Week 9 Reading - Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving

 Stop 1 – The Binary Between Handwork and Mathematics

In the introduction, Susan talks about the historical binary between hands-on work and abstract intellectual work, and how this division was often tied to gender and social class. I agree that this binary has existed for a long time, but I also find it interesting how inconsistent it can be. Many activities like cooking, sewing, or textile work have traditionally been considered “women’s work” when done at home, for family, or for fun. Yet when those same activities become professionalized, the dynamic often shifts. Many of the world’s most famous chefs are men, and high-fashion designers or master tailors have often been men as well. That contrast suggests the issue isn’t really about the activity itself, but about how society assigns value and status to different kinds of work. Recognizing the mathematics embedded in fibre arts, design, and culinary practices helps challenge that hierarchy and reminds us that mathematical thinking has always existed in spaces that were historically overlooked.

Stop 2 – Impossible Shapes

Reading about the impossible triangles reminded me of working with these shapes years ago in an art class. We explored impossible triangles and staircases, but they were framed purely as art or optical illusions. At the time I never thought of them as mathematics. Looking at them now, I can see how interesting they could be in an elementary classroom. They would be a great way to spark discussion about shapes and geometry. You could ask questions like: What works about this shape? What doesn’t? Why does it look possible at first but fall apart when you really think about it? I can imagine students really enjoying the puzzle of trying to make sense of them while also developing ideas about perspective and three-dimensional shapes.

Stop 3 – The Beadwork Illustrations

Another thing that really stood out to me in the article was the photographs of the beadwork. If you looked at the pieces without knowing the mathematics behind them, you would probably just notice how beautiful they are, the colours, patterns, and intricate craftsmanship. They look like jewelry or small sculptures. What I appreciated was how the author moved from that visual beauty into explaining the mathematical structure behind the pieces. I especially liked that she included diagrams showing exactly where each bead is placed. Those diagrams made the structure much clearer and really reinforced the importance of representations. Being able to move from the finished object to a diagram of how it is built helps visualize what is actually happening mathematically.

This reading also made me reflect on my own experiences. I have worked in schools where we brought in Indigenous community members to teach students and staff beadwork. I learned how to make earrings and even a beaded spider, and at the time it was framed as a cultural and artistic activity. Looking back now, I realize there was a lot of mathematical thinking embedded in the patterns, symmetry, and structure of the beadwork. I never really thought about connecting that kind of work to mathematics class before, but this reading makes me see how naturally those connections could be made.

Questions for the group

• In what ways could you use crafts, cooking, or other hands-on activities to help students see mathematics as a human and creative endeavour rather than just an abstract subject?

• Could you see yourself using “impossible” shapes or optical illusions in a math lesson to spark curiosity and discussion about geometry? If so, how might you bring them into your classroom?