Braiding Relationships, Land and Mathematics By Tracy Parkes 

Lesson package for Braiding Relationships, Land and Mathematics supported by Chat GPT and Canva

Week 9 Reflection Mathematics & fiber arts, fashion arts and culinary arts

Viewing  

Quilts as Mathematical Objects (Gerda de Vries)

I chose to watch Gerda de Vries’ presentation on Quilts as Mathematical Objects because of my personal interest in quilting. Quilting is something that I have participated in and seen in my family for many years, so it immediately sparked my curiosity. I was interested to see how something that I usually think of as a creative or artistic activity could also be explored through a mathematical lens.

Stop 1 – Sewing and Generational Knowledge

My first stop happened right at the beginning of the video when de Vries shows an image of herself as a young girl sitting behind a sewing machine. That image immediately made me think about my own family. My mother has sewn and quilted for many years, and recently she gave my granddaughter a sewing machine for Christmas. My granddaughter now keeps it in her room and has started experimenting with sewing. It made me think about how these practices move through generations, my mother quilting and now sharing those skills with her grandchildren and great-grandchildren.

Before quilting or sewing is ever described mathematically, it already exists as family knowledge, creativity, and learning by doing. This moment reminded me that many mathematical ideas are embedded in cultural and everyday practices long before they are formally named or studied in mathematics classrooms.

Stop 2 – Mathematical Vocabulary

Another moment that stood out to me was how quickly the vocabulary used to describe quilt patterns became more complex. What initially looks like simple repeating shapes is actually connected to more sophisticated mathematical ideas such as tessellations, symmetry, and other pattern structures.

While watching the presentation, I realized that my understanding of some of this vocabulary was fairly limited. Instead of focusing too much on the terminology, I found myself paying attention to the visual patterns in the quilts. Even without fully understanding all of the mathematical language, it was still possible to see how the shapes and structures in quilts relate to mathematical ideas.

Stop 3 – Tessellated Animal Images and Visual Perception

Another moment that stood out to me was the artwork showing animals arranged in tessellated patterns. These images reminded me of visual illusions where multiple images exist within the same drawing, such as the classic picture where viewers may see either an old woman or a young woman depending on how they interpret the image.

Images like this cause your eyes to move around the picture as you search for patterns and details you may have missed at first. The tessellated animal artwork created a similar experience. At first you see the animals, but then you begin to notice how the shapes interlock, how symmetry works, and how the pattern repeats across the surface.

Stop 4 – The π Quilt

The π quilt shown in the presentation was another moment that really stood out to me. At first glance it reminded me of what my mom would call a crazy quilt, where many different pieces of fabric from past projects are stitched together. My mom has made quilts like this before using leftover materials, so when I first saw the image it looked somewhat random.

However, as the explanation continued, it became clear that the quilt was actually highly structured mathematically. Each number in the decimal expansion of π was represented by a specific color, and the quilt begins in the center and spirals outward with each colored piece representing the next digit of π.

Initially I tried to interpret the quilt like a hundreds chart, starting from a corner and moving across. Once I understood that it actually begins in the center and spirals outward, the structure made much more sense. The spiral also reminded me of patterns such as Fibonacci spirals where structure grows outward over time.

This example beautifully demonstrates how something that appears artistic or random can actually represent a deeper mathematical idea.

Overall, this video reinforced for me that mathematical ideas often begin with visual noticing, creativity, and making, while the formal vocabulary comes later. Quilts show how mathematics, art, and craft can exist together in the same object. What may appear to be simple patterns created through sewing can actually contain complex mathematical structures such as tessellations, symmetry, and even representations of mathematical constants like π.

Activity

Coast Salish Weaving Mathematics

After watching the presentation, I was curious to try the weaving activity for this week. I chose to explore the Coast Salish weaving mathematics lesson developed by the Burnaby teachers (Goeson, Nicolidakis, Gamble, and Houghland). I wanted to try the activity myself because I may use something similar with my students and wanted to understand the process first.

Instead of weaving only a flat panel, I experimented by creating a small basket, which turned the activity into a three-dimensional structure. This made me think about the example in the Burnaby Weaving Math lesson where Nicolidakis references the Sears Tower structure, where a pattern or module can extend upward into a larger three-dimensional form. Moving from a flat woven piece to a basket helped me see how weaving patterns can expand into spatial structures.

