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.