Week 9 activity: Exploring and noticing with weaving

This week I decided to try weaving for the first time. I tried to notice some mathematical processes/concepts while I was weaving. Below are 3 ‘stops’ I had while weaving. There were more stop moments, but I selected these for my post.

1: Number sense and visualizing numbers in a different way

While I was weaving, I knew that because my pattern at the end of the row was ending with the second color (not the one I started with), I knew I had an even number of rows without even counting them. Then, on the third row, when I was experimenting with a different pattern, I ended my row with 2 pink. But I knew that this was impossible following the pattern I was following because I had an even number of rows. In my mind, I was able to visualize the pattern I should have (1 pink, 2 black, 2 pink, 2 black, 1 pink), thus indirectly giving me the numbers of rows I had (8).

When I thought about it, I found my prediction interesting and decided to count the rows to see if my prediction was right, and it was! When I stopped knowing I had made a mistake somewhere, my brain was actually counting in a different way than I usually count (one, two, three, four, etc.) Now, I wonder if expert weavers have a different way of visualizing counting and numbers. I also wonder if having this visualization of numbers/number sense impacts how they see the world in general.

2: Very big number and length of a thread

I noticed that my sewing teacher is much better than I am at approximating the length of thread I need for how much I need to sew. I have not mastered this skill yet, so when I cut my thread, I usually get three times the amount of thread I think I need because I tend to underestimate this quantity. To do my weaving, I used some old shoelaces that I keep as a toy for my cats. At first, it seemed like long threads would be more than enough to cover the cardboard, but I underestimated again. Although, I think that the more I practice this skill (approximation of thread I need for bigger quantities) the better I get to visualize the length of the thread when weaved/braided/sewn. In the last course, we saw that the human’s inability to feel large numbers is a problem when we think about our relationships with the living things and the Earth (Renert, 2011). I believe that weaving/sewing/breading could help us feel and visualize large numbers better by seeing and feeling those long threads becoming a more manageable size. I also believe that practicing the skill of visualizing how much thread needed for a certain work can help develop an ability to understand large numbers better.

3: Retroaction from the art and what it can teach

Maria Letsiou explains that doing ceramic work creates a meaningful environment to learn, because while someone is creating a ceramic sculpture, the sculpture speaks back to the artist, offering opportunities for lucky discoveries (Chronaki et al., 2025). When I was weaving, I had many moments where I was able to tell myself: “Wow, I finally experienced what it means to have an artwork speaking back to me!” The first example is when I knew I made mistakes; the piece did not look ‘right’. Another example is that the more I was weaving, the more I felt how sturdy the artwork was becoming. I felt how sturdy it would become the more I continued the artwork. I also felt how flexible the piece was even though it was becoming sturdier. The piece taught me the physics of weaving and how useful weaved objects can be since they are certainly sturdy, while keeping a good flexibility, avoiding them to break easily. In this case, this would have been my serendipitous discovery.

References:

Chronaki, A., Gerofsky, S., Nemirovsky, R., Ryan, U., Lazaridour, E., Letsiou, M., Torretta, N. B. & Hillgren, P. (2025). Circular movements of healing with maths, arts and craft: Reimagining disciplinary transversals for learning. In Proceedings of MACAS 2025, University of Moncton, NB.

Renert, M. (2011). Mathematics for life: Sustainable mathematics education. For the Learning of Mathematics, 31(1), 20-29. https://www.jstor.org/stable/41319547

Arts/crafts and productive struggle in mathematics

In Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving, Fisher (2015) explores how to build highly unlikely shapes with beads. This idea came from the impossible triangle first drawn by Oscar Reutersvärd.

This is the impossible triangle made possible by twisting the beads.

The exploration of the impossible triangle led the artist to try different impossible shapes. The artist successfully created an impossible square, an impossible hexagon, and other impossible figures, even one that was never drawn before (impossible polyhedron)!

“An impossible triangle and other similar impossible figures are only impossible to construct in 3D if we assume the edges are straight and the connections are right angles (Fischer, 2015, p.100).”