One aspect of the activity that I really liked was the over–under weaving pattern using two colours of yarn at the same time. The alternating colours made the pattern easier to see and helped highlight the mathematical relationships within the design. When I try this with students, I plan to use the cardboard loom suggested in the lesson because it seems simple and accessible for classroom use.

I also realized that using thicker yarn would likely work well with students. Thicker yarn allows the pattern to appear more quickly, meaning students would not need to weave for as long before seeing the structure emerge.

Another part of the activity involved taking a photograph of the weaving and analyzing it using Desmos. I have not used Desmos before, but it looks like an interesting tool for connecting the woven pattern to ideas such as linear equations and slope. Keeping the yarn lines perfectly straight might be challenging, but if the weaving is done carefully the relationships between the lines should become visible.

Overall, my attempt to create a three-dimensional woven basket helped me see how mathematical ideas such as patterning, structure, and linear relationships can emerge through the process of making. Trying the activity myself also helped me think about how I might adapt it for my students so they can experience these ideas through hands-on exploration.

Reading Reflection 

Adventures in Mathematical Knitting (Sarah-Marie Belcastro)

Before reading this article, I did not think that knitting could be a way to represent mathematics. After trying the weaving activity this week, however, I started to see how mathematical ideas can appear through textile work. When I experimented with weaving, it was interesting to see the potential of a linear pattern emerge visually, which made the mathematics easier to notice.

While reading the article, some of the terminology was unfamiliar to me. One concept I looked up was the Klein bottle, which is a mathematical surface where the inside and outside are connected. It cannot exist in normal three-dimensional space without intersecting itself. Seeing this concept represented through knitting helped make the abstract idea more tangible. The idea that a surface could loop back through itself in a continuous way is difficult to imagine, but the knitted models made it easier to visualize how such a structure could exist mathematically.

Another image that stood out to me showed the structure of knitted stitches, which reminded me of graph paper. Each stitch sits within a kind of grid, and the repeated loops create patterns through repeated movements. This helped me understand how knitting could model mathematical structures such as grids, surfaces, and repeating patterns.

Even though I have never knitted with needles before, the process reminded me somewhat of using a loom for knitting, where repeating steps gradually build a larger structure. When I saw the knitted Klein bottle structures in the article, I immediately thought about circular loom knitting tools. These tools use pegs arranged in circles where yarn loops around the pegs in repeating patterns. The repetition and circular structure made me wonder whether some of the mathematical knitting projects described in the article could potentially be approximated or explored using these looms.

Thinking about these loom tools also connects to the weaving activity we tried this week. Both weaving and loom knitting involve following repeated steps that gradually build a pattern or structure. Through these repeated actions, mathematical ideas such as patterns, symmetry, structure, and iteration become visible.

Overall, this reading helped me see how textile practices such as knitting and weaving can reveal mathematical ideas through repetition, structure, and pattern. Activities like weaving or loom knitting could also make abstract mathematical ideas more accessible to learners because they allow students to see and build the mathematics with their hands, rather than only thinking about it abstractly.

 

Instructions

If you highlight the link and paste it into your browser bar, it should take you directly to the saved Google document. Fingers crossed!

Link to my slides

 https://drive.google.com/file/d/18VJkjoIoaGyQIGXv2i71IqsK5bKIzgqP/view?usp=drive_link

Mathematics and Poetry

 

Week 8 Reflection Draft

Mathematics and Poetry

Reflection

When I first saw the title of this week’s topic, Mathematics and Poetry, I initially wondered how these two ideas could connect. Mathematics is often framed in schools as logical, procedural, and emotionless, while poetry is associated with creativity and feeling. However, after exploring the Bridges poetry collection and reading works by poets such as Alice Major and JoAnne Growney, I began to see that mathematical structure and poetic structure share many similarities. Both rely on pattern, rhythm, repetition, and constraint.

One of the ideas that stood out to me was the concept of creative constraints. In mathematics we often work within defined rules or structures, and poetry does something very similar. The Fibonacci poem is a clear example of this. The mathematical structure of the Fibonacci sequence becomes the scaffold that shapes the poem, allowing creativity to emerge within the pattern.

Writing my own Fibonacci poems was an interesting experience because it required me to think about syllables as numbers and to carefully choose words that would fit the pattern. This process reminded me of the mathematical thinking involved in weaving and braiding. In my own work exploring sweetgrass braiding as a mathematical practice, patterns emerge through repetition and structure, much like the patterns found in poetry.

