Final Project by Sunny & Sukie

 Link to our presentation recording (Zoom recording): Recording

(Passcode: E5cb=J?3)

 

Link to our project handout: https://docs.google.com/document/d/1Rd_fGwEP3Jn0GVSfeA7LgSSL3TTCBNcn93IenWjvsDA/edit?usp=sharing

 

 

Link to our project slides: https://docs.google.com/presentation/d/19PKjZlaSiwAh-yv8yBW6UJCsy2vzECx12GoUEzOqDRY/edit?usp=sharing

Week 9 Origami Activity Reflection + Reading Reflection

I chose to watch Nguyen’s video on origami fashion, and I was amazed by her creativity in designing origami-inspired clothing. The idea of using an oven during the making process also surprised me and made me wonder whether there could be any safety concerns since the materials are fabric. I also found myself wondering whether the clothing pieces she creates are washable or if they are mainly intended for one-time wear. Either way, I was really fascinated by her creativity and impressive hands-on making skills.

For this week’s activity, I decided to try folding the Miura-ori pattern that Nguyen used in her clothing designs. I simply used a Post-it note that was sitting beside my computer. As I followed the instructions in the video, by the time I reached the third diagonal column, I began to notice a pattern in deciding which edges should fold up and which should fold down. What amazed me even more was learning that a simple folding technique like this can eventually be used in applications related to space and satellites. It is incredible to think that folding a piece of paper can connect to such advanced technological uses. I think this would definitely be something worth sharing with students, and it’s the kind of example that can really spark their curiosity and make them go “wow.”

I also wanted to share another origami-related thought. My daughter in second grade has been really into folding paper boats lately. While I was doing this week’s activity, I picked up one of her paper boats and started wondering what kinds of mathematical connections I could make from it. As I looked more closely at the paper boat, I noticed there are many triangles formed through the folds. It made me think that it could be interesting to ask her how many triangles she can find in her paper boat. This could be a simple way to start noticing geometry and patterns in something she already enjoys doing.

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Reading Reflection

Reading option b: Gwen Fisher (Bridges 2015) Highly unlikely triangles bead weaving 

Summary:

This article presents the artwork created by Gwen Fisher based on impossible figures such as the Penrose triangle and other optical illusions. These artistic structures are made using beads and a weaving technique known as cubic right-angle weave (CRAW). In the article, Fisher demonstrates how this technique can be used to construct beaded versions of shapes such as triangles, squares, and frames that resemble impossible figures. She also extends these ideas to polyhedral forms like tetrahedra and dodecahedra, which do not have corresponding optical illusions but still showcase interesting geometric structures. Through these examples, the author highlights how bead weaving can be used to explore mathematical ideas such as geometry, structure, and visual perception. Fisher also notes that this work is ongoing, as she continues experimenting with new ways to create additional impossible figures through bead weaving.

Stop 1:

The idea that impossible figures such as the Penrose triangle appear to be 3-D objects, but they cannot exist in real space really caught my attention because it shows how our brains can be easily tricked by visual representations. When I first saw images of impossible figures like the Penrose triangle, they looked completely realistic to me. However, when I think about how the structure would actually exist in 3-D space, I realize it is impossible. What I find interesting in Fisher’s work is how she used bead weaving to create a physical object that still produces the illusion. This makes me think about how mathematics, art, and perception are closely connected

Stop 2:

The main idea that Fisher used the cubic right-angle weave (CRAW) technique to create geometric bead structures that resemble impossible figures made me reflect on how mathematical ideas can appear in unexpected art forms. At first glance, beadwork may seem purely decorative, but the patterns, color arrangements, and structures actually require careful thinking about geometry, angles, and spatial relationships. This is also another good example that shows how mathematical creativity can exist in craft and handmade art, not just in formal classrooms.

Discussion questions:

• Could creating mathematical art such as beadwork or origami help students who struggle with traditional math instruction? 

• What challenges might teachers face when trying to integrate art-based activities into a mathematics classroom?

Project Draft: 3D Paper Model

 Contributors: Sunny Hu & Sukie Liu

Hi, everyone!  

This is our draft project!  We are working on a project of creating 3D paper models for the secondary math class geometry unit.  We attached the project worksheet that students will use and our project slides.  