This quote reminded me of Doolittle’s (2018) argument for a diversity of geometry, ones that allow us to get ‘off the grid’. In this article, because the artist was able to think outside of the grid (not assuming the edges and angles are straight), the artist was able to create an impossible triangle. This is a very good example of how the grid can fail to represent realities sometimes, and that other geometry could help us open our mind and be a more ‘truthful’ representation of a reality. Because the artist decided to follow unconventional geometry, this creative exercise led to the exploration of mathematics not many thought about before (we know it by the given name unlikely figures!). I wonder if we could reach this level of creativity by solely solving problems. It feels like bringing explorative arts activity in the classroom is more approachable than problem-solving to encourage students’ creativity. Since students are not enough reminded of the importance of creativity in mathematics, they often get really anxious when I ask them to be creative. Then, if we start with those types of activities, we can change the classroom’s mindset to have students who embrace creativity. When they do recognize the importance of creativity, we might see more and more creative approach to problem solving. I believe that creativity is one of the most important qualities a mathematician can have because we know that many mathematical concepts/theorems that we use today came from mathematician who dared thinking outside of the box.



“The right photo in Figure 3 shows my second attempt, the first successful highly unlikely triangle (Fischer, 2015, p. 101).”

This quote resonated with me because it reminded me of the concept of productive struggle I have been looking into for my school this week. Productive struggle, define as overcoming a challenge with the purpose of learning or progressing, is important for students to truly learn and understand the concept, rather than just learning procedures (Sangiovanni et al., 2020). Although, many students do not see the importance of struggling to learn. In my classrooms, this looks like students who are giving right away just because they do not know how to get to the answer right away or do not understand a concept right away. Because I teach grade 9-10-11, it is really difficult for me to break this habit since my students are so used to it and never had to struggle that much to get good grades before.

Thus, I think that using mathematics activities based on arts and craft could help me re-story my students’ idea of learning. In the article, the artist was not successful in the first attempt, but learned from it and was successful in the second attempt. I am assuming that Carolyn Yackel, from the video How Orbifolds Inform Shibori Dyeing (G4G Celebration, 2021), and Uyen Nguyen, from the video Origami fashion (YOUmediaChicago, 2021), also struggle a lot to be able to have such in-depth knowledge about their different patterns (origami clothing or dyeing). All three artists had something else in common: their passion kept pushing them forward. Artistic creation might not develop this type of passion in all of our students, but if it does reach some of them to some degree, it should be accessible to them. If passion makes my student learn to struggle and understand its importance, it is something certainly worth using in my classroom.



Questions

What mathematics do you see in beading and creating 3D shapes with beading?

How do you foster creativity in your classrooms?




References

Doolittle, E. (2018). Off the grid. In Gerofsky, S. (Ed.), Geometries of liberation. Palgrave. https://doi.org/10.1007/978-3-319-72523-9_7

Fisher, G. (2015). Highly unlikely triangles and other impossible figures in bead weaving. Proceedings of Bridges. (pp.99-106)

G4G Celebration. (2021, January 27th). Carolyn Yackel - How Orbifolds Inform Shibori Dyeing - CoM Oct 2020. [Video]. Youtube. https://www.youtube.com/watch?v=hjtc9LJ5ItI

Sangiovanni, J. J., Katt, S. & Dykema, K. J. (2020). Productive struggle: A 6-point action plan for fostering perseverance. Corwin.

YOUmediaChicago. (2021, January 07th). Origami Fashion with Uyen Nguyen Part 1. [Video]. Youtube. https://www.youtube.com/watch?v=i4AoN1DtH6I

Draft presentation

 Below is the link to get access to my presentation's folder on Google Drive. 

https://drive.google.com/drive/folders/1mMtoQEkHZbtP8MpESo9VSOACQFBXMsPX?usp=drive_link

Week 8 activity: Mathematical poems

This week was very cold, so I had to stay inside for most of it. The poem below represents me looking at the land through the window.

