Reading Response: Writing and reading multiplicity in the uni-verse: Engagements with mathematics through poetry.

Radakovic, N., Jagger, S., & Jao, L. (2018). Writing and reading multiplicity in the uni-verse: Engagements with mathematics through poetry. For the Learning of Mathematics, 38(1), 2–6. 

Radakovic, Jagger, and Jao (2018) explore the intersection of mathematics and poetry, focusing on how poetic structures can help students engage with mathematical concepts like scale and place value. The article centers on Nanao Sakaki’s poem "A Love Letter," which uses concentric circles of increasing magnitude, from one meter to billions of light-years, to create a "topological map" of the universe. When students were asked to write their own versions, the authors shifted their focus from looking for "accurate" numerical data to embracing multiplicity - the idea that the reader’s personal experience and emotions are what give the mathematics meaning. By blurring the lines between "mathematical poetry" and "poetic mathematics," the authors argue that math is not a static set of rules but a dynamic, human system of interpretation

Stop 1: My first stop occurred on page 2 when the authors identified the geometric structure of Sakaki’s poem. The poem moves from a one-meter circle to 10 meters, then 100 meters, eventually leaping into light-years. In my classroom, scale factors are often taught through drawing candy wrappers in a scale or building 3D buildings, but here, scale is used to create a "shelter" or a "forest".  It shows that we can teach exponential growth not as a formula, but as a physical expansion of our own "lived experience". It reframes the number line as a journey outward from the self.

Stop 2: I paused again on page 4, where the authors discuss Roland Barthes’ idea that the "multiplicity is focused... in the reader". As a teacher, I am often the one holding the "right" interpretation of a math problem. However, the authors argue that when a student reads or writes a mathematical poem, they are actually "authoring" the math themselves. It challenges the "formalist approach" where every student is expected to decode the structure in the exact same way. It suggests that if a student uses numbers as "representative metaphors" for loss or love, even if they aren't perfectly accurate, they are still engaging in deep mathematical thinking.

Stop 3: The final stop was the analysis of Elizabeth’s poem about her grandfather’s funeral on page 5. The authors note that when she describes holding her mother's hand within a "circle of one meter," she is engaging with mathematics as an embodied experience. Math is so often seen as "disembodied and abstract". Seeing a student use a "third dimension" (referencing things "above" or "overhead") to express grief shows that math is not just in the head, and it’s a system of human interpretation inextricably woven into our nature.

A Question I Wonder

The authors suggest that poetry provides a "safe place" for students who are anxious about mathematics. Does it add to the anxiety of students who are in ELL programs?

Reading Response: A basketmaker’s approach to structural morphology.

 Martin, A. G. (2015). A basketmaker’s approach to structural morphology. In Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015 (pp. 1–8). IASS.

Alison Martin explores how ancient craft techniques like weaving and knitting are essentially physical algorithms. She argues that these traditional methods solve complex engineering problems related to surface curvature and structural integrity. By building physical models, Martin demonstrates how "nexorades" or reciprocal grids allow short, identical elements to support each other through friction and tension. This approach moves away from the idea of a central "hub" or connector and instead relies on the mutual support of the parts. Her work connects basketry to advanced fields like computer graphics and building science, proving that the hands of a maker are often doing the work of a sophisticated computer.

Stop 1: My first stop occurred on page 2 when Martin explains the "geometry principle" of introducing singularities to change the shape of a mesh. In my high school classes, curvature is often an abstract concept we describe with complex formulas, but Martin makes it tactile. She explains that in a hexagonal grid, a pentagon introduces positive convex curvature (like a ball), while a heptagon introduces concave curvature (like a saddle). It suggests we could teach the "math" of curvature by having students literally count the sides of shapes in a mesh to see why a surface bulges or caves in.

Stop 2: I paused again on page 3 where Martin discusses why physical models are superior to drawings. She notes that "weaving a topological object works better than trying to draw a picture" because a woven surface is transparent. In secondary math, we often struggle to help students visualize the "inside" or the connectivity of 3D shapes on a 2D chalkboard. Martin shows that the open gaps in a weave allow us to

"see through the layers," much like how scientists use soap films to understand minimal surfaces. The basket is a scientific instrument that helps us perceive spatial relationships that are normally hidden.

Stop 3:

I stopped again on "Sponge Morphology" on page 6. Martin describes sponges and corals as natural optimizers that use the "simplest algorithm" to create the most surface area with the least amount of material. It moves math out of the textbook and into the natural world. Instead of teaching "efficiency" as a word problem, students could study how these biological "space-filling" algorithms create high-strength, lightweight structures. It turns the classroom into a design lab where nature provides the mathematical strategy.

                                       

Question:

Martin highlights that these "algorithms" are built into the very act of weaving. How might our students' confidence change if we presented "crafting" as a form of "coding"? If they realized that they were already executing complex algorithms with their hands, would they be less intimidated by the symbolic and digital versions of those same concepts?

