Patterns

 Here is the link to my final project video and slides. Happy viewing :)

Week 10 Activity Reflections

I was excited to see net making as an option for trying this week, because my family has generations of fishers and boatbuilders. I remember when I was quite young, gillnets hung in the basement to be mended. This would be done by hand, going through section by section of the net. It was slow, rhythmic work. When I was in my early teens, licensing for fishing in our province underwent a change to better accommodate management and sustainability of the resource. Fishers could only choose one method for which to fish by with their license, and my family chose troll. Gillnets and net making/mending are no longer a part of family routines. A generational skill has been lost with me. This activity gave me a chance to try and appreciate the skill my ancestors were once so fluid with. The patterning is actually quite simple, but the material I had was not the best. It was slippery and the knots did not hold well, leading to the end product being mis-shappen - but the general idea is there :)

This made me think of other generational skills that are becoming lost. For example, the school I work in no longer has a textiles/sewing class and I do not know how to thread a sewing machine. Having never lived outside of the city, I also do not know how to break down a whole chicken into parts; I just buy the cut I want at the grocery store. My family only owned automatic vehicles since I learned to drive, so I cannot drive standard. I will not be passing any of these skills on to my daughters and they will likely not learn them in school. Will we come to a time when these skills are lost altogether? Or only belong to a select few? 

It was interesting to see, in Aström & Aström (2021), that rope and cordage have such a long history with our species but that much of that history comes from secondary artifacts (imprints, paintings, etc.) because fibers degrade over time. It highlights the need for these cultural knowledges to be passed down generationally so that they are not lost. I like that the Q’eswachaka bridge, shown in our viewings, is rebuilt annually with the whole community. It builds in a continuity of knowledge, and not just for specific individuals but for the whole community. Today, we have written records as well, but I don’t think that these are the same. In the video clip Closed by Hand, ropemaker Ingunn says, “the knowledge is in the body and in the hands. I had to learn how.” Do written records capture this wholly?  

It made me think, what practices do I want to do as annual traditions with my family? With the community? Should we be doing some of these things at school? What could that look like? I feel as though the knowledge that I have to pass on in the school capacity is limited, so perhaps it looks like bringing in guests? (This would also tap into the “power of the intergenerational exchange” that McKenzie (2021) recognizes in her article, The Spirit of the Medicine Will Lead Us Back: How Avis O’Brien is guiding elders to weave their first cedar hats.) Or exploring through videos and trial and error? I really liked that the Trillium park in the Wildfibers video clip grows plants for use in fiber arts. Our school has been thinking about putting in a native plant “garden” and perhaps considering some plants for use like this would be beneficial. I wonder if invasive plants could be utilized this way? Perhaps a clean up and create something task could be developed.   

I will need to spend more time pondering how to bring this into the classroom well. But, I like the idea that math class can be linked to culture and identity, and position students to be both learners and teachers of these knowledges.

References: 

Åström, A., & Åström, C. (2021). Art and science of rope. In B. Sriraman (Ed.), Handbook of the mathematics of the arts and sciences (pp. 409–442). Springer. https://doi.org/10.1007/978-3-319-57072-3_15

Ensby, S. (2017). Closed by hand [Video]. Vimeo. https://vimeo.com/198049602

Kallis, S. (2015). Wildfibres [Video]. YouTube. https://www.youtube.com/watch?v=p936TM65Q6Q

McKenzie, A. (2021, April 11). “The spirit of the medicine will lead us back”: How Avis O’Brien is guiding Elders to weave their first cedar hats. APTN News. https://www.aptnnews.ca/national-news/the-spirit-of-the-medicine-will-lead-us-back-how-avis-obrien-is-guiding-elders-to-weave-their-first-cedar-hats/

National Museum of the American Indian. (2015, June 5). Weaving the bridge at Q’eswachaka [Video]. YouTube. https://www.youtube.com/watch?v=dql-D6JQ1Bc

Week 10 Reading: The Spirit of the Medicine Will Lead Us Back: How Avis O’Brien is guiding elders to weave their first cedar hats (McKenzie, 2021)

Summary: Haida and Kwakwa̱ka̱ʼwakw artist Avis O’Brien is guiding Elders in her community to weave cedar hats. A cultural practice that they never had the chance to learn due to colonial policies, such as residential schools and potlatch bans, trying to erase Indigenous cultures. O’Brien explains how cedar functions as both a material and a form of medicine that supports healing, identity and community. She describes a time when she was resistant to learning weaving because she was ashamed of her culture, but when she did choose to engage, cedar became a pathway back to a sense of belonging. The work is especially meaningful as an intergenerational exchange, where Elders reclaim knowledge and a community is positioned to preserve it.

