Final Project

 

A link to our Slides and Resources: Link to slides

Week 9 Origami Activity

 

For the activity I tried the Miura-Ori origami folding technique. I struggled a bit with the first instructional video because the presenter’s hands were often out of frame, so it was hard to see exactly what was happening. I also think the paper I was using may have been a bit too stiff. The second video was much easier to follow, and once I switched to that one the folding worked out much better.

I also really enjoyed the video on Uyen Nguyen and her origami fashion designs. I have recently started sewing again, so seeing how she incorporates origami structures into clothing was really inspiring. I would love to experiment with that idea someday.

Interestingly, I also happened to do an origami activity with a Grade 4 class I visited this week. We made origami basketball nets, and then students rolled small basketballs out of paper and took 20 shots from different distances. Afterward, they calculated their shooting percentages and created bar graphs to represent their results. One thing I noticed was that a number of students struggled with the folding and with following the step-by-step directions. It reminded me how complex spatial reasoning and procedural thinking can be for students at that age. At the same time, I could see how activities like origami could be very useful in the classroom—not only for connecting to mathematics, but also for developing perseverance, spatial thinking, and the ability to follow and interpret sequences of instructions.

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?

Draft Group Project: Multiplication Through Art, Play and Place

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Week 8 Readings and Activity

 The article (Radakovic, Jagger & Zhao: Writing and reading multiplicity in the uni-verse) explores the relationship between mathematics and poetry and suggests that poetry can provide a meaningful way for students to explore mathematical ideas. The authors found that students engaged with mathematics in different ways through their poems, sometimes through structure, sometimes through metaphor or personal experience. They also argue that the meaning of a mathematical poem depends partly on the reader, meaning that different people may see different mathematical ideas in the same poem. 

Reading this article connected closely with my own experience working with poetry this week. I initially expected mathematical poetry to focus more explicitly on mathematical topics, similar to poems like Sarah Glaz’s What Can We Do If We Crave Certainty in Mathematics? I was also familiar with poems that follow mathematical structures, such as Fibonacci poems or Pi Day poetry where word lengths follow the digits of 3.1415…, and even traditional poetic forms like haiku which follow a 5-7-5 syllable structure. In the bridges poetry I also really enjoyed Marian Christie's Tree Clambering", which follows inspired by the Markov tree, a technique for obtaining solutions to the Markov equation 𝑥 2 + 𝑦 2 + 𝑧 2 = 3𝑥𝑦 - reading it in a different context, I would never have associated it with math. What I had not really thought about before was the idea that mathematics might simply exist within the poem itself, rather than being the explicit topic or rule guiding the poem.

First stop

My first stop in the reading was the poems themselves, particularly the ones structured around circles of increasing size. In Sakaki’s poem, the scale grows from one meter to ten meters to one hundred meters and continues expanding outward. While the poem describes everyday experiences and reflections about place and life, the structure reflects mathematical ideas about scale and patterns of growth. The mathematics is not necessarily the subject of the poem, but it shapes how the poem unfolds. It helped me see how math can exist in the structure and relationships within a poem rather than only through explicit mathematical language. As I read the poem, I also found myself imagining what I would place within my own concentric circles, which to me is a mark of a good poem.

Second stop

My second stop in the reading was the quote: “when we invited students to write mathematical poetry and necessarily consider what it might mean to read and to write mathematically and poetically.” This stood out to me because it made me realize that reading and writing mathematical poetry is not as straightforward as I first assumed. The authors explain that the meaning of poetry is influenced by the reader’s own experiences, understandings, and beliefs. In other words, different readers might see different mathematical ideas in the same poem. This made sense to me because the students in the article didn’t always show mathematics in the ways the instructors expected, but they were still engaging with mathematical ideas in their own ways.

Third stop

My third stop connects to the activity we did creating the four-word poems. I liked this activity because it followed a clear pattern, which felt very mathematical to me and by the end I didn't even need to sketch out the pattern anymore, it just flowed.. At the same time, I struggled to find words that actually worked within the structure. I tried the suggestion of using words that could function as both nouns and verbs, and I also experimented with whether punctuation helped the lines make more sense. I tried several different word combinations and, somewhat surprisingly, I found the process quite soothing. There was something calming about following the pattern and watching how the meaning shifted as the words moved. This is also the type of poetry I feel safest with, where there is a clear structure to follow. In some ways it reminded me of mathematics, starting with a pattern or rule and then exploring within it. At the same time, it made me realize that both poetry and mathematics probably ask us to move beyond the structure at times and I need to become more willing to experiment.