This week reinforced the idea that mathematics is not separate from human experience. Like poetry, mathematics is deeply connected to pattern, beauty, and the ways we make sense of the world.

Viewing

Stop 1

When reading Susan Gerofsky’s poem “Diagonal Eyes Enter Leaving,” I had an unexpected connection. The poem reminded me of a Family Guy episode where Stewie asks Brian to write down his last words, which turn out to be about a squiggly line in his eye. It made me laugh when I made that connection, but it also felt surprisingly relevant because I experience something similar in my own vision. It reminded me that mathematical imagery and visual patterns can appear in everyday experiences in ways we might not expect. 

https://www.youtube.com/watch?v=ZqT4W5oe81s

Stop 2

The second poem that made me stop was by Madhur Anand, Parasitic Oscillations. I loved the visual accompaniment of the poem. The way she connected scientific explanations with poetic phrasing was something I would not have thought to try on my own.

It made me think about how inspiration can come from many sources. When reading or observing something, whether it is a scientific explanation, a piece of art, or a mathematical inquiry, we sometimes hear or see poetic phrasing embedded within it.

I especially appreciated how Anand revealed the poem gradually. The sounds of birds and the egg image that the poem begins with drew me in immediately. Starting from a simple idea, in her case bird, and expanding it into poetry that contains underlying mathematics was fascinating. The concept of harmonic sound patterns connected the natural world with mathematical structure.

I also appreciated the interactive element she added. At the end of the poem she included QR codes linked to the sounds of the birds referenced in the work. One of the links did not work for me, but the other two did. One linked to a webpage with recordings and additional information about the species, while the other linked to a video of the bird sounds themselves. This made the poem feel like a multi-sensory experience. 

Stop 3

The third stop happened when I listened to Mike Naylor’s poems.

The first poem used binary code, consisting of zeros and ones, representing a counting system. He then transformed this numerical pattern into a structure containing two words in the same binary-inspired arrangement. This showed how a mathematical number system can directly inspire poetic form.

The second poem, “Water’s Edge,” reminded me of waves moving toward the shore. At the beginning of the poem the lines appear calmer and more regular, but as the poem progresses the structure becomes more uneven and “wavy.” I wondered if this visual shift represents moving further out into rougher water.

Looking at the words themselves also added meaning. The poem begins with the line:

“I walk along the water’s edge…”

This could literally represent the shoreline path. The final lines describe the sea as endless:

“…is as endless as the sea…”

The visual arrangement of the words on the page gave me clues about how to interpret the movement and emotion within the poem.

https://www.youtube.com/watch?v=H_CTB6sLnR4

Activity

Fibonacci Poetry

A Fibonacci poem follows the Fibonacci sequence in its structure. The count can refer to syllables per line, words per line, lines per stanza, or another countable element within the poem.

A Fib is a special case of a Fibonacci poem consisting of six lines whose syllable count follows the first six numbers of the Fibonacci sequence:

1
1
2
3
5
8

Fibonacci Sequence Poem

My Attempt

Explanation of My Fibonacci Poems

When I chose to write Fibonacci poems for the activity, I realized that in order to write poetry I need to begin with something I feel emotionally connected to. The mathematical structure of the Fibonacci sequence provided the framework, but the topic needed to be meaningful to me.

I chose to write about my grandchildren, Addie and Archer. Using their names became the starting point for the poems. As I was writing, I began thinking about the idea of generational learning and the passing down of stories and culture, which is something I am also exploring in my final assignment. The Fibonacci structure felt appropriate because it represents growth and continuation, which mirrors the way knowledge and traditions move through generations.

These two little people that I get to have in my life are incredibly important to me. The poems became a small reflection of that feeling. I do not take this time for granted, and writing about them allowed the mathematical structure of the poem to connect with something deeply personal.

Generational Learning

1	Two
1	seeds
2	growing
3	together
5	Addie and Archer
8	carry stories into tomorrow

 

My Favorite

1	Two
1	roots
2	growing
3	through time
5	Addie and Archer
8	holding stories yet to come

 

Very Grandparent Focus

1	Two
1	names
2	spoken
3	softly now
5	Addie and Archer
8	learning what was given to me

 Reading

Can Zombies Write Mathematical Poetry?