Dreaming through the window on a cold Wednesday

Wind blowing over spirits

Blowing wind spirits over

Blowing spirits wind over

Spirits blowing over wind

Spirits over blowing wind

Over spirits wind blowing

Over wind spirits blowing

Wind over blowing spirits

Wind blowing over spirits

The Gift of Love

A

hand

Holding

my cold hand

On a summer day

The sun shines through the gray clouds

Firstly, I really liked to be able to connect my whole self (body, mind, and emotions) with mathematics because we have so few opportunities to do so. Furthermore, I enjoy poetry and I am always amazed by how poets can be impressively creative with the patterns they use to write and express different meanings. Before this week, I never made the connections between these patterns and doing mathematics, so it was an enlightening moment.

Secondly, after trying out some poems, I discovered some mathematical thinking processes that can be involved in poetry. I had to guess and check, count, try out and verify my work, work systematically and find an efficient way to record my trials. Sadly, I used my eraser a lot, so I do not have all the attempts, but you can see in this picture my original poem.

I decided that I did not like some of the combinations with the part ‘a tree’, so I started the first few lines again. And then, I changed the different parts and tried different combinations (I erased a lot) for the first 3 lines and finally liked one enough to continue writing the whole poem.

To make a connection with my article this week, the process that I used is a demonstration of how I used knowledge (patterns) in a dynamic way: using it to carry a meaning, trying out ideas and verifying them, simplifying it to make my work easier, mentally visualizing the pattern, etc.

Finally, I believe that many of my students would like to do an activity like this one (writing a mathematical poem). Like me, they would like to feel human while doing mathematics. Also, like mentioned in Writing and reading multiplicity in the universe: engagement with mathematics through poetry, poems can be a way to feel safe while engaging with mathematics (Radakovic et al., 2018). I have many students who demonstrate math anxiety while problem-solving, even if the problem is open and have multiple ways to get to the answer. Making them engage with mathematics through a poem could help them not feel this anxiety while doing mathematics, at least for this activity. Finally, poems can also be a way to connect mathematics to students’ world (Radakovic et al., 2018). In grade 9-10-11, there are not that many concepts that we can connect to my students’ daily life. Using mathematics within poetry could give them a rare chance to make this connection.

Reference:

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.

Mathematics is dynamic

This article relates the experience of using a poem A Love Letter by Nanao Sakaki to engage university students (in a mathematics teaching course) with mathematics and poetry. This entryway was chosen because the writers believed it was a safe way to engage the students with mathematics. Even though there were some challenges and uneasiness felt by the students (some even not doing the assignment), 10 students created a similar poem as A Love Letter. To the authors’ surprise, they did not use accurate representations and scales, but they did engage with mathematics and use mathematics to create meaning in a poem.

“Our opening of teaching mathematics to the inclusion of poetry also required an opening of our thinking about mathematics, of what it was and what it could be. (3)”

This quote made me stop because it tied in well with what we were exploring last week. First, it reminded me of Katelyn’s manifesto. In her manifesto, she is really thinking about how to move from the ‘traditional view of mathematics’ brought by Western philosophical tradition toward a broader definition that can include more activities/behaviours in the field of mathematics. Secondly, it ties into Nicholas B. Torretta’s (2025) idea of how to reorient practices under a decolonial perspective by asking ourselves what needs to be respectfully challenged in the field of mathematics, what needs to be undone, to what should we come back, and what should we continue?

I am often wondering how I could convince a skeptical colleague that mathematics can be found in arts because to include those practices in our classrooms, we need to be convinced that they are useful and work. A possible answer to my questions is to discuss with skeptical colleagues about their idea of math, what is good, what should be rejected, what we want students to be able to do with mathematics, and thus, write our own manifesto.

Have you ever tried to convince a skeptical colleague/any other person that the ‘innovative’ activities you are doing with your students are mathematics? Were you able to convince them mathematics is broader than what we normally see?