Response to the interview with mathematical/ STEAM artist, Nick Sayers

Sayers, N. (2025, January 21). Nick Sayers interview [Video]. Vimeo. https://vimeo.com/1166172275/3a7a243bce?share=copy&fl=sv&fe=ci

It was lovely to learn and listen to Nick Sayers's experience in bridging the gap between mathematical and scientific concepts and artistic practice.

Stop 1:  02:43 – 03:34

Sayers discusses how he began tearing and slotting together plastic tea cups to create modular polyhedral sculptures. He was looking for a more "geometrically symmetric" way to build a sphere than traditional methods. For a teacher in BC, this is a great look at the ADST (Applied Design, Skills, and Technologies) cycle. It moves geometry from a textbook exercise into a hands-on prototyping challenge. It’s a "low-floor, high-ceiling" activity where students can explore Shape and Space (Math 8/9) by physically building the "nets" of 3D objects using recycled waste. This is another activity that I could try with my Math 8.

Stop 2: 06:48 – 07:11

Sayers recalls his childhood experience with a Sinclair ZX81 computer, calling programming "maths by stealth". He mentions that while he found mental arithmetic "terrifying," he thrived in the logic of coding. This is a vital perspective for reframing Numeracy in our classrooms. At McRoberts, I see this daily in my IT classes: students who struggle with the "number facts" of regular math often excel when the focus shifts to pure logic and reasoning. By emphasizing symbols and structures over arithmetic, we can reach students who have a high potential for Computational Thinking but suffer from traditional math anxiety. These classes allow them to develop the logical thinking required for university-level work, even in majors where traditional calculus is not a prerequisite.

Stop 3:  36:00 – 38:00

Sayers demonstrates a bicycle-based drawing machine where the complexity of the art is dictated by the prime factorization of the teeth on the gears. He notes that complexity comes from mathematical relationships, not speed. This is such a powerful visual for teaching fractions and ratios. Often, when I review prime factorization in the fraction unit, it feels like an abstract chore for students, just a way to simplify fractions. But seeing it manifest as the "petals" of a drawing makes the math feel alive. It connects to the "Power Technology" side of our curriculum and reminds me that my job is to show students the "invisible engine" of prime numbers that runs the world around them.

Stop 4: 01:46:20 – 01:55:10

Sayers discusses his "Body Miniaturizer," a mechanical drawing machine that traces a person while a pen draws them at exactly 1:6 scale through a mechanical linkage called a pantograph. In the Math 9 curriculum, we teach linear relations and scale factors as static concepts on a Cartesian plane. This machine turns those coordinates into a physical performance. It’s a powerful reminder that scaling isn't just a multiplication problem on a worksheet - it’s a physical reality. Students who struggle to solve for x in a proportion can immediately see the point of it here: if the math is wrong, the drawing is distorted. This stop makes me want to move the desks aside and have students build their own linkages to see how a change in a pivot point (a variable) changes the entire output.

Understanding math-art connections and what to offer

Sayers’ work shifts the perspective of math from a "filter" (something you have to pass to get somewhere else) to a "medium" (something you use to build). It shows that art isn't just about the finished drawing; it’s about the mathematical constraints you set up to let that drawing happen. The "beauty" in his work lies in the elegance of the logic behind the visual. Sayers demonstrates that the logic employed in a computer lab is the same logic used in a bicycle gear or a sandcastle fractal. He provides a model for experiential learning, demonstrating that we don't just learn math to know it - we learn it to apply it. It validates the shift in our curriculum toward "Big Ideas" - understanding that ratios, symmetry, and scale are tools for interpreting the world.

Question:

In our current digital age, students are used to seeing images as 'data.' Your walk-in cameras make the physics of light a physical, 'embodied' experience. Do you think there is a mathematical 'truth' that students miss when they only interact with geometry and light on a screen versus seeing it projected in a physical room?

Project Outline

 Project Outline

https://drive.google.com/file/d/19ZzhM64hxteQBl3j768p84flquH7Csz6/view?usp=sharing

Original References

https://drive.google.com/drive/folders/14pkKKFAOj3rAdFPPInSpVnhupAc8RVRC?usp=sharing

Reading Response: Reenacting mathematical concepts found in large-scale dance performance can provide both material and method for ensemble learning.

 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 – Mathematics Education, 51(2), 331–346. https://doi.org/10.1007/s11858-019-01030-2

The article explores how groups of learners (quartets) can develop mathematical understanding by reenacting and remixing large-scale choreographed performances, specifically from the 2016 Rio Olympic Games opening ceremony. The researchers argue for a "design research" approach that forages for public media, like professional dance, and uses it as a "mathematical playground." By viewing video clips and then using their own bodies and simple props (like elastic bands) to recreate the patterns they saw, participants engaged in "intercorporeality." This process allowed them to explore complex concepts like symmetry, transformations of quadrilaterals, and the properties of triangles through a hybrid of dance and mathematics. The authors suggest that reenactment acts as a bridge between the physical performance and formal mathematical notation.