Stop 1: Elder Theresa Wasden is quoted within the article as saying: “Cedar is who we are and where we come from. It’s entwined in everything we do — from birth on a cedar mat, to death in a cedar box. It’s used for potlatches, for skirts, wreaths, head pieces. It was used for storage, cooking, blankets, mats, and even personal hygiene. It’s a part of our art. We use it when carving masks, poles, and making hats. I just think, wow, our Ancestors were so smart in how they thought about all these different uses and ways.” This quote reinforces how central cedar is; how important it is. The article goes on to mention that making cedar hats is the first thing Wasden has ever made out of cedar, sadly pointing out how colonial efforts stripped these practices in such a short amount of time. What knowledges will be lost completely in this timeframe? Not remembered how to be brought back? I love that Wasden celebrates the “smartness” of her ancestors for all the uses of cedar. I think that it can be easy for younger generations to see ancestral practices as outdated and not holding value in a modern world. How can we flip this mindset, and celebrate knowledges and ways of many cultures within the classroom as “smart” and valuable?     

Stop 2: “The power of this intergenerational exchange.” Across out readings, viewings and activities this week the power of intergenerational exchange is really prevalent. It preserves knowledges and ways of being, and it builds community, identity and sense of belonging. How can we develop teaching practices that position students to be receivers and givers of intergenerational exchange?   

Question: (trying to capture all of my questions above...) How can we celebrate culture and identity in the mathematics classroom, in a way that preserves and passes forward knowledges of the body and hands? What specific tasks may help with this?   

Reference: 

McKenzie, A. (2021, April 11). “The spirit of the medicine will lead us back”: How Avis O’Brien is guiding Elders to weave their first cedar hats. APTN News. https://www.aptnnews.ca/national-news/the-spirit-of-the-medicine-will-lead-us-back-how-avis-obrien-is-guiding-elders-to-weave-their-first-cedar-hats/

I was excited to watch the video interview with Lisa Lajeunesse because she was one of the poets that I looked at/listened to in week 8 and I really enjoyed her work. I also liked that she added a telling on how the structure of each of her poems linked to mathematics, making the connection more transparent. I was happy to hear/see more examples of Lisa’s poems, poetry styles, and math connections in the interview. I am excited to try many of these - thanks for including handouts! I also appreciated hearing about her creative processes and inspirations in writing her poetry. The story of the chaos theory graph (~57:00) was very moving. Here is my attempt at a goldie: 

Devices

It sucks her in, 

instant and continuous. 

Headphones block out the world. 

Influencers and cat clips. 

Parent wait to connect, pets wait to play. 

Like being underwater, 

joyous, serene, your body feels light. 

Until you can’t breathe.  

While I was expecting to hear more about poetry, I was surprised to see so many connections made to music and other art forms too! I love the connections made with these graphs: Red being like human face symmetry, left to right; green being like a mountain reflecting on a lake; top blue is a combination of red and green, or rotational symmetry; bottom blue is a repeating pattern.   

Once I had these connections I was able to see them in the sculptures, music and other forms of art presented. Not having any music (theory) back ground I felt I was able to keep up because the “mathematics gave me a language for connecting.” (31:30) 

Having a very “traditional” math (education) experience, I continue to have the world of math broadened. Lisa mentioned that if you aren’t introduced to these things (connections between maths and arts) as a child you sometimes don’t reexamine them until triggered later in life. (~9:12) I feel lucky to be able to reexamine them now, and sad for those that will never have these triggers later in life and get to see a bigger picture of what maths is and can be in their lives. When we know better we do better, and I am excited to introduce these experiences into my mathematics teachings.

Thank you Susan and Lisa for this great interview! 

Reference: 

Lajeunesse, L. (2026, March 13). Lisa Lajeunesse interview [Interview by S. Gerofsky] [Video]. Vimeo. https://vimeo.com/1173500795/9c65fde7a1?share=copy&fl=sv&fe=ci 

 This week I watched Carolyn Yackel’s (2020) presentation How Orbifolds Inform Shibori Dyeing. This is a Japanese dying technique, like tie-dying but the goal is to get a repeated pattern across the fabric. This is tricky, because you need to fold and clamp the fabric in ways that will allow spaces for the dye to access and spaces where it cannot go. (Which connects to the idea of absence again, and limitations of products and maths.) The result is really neat though. This example below is folded like a hexaflexagon: the fabric is pleated accordion-style into a strip and then folded in equilateral triangles and clamped before exposing to dye.