Gizem Karaali

Reading Summary

In Can Zombies Write Mathematical Poetry?, Gizem Karaali argues that mathematics is fundamentally a human activity, not simply a mechanical or procedural one. She explains that mathematics involves three important human characteristics: cognition, consciousness, and creativity. Because of this, mathematics should be understood as a creative practice that involves imagination, intuition, and exploration.

Karaali suggests that mathematical poetry helps reveal this human side of mathematics. Although poetry and mathematics may appear very different, both rely on structure, precision, and creativity. By combining these two forms, mathematical poetry challenges the common belief that mathematics is cold or detached from human experience.

Ultimately, Karaali proposes that mathematical poetry can act as an “ambassador” for humanistic mathematics, helping students and the public see mathematics as creative, expressive, and deeply connected to human life. 

Stop 1

One idea that stood out to me was Karaali’s discussion about writing poetry in Turkish, while mathematics felt easier to express in English. This made me pause and think about the relationship between language, identity, and expression.

I wondered whether writing poetry in one’s first language might feel more intimate or personal. In poetry classes I have taken in the past, I often had to dig deeply into personal experiences in order to write meaningfully. Perhaps this is why the author chose Turkish for poetry while mathematics felt more natural in English.

This moment also reinforced how unusual it can feel to place mathematics and deeply personal expression side by side. 

Stop 2

Another moment that made me stop was when Karaali explained that her students initially did not think mathematics and poetry belonged together. That reaction was very similar to my own at the beginning of this week.

When completing the activity, I chose to experiment with Fibonacci poetry because the structure felt more accessible. Even with that mathematical scaffold, however, I found myself turning toward personal themes in order to write.

This made me wonder how other classmates approached the activity. Did they focus on mathematical ideas within the poem itself, or did mathematics primarily provide the structure for their writing? I am not sure which approach is more common, but this was a moment where I paused to reflect on how creativity emerges within mathematical constraints.

 

Watching Nick Sayers’

 

When Math and Art Fit Like a Tight Glove

Watching Nick Sayers’ work felt less like observing finished products and more like entering into his way of thinking. Several moments made me pause, connect, and question my own assumptions about mathematics, art, and identity.

Stop 1: The Spheres and the Spirograph Machine

One of the first moments that caught my attention was his use of a spirograph-style machine to trace the outlines of students lying on the ground. Their bodies became arcs, rotations, and circular forms. The translation of something organic into structured geometry fascinated me. The machine did not remove the humanity of the work; instead, it revealed pattern within it.

As I watched, I immediately began thinking about fabrication tools like CNC machines. If those traced forms were cut from wood or plastic and assembled, would the machine be diminishing the art — or extending it? This stop connected directly to my own final project thinking. I began imagining how similar processes might generate forms inspired by sweetgrass braiding. Could technology support a cultural medium without replacing it? In that moment, math and art felt inseparable — fitting together like a tight glove.

 Stop 2: “I Wasn’t a Math Person”

When he described feeling intimidated by numbers and not seeing himself as a “math person,” I felt both recognition and tension. In Manitoba, mathematics is organized into multiple strands: Number; Patterns and Relations; Shape and Space; Statistics and Probability; and Mental Math and Estimation. Yet culturally, we often collapse “math” into “numbers.”

Listening to him, I wondered whether he simply wasn’t number-dominant. His fluency in ratio, proportion, spatial reasoning, angles, and structural relationships was unmistakable. This raised an important question for me: have we defined mathematical identity too narrowly? Some learners are pattern-strong. Some think relationally. Some visualize space with ease. Some manipulate symbols comfortably. Mathematical competence is not singular. As a school leader, this stop challenges me to consider how many students quietly carry mathematical strength that goes unrecognized because it does not fit a traditional image of math success. 

Stop 3: Art and the Issues of the Time

Another moment that stayed with me was how clearly his environment shaped his work. His projects respond to outer space, environmental concerns, engineering, fabrication, recycling, travel, and family history. His art does not exist in isolation; it engages with the world he inhabits.

This led me to ask: do issues of the time influence art, or does art influence how we see the issues of our time? It seems reciprocal. His reuse of materials and attention to environmental systems position art as both response and commentary. This resonates with my own thinking about sweetgrass, land, and stewardship. Mathematics and art are not abstract exercises; they are ways of understanding and responding to context. His work reinforced that connection for me. 

Stop 4: Coding, Braiding, and Algorithms

When he spoke about growing up with cameras, coding, and early computing, I felt a generational recognition. Coding, at its core, is structured instruction — a sequence of directions. As I listened, I realized that braiding is also structured instruction. A spirograph produces patterned movement through repeated rules. A CNC machine follows algorithmic paths.