Stop 1: My first stop was on page 334, where the authors discuss "foraging" in public media for performances with mathematical potential. This shifted my thinking because I usually look for math in textbooks or pre-made manipulatives. The idea that a massive dance performance could be a "text" to be dissected and reenacted is powerful. It tugged on my sleeve because it suggests that our world is full of "found" mathematics that we just haven't learned to "read" or "perform" yet. It makes me wonder what other cultural performances, like sports plays or marching bands, could be used as rigorous math curriculum.

Stop 2: I paused again at the discussion of "intercorporeality" on page 339. In previous readings, we've looked at how an individual’s hands or movements help them think. Vogelstein and her team go further, showing how four people holding a single elastic band must coordinate their bodies to "become" a rectangle. This stop was significant for me because it highlights that math can be a team sport. In my classroom, students usually work on their own papers or in small group projects. Here, the "proof" of a rectangle’s properties isn't written, and it is felt through the tension of the band and the physical positioning of four different people.

Stop 3: The final stop that got my attention was on page 344, where the authors describe reenactment as a "supplemental" way to move toward abstraction. They aren't saying dance replaces formal math, but that it provides a necessary "material" experience before the symbols. This is a crucial distinction for a secondary teacher. Often, we jump straight to the symbols (like a^2 + b^2 = c^2) or use visuals to develop the mathematical proof of the formula. This paper suggests that if students first "reenact" the relationships between the sides of a triangle with their peers, the formula becomes a summary of an experience they’ve already had, rather than a foreign language they have to memorize.

A Question I Wonder

The researchers used professional choreography as the starting point for the students. What would the “story” of mathematics look like if the students were challenged to choreograph their own original dance based on a specific geometric theorem, rather than reenacting a choreography that has already been done? How would this fill the gap for students who are too self-conscious to move their physical bodies in front of the class?

Reading Response: What mathematics education can learn from art: The assumptions, values, and vision of mathematics education.

Dietiker, L. (2015). What mathematics education can learn from art: The assumptions, values, and vision of mathematics education. Journal of Curriculum and Pedagogy,  https://doi.org/10.1080/15505170.2015.1018943 

Summary

In this article, Leslie Dietiker draws on Elliot Eisner’s work to propose that mathematics curriculum should be conceptualized as an art form - specifically, a narrative or "story." She argues that the traditional North American math experience is often uninspiring because it lacks a compelling sequence or aesthetic arc. By reframing mathematical content through narrative elements such as characters (mathematical objects), setting (the context), and plot (the sequence of events and tensions), Dietiker suggests that teachers and curriculum designers can craft lessons that evoke wonder, surprise, and anticipation. Using a Grade 7 textbook example, she demonstrates how a "mathematical story" can transform the learning experience from a passive reception of facts into an active journey of discovery, ultimately aiming to "rewrite" how students perceive and experience the subject.

Stop 1: My first stop occurred on page 5, where Dietiker describes mathematical objects, like variables, functions, or geometric shapes, as "characters" in a story. In my classes, I usually introduce these as tools or definitions to be used. The idea that a parabola or a square root could have a "personality" or a role to play in a developing plot arrested my attention. It
made me realize that when we strip away the narrative, we turn these vibrant mathematical entities into static, lifeless symbols. It makes me wonder how my students’ relationships with math might change if they saw these objects as active participants in a mystery.

Stop 2: I paused again on page 7 during the discussion of "mathematical tension" and the "arc of a story." Dietiker points out that in a good story, we don't know the ending right away, and there is suspense. In math class, however, we often give away the "ending" (the formula or the answer) at the very beginning of the lesson. This point really stood out because it highlights why students often disengage - we have removed the drama. By providing the resolution before the conflict, we rob them of the aesthetic pleasure of the "aha!" moment. This stop suggests that I need to be more intentional about holding back information to let curiosity build.

Stop 3: The final stop was the idea of the "enacted curriculum" as a performance (page 4). Dietiker suggests that even a well-written "story" in a textbook can be ruined or elevated by how the teacher "tells" it in the classroom. This shifted my perspective on my own role. It’s not just about delivering content, and it’s about being a storyteller who manages the rhythm and "beats" of the mathematical discovery. It made me reflect on how often I rush through the "rising action" of a lesson just to ensure we cover the curriculum, effectively killing the story for my students.

A Question I Wonder

Dietiker focuses heavily on the "story" within a single lesson or textbook chapter. How can we maintain this sense of narrative and "aesthetic tension" across an entire secondary school year?