 

Project Worksheet: https://docs.google.com/document/d/1Rd_fGwEP3Jn0GVSfeA7LgSSL3TTCBNcn93IenWjvsDA/edit?usp=sharing

 

Slides for the project: 

https://docs.google.com/presentation/d/19PKjZlaSiwAh-yv8yBW6UJCsy2vzECx12GoUEzOqDRY/edit?usp=sharing

Week 8 Fib poem & reading reflection

Here is my attempt to write 2 Fib poems on random themes I thought of at the moment...

A Simple Promise

Oh 

My

Princess 

Take my heart 

Though I am not rich

I shall give you all I can make

For a Great Mate

Hey 

You

You are 

Doing great

Know you are awesome 

Know you are great to be a mate

============ READING REFLECTION ==============

Reading option C:

Writing and Reading Multiplicity in the Uni-Verse: Engagements with Mathematics through Poetry”

by Nenad Radakovic, Susan Jagger, and Limin Jao

Summary: 

In this article, the authors explore how poetry can be used as a way to engage with mathematics beyond traditional methods. The authors describe their experience with pre-service teachers writing mathematical poetry and reflect on how reading and writing poems opened up different ways of thinking about mathematics. Although not all poems include explicit mathematical content, the authors realized that poetry allows learners to express personal experiences, emotions, and interpretations related to mathematics. The article suggests that poetry can help learners see mathematics in a different way, and encourage deeper reflection and engagement with mathematical ideas. 

Stop 1:

The example of students writing mathematical poems reminded me of an algebra poem project I saw during my practicum. I vaguely remember that students were asked to write a poem about an inspirational figure and then create an equation based on details from the poem to calculate the age of death of that person. It was definitely eye-opening to see a poetry writing project like this in a math classroom. At the time, I remember thinking how creative the assignment was, but also how challenging it could be for students who are not comfortable with poetry. I personally don’t think of myself as a poetic person, so I can imagine feeling a bit intimidated by a task like this. Still, it is a good example of how poetry and mathematics can intersect in unexpected ways. Activities like this show that mathematics can be expressed through language and storytelling, not just numbers and formulas.

Stop 2:

“ We hoped to read poems that took up our invitation to engage with mathematical poetry, and poetic mathematics, and illustrated their understanding and application of mathematical content. And, we were disappointed to find that students’ engagement and enthusiasm about mathematics was very different from ours” (p.3)

I think this quote reflects a situation that many teachers experience. Sometimes educators introduce something new with a lot of excitement, but students may not respond in the same way. Poetry, for example, was always a challenge for me because I never felt very confident writing it. I can imagine that some students might feel the same hesitation when they are asked to combine poetry with mathematics. In situations like this, I think it is important for teachers to create a supportive environment and provide examples to help students get started. Offering multiple entry points or different formats might also help students feel less intimidated. Encouraging students to try something new, even if it feels uncomfortable at first is an important part of learning.

 

Discussion questions:

1. Do you have any experience of doing poetry in math class? Do you think mathematical poetry helps students see mathematics differently?

2. If poetry is used as a way to explore mathematical ideas, should the focus be more on the mathematical accuracy or on the creative expression? How can teachers balance these two aspects in the classroom?

Week 7 Interview & Reading Reflection

 I finished watching the interview and found myself thinking about how much time, effort, and commitment artists like Nick Sayers dedicate to their work. I was really struck by the depth of thought behind his projects, as well as his persistence in seeing complex ideas through to completion. As I watched, I had a few “stop and think” moments along the way.

Around the 6-minute mark, Nick talks about how both he and his mother believed he wasn’t good at math until he got his own computer and started programming. This really resonated with me. I think this is the case for many students who believe they are “not math people.” Often, their mathematical interests or strengths don’t emerge until later, or until they encounter the right context or tool. Personally, I didn’t think I liked math until Grade 11, and I didn’t even consider majoring in mathematics until my second year of university. This made me reflect on how important timing and opportunity are in shaping students’ relationships with math.

Between about 18 and 23 minutes, Nick discusses his mathematical sculptures created from everyday materials such as garbage bags, cola bottles, and plastics. This section reminded me that both art and mathematics can be highly accessible if we pay attention to what’s around us. It made me think about how powerful it could be to invite students to see mathematical potential in ordinary, even recycled, materials.

At around 35 minutes, Nick introduces his work with spirographs, which instantly brought back childhood memories. I used to have a spirograph set and loved drawing the intricate, flower-like patterns, but at the time I had no idea there was mathematics behind them. Seeing this now highlights how mathematical ideas can be present in playful, aesthetic experiences long before we formally name or understand the concepts.