While working on the activity, I was also listening to a session from a virtual math conference last weekend. When the host was introducing the speakers, she mentioned Pam Harris' (from math is figureoutable!) philosophy is that Students math with confidence. She joked about struggling with using the word math as a verb, and I immediately wanted to try that combination in the four-word structure. I ended up with:

Students math with confidence

math students confidence with

math confidence students with

confidence math with students

confidence with math students

with confidence students math

with students confidence math

students with math confidence

Question for the group

After reading the article and trying the poetry activity ourselves, do you think mathematics in poetry needs to be explicit, or can structure and pattern alone be enough for something to feel mathematical?

Week 7 Activity - Nick Sayer's video

As I watched Nick Sayers’ talk, I found myself stopping a few times to scribble notes and just sit with certain ideas. His projects feel playful and inventive on the surface, but the more he explained his thinking, the more I realized how intentional and layered they are.

Stop 1 – 13:00

Around the 13-minute mark, I was struck by how Nick talks about mathematics and science as the mediums he uses to communicate bigger ideas - political, environmental, and social issues. Math isn’t the end point in his work; it’s the language he uses to tell a story. That immediately connected me back to our class discussions about teaching math for social and ecological justice. He’s not separating math from the world, he’s using scale, measurement, systems, and modelling to surface questions about sustainability, power, and impact. It reminded me of when we looked at redlining maps and how mathematical tools (mapping, data, scale) can expose inequities. His work feels like a lived example of math not as neutral, but as a way of making issues visible and tangible.

Stop 2 – 40:00

Around the 40-minute mark, when he starts talking about using bikes to create spirographs, I stopped again. What really caught me was that the patterns aren’t just about speed or rotation, they involve prime numbers. That immediately reinforced the idea of primes as the building blocks of numbers. I’ve done a “City of Primes” lesson before and I love how it elevates prime numbers and their importance in structure and pattern. Seeing primes show up in something as visual and dynamic as a giant bike-powered spirograph just makes that idea feel even more alive.

I also love spirographs in general, they fascinate kids (and honestly, me too. I never had one as a kid, so I made sure my kids had one and I probably played with it more than they did). The combination of bikes, gears, ratios, rotation, and pattern crosses beautifully into science with simple machines and proportional reasoning. It feels like such a natural STEAM connection. I would absolutely love to see a STEAM class try to recreate something like this or even a smaller-scale version of his sketchograph machine. Something where students physically build, test, adjust, and see the mathematics emerge through motion.

Stop 3 – 1:00:00

Around the one-hour mark, when he described Cycle the Solar System, I immediately started thinking about how powerful that would be in a Grade 6 classroom. Those massive space numbers are so hard for students to comprehend when they’re just written on the board. Scaling the solar system and physically travelling the distances makes it embodied, you feel the vastness instead of just hearing it. I could see this mixing beautifully with rate, ratios, proportions, percentages, and getting students outside and moving. It’s such a concrete way to make abstract scale meaningful.

It also connected to something I was doing just this Friday. I was working with a school and their Aboriginal Education worker using the large 11 m by 8 m Indigenous Peoples Atlas of Canada floor map. We were looking at how some Indigenous groups were displaced from their homelands and talking about potential math lessons using the map’s scale. We discussed tracking and measuring Chanie Wenjack’s journey - or at least how far he would have needed to travel to get home - and there are also arrows on the map showing forced relocations over distance. It struck me how similar this is to Nick’s solar system project: using scale and movement to help students understand distance in a way that carries emotional and historical weight, not just numerical magnitude.

What Nick Sayers’ work offers me

Nick’s work deepens my understanding of math-art connections by showing that mathematics doesn’t have to sit quietly behind the scenes. It can be visible, kinetic, public, and participatory. Math becomes something you ride, walk, draw, build, and experience. As a math teacher, this reminds me that conceptual understanding often strengthens when students feel scale, pattern, ratio, or structure in their bodies, not just on paper.