While this is a really neat exploration of folding (3D) and its resulting symmetries (2D), I’m not sure I would be brave enough to try dying with a whole class of students. Having just had paint and hot glue out for my final project activity, it doesn’t seem realistic. Maybe starting with a smaller group - a math club? 

Something more tangible for classroom exploring might be along the lines of Polster’s (2020) What is the Best Ways to Lace Your Shoes. Always finding that I need more lace to tie in my own shoes, I was quite interested in trying the shortest lacing methods to see if I could gain more tying length. It made sense that the shortest method would be the straightest distance, like a rectangle. But, wearing this one was not very supportive. The next shortest alternates rectangular straight sections with a criss-cross and this one I found just as supportive as my regular criss-cross all the way up, and it did leave more tying room!      

                                

Polster’s video also poses thought provoking questions besides shortest lacing like, longest, strongest, what would it look like with a shoe that has 100 eyelets, etc. He also explains how he came up with proofs for his findings which is kinda neat. I stopped at the Dollar Store to see if I could get bright laces - neon pink or green - but, they didn’t have any :( I would like to pick some up and try doing some of the more visual patterns and wear them into work just to see if they spark some mathematical conversions, like a little provocation. 

    

  Maybe bulk buying some funky coloured laces and letting students explore and create some of their own lace patterns would be a fun way to provide opportunity to explore and play. These themes, that we were first introduced to with Francis Su in 550, were something I noticed this week (and other weeks in this course too.) They are a key piece to finding new perspectives and learnings about/with maths. What happens if I try that with this medium? How can I get that outcome within the constraints of this medium? I think exploration and play are also key in accessing that space in between math and art, that Susan mentions in our introduction this week: “the 'flow' can go from mathematics to needlework, or from needlework to mathematics, or a third space can be created where mathematics and fiber arts inform each other!” 

References: 

Polster, B. (2020, June 20). What is the best way to lace your shoes? Dream proof [Video]. YouTube. https://www.youtube.com/watch?v=CSw3Wqoim5M

Su, F. (2020). Mathematics for Human Flourishing. Yale University Press.

Yackel, C. (2020). How orbifolds inform shibori dyeing [Video]. YouTube. https://www.youtube.com/watch?v=hjtc9LJ5ItI

Week 9 Reading: Highly unlikely triangles bead weaving (Fisher, 2015)

Summary: Impossible figures are optical illusions. In 2D they create the perception of a possible 3D object, but the 3D form is impossible to form - that is, if we assume rods are straight and connections are at right angles. Fisher creates impossible shapes with beading, and because of the flexibility of the beading joints they become possible to make in 3D. She calls the beaded shapes highly unlikely shapes. You can see that the rods that make up the shapes have a twist.  Here is an example of an impossible triangle and a beaded highly unlikely triangle.  

   

As Fisher replicates more impossible shapes, and extends the process to make highly unlikely polyhedra she finds new patterns. For example, faces that twist in unexpected ways and beaded paths on the faces that converge or diverge in different ways.  

Stop 1: Fisher’s article was published in 2015, but she mentions that impossible figures were discovered by Oscar Reutersvard in the 1930s and popularized in art and graphic design in the 1950s. This timeline struck me because a new setting (beading as opposed to drawings) provided a new perspective that led to new/deeper mathematical understandings decades later. If no one had tried a new medium, we would be lacking this new knowledge. Creativity and modality in math are meaningful.   

Stop 2: This exploration fits the framework that Vogelstein et al. (2019) outlined in my week 6 readings. Fisher foraged for an already existing shape in art/math. Then analyzed and recreated it with beads. And, finally she created something new (the highly unlikely polyhedra.) It feels like a framework that extends off the shoulders of giants.    

Question: I feel like beadwork of this complexity may be out of the scope of what I can do with students in the classroom, in terms of time and skill. What other settings (or media) might be doable with students to follow this framework and look at discovering new maths connections and meanings?  

References: 

Fisher, G. (2015). Highly unlikely triangles: Bead weaving. In G. W. Hart & R. Sarhangi (Eds.), Bridges 2015: Mathematics, art, music, architecture, education, culture (pp. 493–496). Bridges Organization.

Vogelstein, L., Brady, C., & Hall, R. (2019). Reenacting mathematical concepts found in large-scale dance performance can provide both material and method for ensemble learning. ZDM: The International Journal on Mathematics Education, 51(2), 331–346.