Near the end of the interview (around 1:47–1:50), Nick presents his work with space-filling fractals and empires, connecting them to histories of colonization. This part stood out to me as it showed how art, mathematics, culture, and history can be deeply interconnected, rather than existing as separate domains.

What does this artist’s work offer in terms of understanding math–art connections, and what does it offer me as a math teacher?

As a math teacher, I’m fascinated by the many ways mathematical ideas are embedded in Nick’s artwork. While some of his pieces operate at a level of complexity that may not be easily replicated in everyday classroom practice, they open up powerful possibilities for thinking about math–art connections. His use of accessible, everyday materials especially inspires me to think about how recycled or found objects could be used to create math-related art with students. This feels like a meaningful and worthwhile direction to explore, particularly in helping students see mathematics as creative, connected, and present in the world around them.

===========READING REFLECTION ================

Reading: Writing a Mathematical Art Manifesto by Fumiko Futamura

Summary: 

This reading builds on a workshop from the 2025 Bridges Conference proceedings,and explores the aim of developing a mathematical art manifesto that frames mathematical art as a form of expressive artistic practice rather than as illustration, demonstration, or pedagogy. The article discusses the historical context of manifestos, examines definitions and examples of works that may be considered mathematical art, and outlines the defining characteristics of an art manifesto. It also incorporates reflections and quotations from mathematical artists and identifies “rejected paradigms” that challenge conventional assumptions about both art and mathematics.

Stop 1:

“Doris Schattschneider wrote in her review of the 2005 Bridges Conference [11] that “Mathematics creates art”; “Mathematics is art”; “Mathematics renders artistic images”; “Hidden mathematics can be discovered in art”; “Mathematics analyzes art”; “Mathematical ideas can be taught through art.”

This quote reminded me of an earlier task in this program with Dr. Nicol, where we were asked to identify mathematics in nature. Examples included patterns in sunflowers and leaves, symmetry in butterflies, as well as fractals and spirals. These observations align closely with Doris Schattschneider’s ideas that mathematics can be understood as art and that hidden mathematics can be discovered through artistic and natural forms. At the same time, I believe that natural beauty involves more than just mathematics, even though mathematics often renders what we perceive as artistic images, such as those associated with the golden ratio. Although traditional mathematics textbooks do not always explicitly connect mathematical concepts to art, I agree with Schattschneider that mathematical ideas can be meaningfully taught and explored through artistic contexts.

Stop 2:

“What is Mathematical Art? I will choose work that meets at least one of the following three criteria: The art 

1. is based on a Mathematical phenomenon, or 

2. it is generated by a Mathematical process, or 

3. it is a personal response to Mathematics by the artist. 

Susan Happersett, artist [6]‘

This definition has changed how I view art, as it encourages me to actively consider how mathematics may be embedded within or connected to an artwork before identifying it as mathematical art. However, the third criterion prompted me to reflect more deeply on what a “personal response to mathematics” might mean. Does this suggest that the artwork is intentionally created in response to a specific mathematical concept, such as a piece developed for a mathematics-related project? In many cases, these criteria may be difficult to identify unless the artist explicitly articulates their intent or process. Nevertheless, I understand Happersett’s broader point: mathematical art invites viewers to look beyond surface aesthetics and thoughtfully examine the mathematical ideas underlying the artwork.

Week 6 Reading + Activity Reflection

Reading:

Dancing Mathematics and the Mathematics of Dance by Sarah-marie Belcastro & Karl Scaffer

Summary:

In this article, the authors explore the deep connections between dance and mathematics through ideas such as patterns, symmetry, graph theory, and choreography. By providing concrete examples of how mathematical concepts can be embodied and expressed through movement, they show that mathematics is not only present in dance but can also be experienced through it. The article highlights the usefulness and relevance of mathematics in different forms of dance, with the aim of helping readers see mathematics beyond abstract symbols and recognize its beauty and creativity in embodied forms.

Stop 1

“Each dance tradition has its own characteristic way of using mathematical concepts. For example, classical western ballet and Bharatya Natyam both use a strong sense of line” (p. 16)

It’s interesting to see that although there are so many different kinds of dance, they are all connected to mathematics in some way. In other words, there is always math behind the dances we see. When we watch a dance performance, we don’t usually notice the mathematics right away, but it’s fascinating to realize that mathematical concepts are embedded beneath the movements. This also reminds me of how mathematics can be a universal language. While different cultures and traditions have their own unique dance forms, there is still mathematics underlying the movements and choreography. That connection across cultures is really cool.