More than anything, I feel like his process gives permission to just try things - to build, test, adjust, and figure things out as you go. It shows that math can help tell important stories and that STEAM learning doesn’t need to be fancy or expensive. It really just takes curiosity, some risk-taking, and a willingness to let math move off the page and into real experiences.

Week 7 Reading

This article, written for the MACAS (Mathematics and its Connections to the Arts and Sciences) conference, introduces the theme of “circular movements of healing” through mathematics, arts, and craft. The authors bring together a series of collaborative projects - intergenerational labyrinth-making, fabric sculpting to explore curvature, embodied geometry in a spiral playground, ceramic practice-based research, crafting artifacts as collective “matters of care,” and learning from the circular structure of Capoeira - to examine what it means to work across disciplinary boundaries in slower, more embodied, and affective ways. They argue that efforts to integrate math with arts and craft often run up against institutional expectations and rigid views of mathematics, and they call for transdisciplinary spaces that attend to fear, alienation, embodiment, materiality, dialogue, and social justice as part of reimagining how mathematics can be experienced and learned


It was honestly hard to pare down my “stops” this week because each project felt unique, offering a slightly different entry point into what math could be. I took the course this summer that allowed me to virtually attend the MACAS conference, and I really appreciated the openness of ideas and willingness to rethink mathematics. My first stop was reading about Susan and Cynthia’s labyrinth work (which we’ve watched videos about in other courses). After last week’s reading, where students in a college liberal math class chose their own focus, I saw the parallel, this community chose labyrinths as their way into mathematics and as a way to confront math fear. There’s something powerful about allowing learners to make choices that matter to them. I was also reminded of a podcast I listened to this week about how differently our students are being raised - they are encouraged to advocate and think critically. They want to understand why they are doing the math we ask of them. I remembered my own students being fascinated by a labyrinth at a nearby church and could see how that could be a meaningful entry point. I was curious about why there was a labyrinth at a church, When I looked it up, I learned that a labyrinth isn’t a maze with dead ends but a single winding path to the center and back out again. It is a purposeful, reflective journey, and several churches have a long relationship with having labyrinths.

“By engaging with art in ways that honours these subtleties, learners and educators can cultivate a mindset that appreciates complexity, embraces uncertainty, and recognizes the creative potential inherent in chance. Experiences shaped through such practice can inspire learners to overcome hesitation, take initiative, make thoughtful choices, and grow, ultimately contributing to the transformation of their learning communities.

My second stop was in the section on ceramic sculpture and the idea of navigating real risks - collapses, cracks, unexpected outcomes - but how clay as a medium actually invites play, experimentation, and risk-taking. That immediately made me think of our push toward whiteboards and non-permanent surfaces in math classrooms to lower the stakes and encourage that same kind of intellectual risk. At the same time, it made me think about the downsizing of dedicated art, music, and shop classes. Fewer students get sustained opportunities to work deeply with materials like clay or instruments, and classroom teachers are often trying to compensate with limited supplies and support. I found myself wondering what we lose, not just artistically but mathematically, when students have fewer chances to engage materially, take risks, and learn through making.

“Could one radically re-imagine a mathematics department that is built around openness regarding epistemological and ontological approaches?”

My final stop was in the closing section where the authors discuss themes across the projects and return to the idea of re-imagining our institutions. This connects so clearly to the thread we’ve been following since our first curriculum course - questioning the structures we work within and asking what might be possible if we truly loosened them. The discussion of slow science and the values of slow practice in arts and design stood out to me. Rather than prioritizing efficiency, coverage, and acceleration, the authors point toward embodied making, intergenerational learning, material engagement, and time for resonance. It feels like a reminder that if we want different outcomes in mathematics education, we may need to rethink not only classroom practices, but the institutional rhythms and values that shape them. I feel like this course is really completing the circle we started.Returning to the questions we began with about curriculum, institutions, and what mathematics could become, but now with deeper language, broader perspectives, and a greater willingness to imagine something different.

Chronaki et al (2025). Circular movements of healing with maths, arts and craft: Reimagining disciplinary transversals for learning. In Proceedings of MACAS 2025, University of Moncton, NB.