Braiding is an algorithm.
Coding is an algorithm.
Fabrication is an algorithm.

This stop pushed me to rethink originality. If a machine assists in generating form, does that make the work less authentic? Or is authenticity rooted in intention, context, and relationship rather than in the absence of technology? These questions feel especially relevant as I consider how math, culture, and fabrication tools might coexist in my own work. 

What This Work Offers Me

Nick Sayers’ work expands my understanding of math–art connections by demonstrating that mathematics is not merely symbolic; it is structural, spatial, relational, and embodied. His projects make visible the mathematical thinking embedded within artistic creation. They show that math can be discovered through form, movement, and fabrication rather than solely through calculation.

As a math and science educator, his work challenges me to broaden what counts as mathematical fluency. It encourages me to honour spatial and relational thinkers and to use tools such as fabrication devices not as replacements for thinking, but as extensions of it. Most importantly, it reinforces the importance of curiosity. Throughout the video, he did not present himself as someone who had mastered disciplines; he presented himself as someone exploring them. That disposition is one I want students to see and inhabit. 

Questions for Nick Sayers

1.      Do you see yourself primarily as an artist, engineer, mathematician, or something else entirely?

2.      Do your projects begin with a mathematical idea, or with a question about the world?

3.      Has working with machines changed your understanding of originality?

4.      How do you respond to those who suggest that math-based art is less expressive?

5.      When did you begin to see yourself as capable in mathematics, even if not in numerical ways?

Week 7 Mathematical Art

 

 Writing a mathematical art manifesto by Fumiko Futamura

Confusion, Inclusivity, and Sweetgrass

When I first read Futamura’s Writing a Mathematical Art Manifesto, I found myself confused. The article kept building toward the idea of creating this manifesto, a bold declaration of what mathematical art is and what it rejects. I felt like I was left hanging. The more I delved into this idea of a manifesto the more it became clear. In my understanding a manifesto would  name a paradigm, criticize it, and introduce a new direction. They are passionate, declarative, and sometimes intentionally provocative. But I struggled with the narrowing impulse. If someone creates something, whether by hand, by code, through weaving, carving, programming, or patterning, is it not art? Why must we define it tightly? Why must something be rejected?

My instinct is inclusivity. As I reflected more deeply, I realized that my discomfort was not about manifestos themselves, but about the fear that replication, especially through technology,  might somehow disqualify something as original art. If a mathematical pattern can be generated through code, does that make it less authentic? If a structure can be repeated, does it lose its originality? I used the idea of sweetgrass to help me think this through.

 

 

Traditional sweetgrass braiding may have begun as practical for ceremony, medicine, or utility. Yet it is undeniably expressive. The braid carries rhythm, repetition, proportion, structure. It holds embodied knowledge. Patterns are passed down. They are replicated. And yet each braid remains deeply meaningful. The originality is not erased by repetition. It lives in intention, relationship, and cultural context. In that sense, replication does not remove art.

Similarly, if a mathematician writes code that generates a woven structure based on braid mathematics, the computer becomes a medium, much like a loom. The artistry resides in the choices: the constraints, the structure, the transformation, the framing. Technology does not erase creativity; it shifts the form of expression.

 

 

 

 

 

 

 

 

 

What Futamura’s article began to clarify for me is that a manifesto is not about excluding. It is about articulating values. It asks: What role does mathematics play in this art? Is math a tool, a demonstration device, or the generative engine of beautiful expression? Where does mathematical thinking, pattern, abstraction, transformation, rhythm, live in the creative act?

For me, mathematical art is not about illustration or education. It is about structure meeting story. It is about pattern holding meaning. It is about logic and emotion coexisting. In sweetgrass weaving, mathematical structure is inseparable from cultural narrative. In code-based generative art, mathematical structure may be inseparable from conceptual design. In both cases, mathematics becomes a language of form.

If I were to gesture toward a manifesto of my own, it would not reject replication. It would reject the false divide between logic and creativity. It would reject the hierarchy that elevates “fine art” above craft or digital creation above expressed making. It would affirm that mathematical art is creative human expression shaped by structure, rhythm, transformation, and intention, whether braided by hand or generated through algorithm.

Perhaps that is what a manifesto offers after all: not a narrowing of art, but a clarifying of what we believe about its heart.