Stop 2

“He has explored polyhedra in dance using various props: PVC pipes, loops of string, and even fingers. In one dance, he used linked and glow-painted PVC pipes to make both polyhedra and whimsical shapes. This is an example of how mathematical ideas have led to dance movements that then led back to a mathematical question.” (p.19)

In the article, the authors provide many concrete examples of how mathematics is deeply linked to dance. What stood out to me is how simple, everyday materials such as PVC pipes, string, or even our own fingers, can be used to explore complex mathematical ideas like polyhedra. This highlights how mathematical thinking does not always require formal tools or written notation. Instead, it can emerge through movement, manipulation, and play. This makes me stop and feel both curious and amazed at how common mathematics is in our everyday lives, even in places we might not expect, like dance and art. 

Wonder:

How might using simple, everyday materials like string, sticks, or our own bodies change the way students experience and understand mathematical ideas? 

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Activity Reflection:

I tried the star-making activity inspired by Scott Kim and Karl Schaffer with my daughter, and it immediately reminded me of Cat’s Cradle, which seems to be a big hit among elementary students. My daughter loves playing it with her friends, creating increasingly intricate figures until there are no more twists left and the string returns to a simple loop again.I think this would be a great activity for teaching concepts related to geometry, sequences, and spatial reasoning. It can also be connected to ideas from knot theory in an intuitive, hands-on way. Beyond the mathematical concepts, this activity naturally encourages communication and collaboration, as students often need to explain, demonstrate, and problem-solve together. This feels especially suitable for younger grades since the materials are simple and accessible, as you only need a piece of string. Students can also explore and invent their own patterns, which opens up space for creativity and playful mathematical thinking.

My Star

My daughter's star

Our star

Week 5 Reading Reflection

Reading option A:  

Leslie Dietiker: What Mathematics Education Can Learn from Art: The Assumptions, Values, and Vision of Mathematics Education

Summary:

In this article, Dietiker draws on Eisner’s (2002) proposal of applying an artful lens to educational challenges and re-imagines the mathematics curriculum as a form of art. She argues that traditional mathematics instruction often follows predictable, standardized structures that can feel uninspiring and limit imagination. Instead, Dietiker invites educators to view mathematics learning as an art form that can spark creativity, insight, and renewed ways of seeing. She also suggests conceptualizing mathematics lessons as stories, intentionally crafted experiences rather than instructional manuals, to create richer and more engaging learning opportunities for students.

Stop 1: “ Mathematical aesthetic can generally be understood to be an individual's response to a mathematical experience, such as a sense of fit of a possible pattern or insight into an underlying structure of a particular problem.”

This made me pause to think about what mathematical aesthetics really means. Many people may not naturally associate mathematics with aesthetics or art, so I appreciated this explanation. Framing mathematical aesthetics as an individual’s response to a mathematical experience highlights the personal and experiential nature of learning mathematics. Rather than focusing solely on correct answers or outcomes, this perspective shifts attention toward the process, the moments of insight, and the feelings that arise when a pattern “fits” or a structure becomes clear. I think this approach has the potential to make mathematics more engaging and meaningful for students, especially those who struggle with viewing math as rigid or purely procedural.

Stop 2: “Interpreting mathematics as a story repositions mathematics curriculum from an instruction manual or a collection of facts to a form of art, intentionally crafted to offer aesthetic experiences for a set of students, whether positive or negative.”

The idea of conceptualizing mathematics lessons as stories resonated strongly with me. It reminded me of a course I took on teaching with illustrated materials, where one assignment involved creating a math concept book focused on patterns in nature. The book introduced foundational math ideas in a way that felt natural, engaging, and age-appropriate, particularly for students in Kindergarten to Grade 2. Connecting this experience back to Dietiker’s argument, I agree that integrating storytelling and artistic elements into math instruction can create meaningful aesthetic experiences. These experiences may help students see mathematics as something alive and connected to the world around them, rather than a set of isolated rules or procedures.

Discussion questions:

• What might it look like to intentionally design a mathematics lesson around creating an aesthetic experience, rather than focusing primarily on efficiency or coverage of content?

• In what ways could viewing mathematics as a story or art form challenge traditional expectations of what “good” math teaching looks like?