Project draft

Here is the link to the draft of my final project using printmaking to deepen understanding of linear relations with grade 9 students. 

Week 8 Activities Reflection: Reading, listening to and creating mathematical poetry

I am not a regular poetry reader. To explore examples of mathematical poetry I read some sample poems from the Bridges 2026 Mathematical Poetry page: 

Parallel Universe by Lisa Lajeunesse, a modular poem, where each “tile” can be a standalone poem, and they can also be read together additively to gain a new poem. This would be an easy structure for students to emulate. 

Hill Country, Old Mercedes, and Parturition by Madhur Anand, a poem about selective breeding and the movement towards efficiency in recovery rates. While I see connections to science, I do not see a mathematical structure within the poem yet.     

I also listened to poets reading their works from the 2022 Bridges conference, including:

Parasitic Oscillations by Madhur Anand, an expression of her scientific paper titled, Beyond harmonic sounds: a simple model for birdsong production (2008). Words that make up the poem are pulled from the paper, and when read aloud form structured sound wave patterns.  

Stolen Children by Lisa Lajeunesse, which is about residential schools. The repeating phrases, based on how each line number uniquely factors as a product of prime numbers, are very powerful.

Decision Tree by Mike Naylor - is about the decision making process. It is based off the structure of a binary tree and was fun to read, like a choose your own adventure! But, I’m not sure I would have read it the way it was intended if I hadn’t heard his explanation of the structure. 

I also listened to Mike Naylor’s Bridges 2020 poetry reading of:

Run, Hero, Run!, Water’s Edge and Entirely Nothing. Like Decision Tree, these are quite visual in their design and readability. I think this makes them quite engaging and approachable for using in the math classroom, as the math connections are easy to see/find. 

I liked it when the poems had a description (either written or verbally explained with the readings) of the mathematical structure or connection. I also appreciated hearing the poets read their work out loud so I could experience the intended tone and rhythm. This made me wonder: how much of the poetry experience should be what the author intended and how much should be left for the reader to interpret through their own emotions and experiences? I guess this question can mirror one of teaching math: how much of the math should be explored and discovered by the students and how much should be directly taught? 

I appreciate the idea of poetry as an expression of the human experience and that math is part of the human experience too. In my reading this week, Karaali (2014) notes everyone “can contribute, as they too have experienced both mathematics and poetry, in very emotional ways, and now they have the chance to unleash these emotions and share with others.” (p. 44) Poetry seems accessible for all to create and consume as we all have human experiences to draw on. (It may be an accessible way for all to create and consume mathematics too - even those who are not “math people.”)     

With that in mind, I tried creating some mathematical poetry this week. My experience this week was the chaos of life, as parent conferencing aligned with my own schooling and home responsibilities. A lot of my thoughts were around balancing all that needed to fit in, so it is not surprising that the 4 words that came to me in my attempt at a braided bellringer PH4 poem (Gerofsky, 2020) were roles that needed fulfilling this week.

I gravitated to the visual braided pattern of this poem and it made me wonder how it would change in meaning, structure, impact if it took on more of a French braid aspect, where strands are scooped into the braid at each outer edge.

References: Anand, M. (2026). Hill country, Old Mercedes, and Parterition [Poem]. In Mathematical poetry at Bridges 2026. Bridges Organization. https://www2.math.uconn.edu/~glaz/Mathematical_Poetry_at_Bridges/Bridges_2026/The-program-and-the-poets-2026.html

Anand, M. (2022). Parasitic oscillations [Poetry reading]. In Bridges 2022 mathematical poetry readings. YouTube. https://www.youtube.com/playlist?list=PLBMMY3UMNbPlUz-2WS7AwvtmOiLTsRecY

Gerofsky, S. (2020). Two new combinatoric poetry forms: Braided bellringing PH4 poems & anagrammatic, Anglo Saxon-inspired poems. In Bridges Conference Proceedings: Bridges 2020: Mathematics, Art, Music, Architecture, Culture (pp. 273–280). Bridges Organization. https://archive.bridgesmathart.org/2020/bridges2020-273.pdf Karaali, G. (2014). Can zombies write mathematical poetry? Mathematical poetry as a model for humanistic mathematics. For the Learning of Mathematics, 34(2), 26–32.

Lajeunesse, L. (2026). Parallel universe [Poem]. In Mathematical poetry at Bridges 2026. Bridges Organization. https://www2.math.uconn.edu/~glaz/Mathematical_Poetry_at_Bridges/Bridges_2026/The-program-and-the-poets-2026.html

Lajeunesse, L. (2022). Stolen children [Poetry reading]. In Bridges 2022 mathematical poetry readings. YouTube. https://www.youtube.com/playlist?list=PLBMMY3UMNbPlUz-2WS7AwvtmOiLTsRecY

Naylor, M. (2022). Decision tree [Poetry reading]. In Bridges 2022 mathematical poetry readings. YouTube. https://www.youtube.com/playlist?list=PLBMMY3UMNbPlUz-2WS7AwvtmOiLTsRecY

Mike Naylor. (2020). Bridges 2020 poetry reading: Run, Hero, Run!; Water’s Edge; Entirely Nothing [Video]. YouTube. https://www.youtube.com/watch?v=H_CTB6sLnR4

Week 8 Reading: Can zombies write mathematical poetry? Mathematical poetry as a model for humanistic mathematics (Karaali, 2014)

Summary: Karaali (2014) notes that mathematics is the “perfect model for what makes an activity human” because it involves the three aspects that makes our species unique: cognition, consciousness and creativity. (p.38) When mathematicians create new work, they do so with passion, frustration, analysis, intuition and creativity (often in flexibility to interpretations and approaches) in order to reach truth; a parallel to the work of a poet. Both poetry and mathematics then, are human endeavors. Unlike poetry though, math is usually not perceived this way by those outside the field. Traditional teaching methods tend to mask the humanity and creativity of mathematics. Karaali suggests that poetry can be a bridge for teaching mathematics (and for reaching the public) in a more humanistic way, a way that “studies the human face of mathematics.” (p. 41) 

In an attempt to do this at a post secondary institution, Karaali taught a first year course introducing humanistic mathematics called, “Can Zombies Do Math?” It explored ideas about what makes us human and how mathematics is related to humanity. As part of this class, students created mathematical poetry and Kataali found it to be the “perfect ambassador for humanistic mathematics.” (p. 44) While she does not answer the question “can zombies do math” in the article, the answer is clearly no, because zombies lack the human qualities like emotion and creativity that engaging in mathematics (and poetry) requires.            

Stop 1: “Both poetry and mathematics may, in fact, be conceived of without or before language, but only with words will they become communicable and complete.” (p. 39) This connects to the idea that we often understand emotions, movements  and patterns before we can articulate them with words. In week 1, Antonsen (2016) stated in his TED talk that it is OK to make up notation and language to represent mathematical patterns as we learn and explore them. It can be a step in solidifying deeper cognitive understanding and lead to a level of cognition where we can then articulate it. Words can give this level of understanding to concepts, experiences, and emotions.     

Stop 2: In mathematics “a wide range of emotions is involved too.” (p. 40) “We encourage the timid to venture into the world of mathematics, as they too have experienced both mathematics and poetry, in very emotional ways, and now they have the chance to unleash these emotions and share with others.” (p. 44) This article reminds me of the work we have done in previous courses with Francis Su’s book around the human connection to math and with the role of emotions in mathematical thinking. Connections that I still find underrepresented in math education. Everyone has connections to math, experiences with math and emotions linked to math. These can be expressed through poetry and/or drawn out from poetry examples by everyone. A very accessible way to approach humanistic mathematics, and remind us that math does not have to be a stand-alone discipline. It is interconnected to languages, arts, our world and culture, etc.   

Stop 3: “Everybody accepts without question the place of poetry in our world…On the other hand, mathematics for most is a dreary subject, and even those who find it appealing are oftentimes unaware of its connection to poetry.” (p. 44) This made me a bit sad, that math continually gets a bad rap. It also made me a bit hopeful. What if we could teach and represent mathematics in a more humanistic way that connected with more people? How would the world look differently if mathematics was as accepted with its place in the world as poetry? 

Question: 

How would you structure the use of mathematics poetry in your classroom? Would you host an open mic? Would you analyze sample poems? If so, would you do it from a place of knowing the mathematical structure first or would you let that be discovered? If getting students to create mathematical poetry, would you start with the math structure or have them write and then look for any mathematical connections? 

References:

Antonsen, R. (2016, December 13). Math is the hidden secret to understanding the world [Video]. TED. YouTube. https://www.youtube.com/watch?v=ZQElzjCsl9o

Karaali, G. (2014). Can zombies write mathematical poetry? Mathematical poetry as a model for humanistic mathematics. For the Learning of Mathematics, 34(2), 26–32.