“According to Derrida, meanings are not stable but are instead caught up in the endless play of relations and difference between signifiers (words) and signifieds (concepts). And this play is dependent on the reader and the reader’s prior uses and understandings of and experiences with those signifiers and signifieds” (4)

I had to re-read this a couple of times to understand the idea. It was applied to reading poetry, but I think it can also be applied to mathematics. Now, I understand that meaning can be different depending on the learner’s previous experiences. I also understand that there could be more than one meaning. Both elements make meaning making a dynamic process that is dependent on the learner. During this course, we learned that using different perspectives to teach mathematics concepts can help students build meaning because everyone is different and has different ways of seeing/understanding the world. Thus, meaning making in mathematics is just as dynamic and dependent on learners’ prior experiences than reading and analyzing a poem. Is it why people started making connections between mathematics and poetry? Do you understand something else or different from this passage?

“In this way, we see mathematics and poetry aligned with Davis and Renert’s (2014) view of mathematics as collective, connected, and context-dependent enterprise in which the focus is on knowing (something dynamic) rather than knowledge (something static).” (6)

I believe that this definition of mathematics is a good summary of what we learned in this program about mathematics and thinking mathematically. For example, Sfard (1991) explains that even if seeing mathematical concepts as static objects is prevailing in the mathematics field, mathematicians also use processes, algorithms, and actions associated with the concepts, they manipulate concepts (thus making mathematics also dynamic). We can also think about Cuoco’s et al. (2010) mathematical habits of mind that defines doing mathematics. Lastly, Dan May’s poem Division by Zero represents well this idea of mathematics being dynamic by looking into someone’s mind while investigating a concept. We can see the actions happening in someone’s mind while doing mathematics.

Remembering that mathematics focuses on knowing (how you use the mathematical concepts that you know) is essential to understand how poetry can be used to teach mathematics. I am thinking about using the poem with my grade 10 class. I expect my students to know and have an accurate idea of what we can find in an area with a radius of a meter, 10 meters, 100 meters, etc. I am also expecting them to be able to continue the exponential pattern. But what I want them to learn is how they are going to use this knowledge to create meaning in a poem, thus changing the focus to a dynamic use of the concepts.

Questions:

Have you ever tried to convince a skeptical colleague/any other person that the ‘innovative’ activities you are doing with your students are mathematics? Were you able to convince them mathematics is broader than what we normally see?

Do you understand something else or different from this passage?

References:

Cuoco, A., Goldenberg, E. P., Mark, J., & Hirsch, C. (2010). Contemporary curriculum issues: Organizing a curriculum around mathematical habits of mind. The Mathematics Teacher, 103(9), 682-688. https://doi.org/10.5951/MT.103.9.0682

May, D. Division by zero. Mathematical Poetry at Bridges 2026. Retrieved on https://www2.math.uconn.edu/%7Eglaz/Mathematical_Poetry_at_Bridges/Bridges_2026/The-program-and-the-poets-2026.html

Sfard, A. (11). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.

Nick Sayers Interview

Stop 1: “Number as mathematicians are neutral, they have no meaning. Inside my brain, numbers have massive significance, and I’m massively superstitious about it (29 min 33s).”

This moment was a stop for me because it opened my mind to a different way of seeing/living numbers. I like art, but very differently than Nick Sayers. I enjoy art once in a while, but I am not craving art. I do not have the talent/creation creativity to do what he does, and I am more the type of person to see numbers as neutral. But by hearing him explain how he sees and lives numbers helped me understand how some of my students might feel toward numbers. Now, I think it would be a waste of talent and opportunity to not let those students use their strengths and develop them. I understand better the necessity of having a balance between learning traditional math and learning math through other disciplines like the arts. To make a connection with the article I read this week, this is a good example of why we need to start implementing more activities that transverse the traditional boundaries associated with mathematics. By opening this door to students, we might discover talents and different perspectives on certain topics.

Stop 2: “It was an interesting sort of thinking of places where here would be enough big movements over the year […] and it was a complete guessing game of what would work and what wouldn’t (1h 44min)”

This moment inspired me to create the same type of project with my students. I think this is interesting because having to think about the environment and the living things to create art and investigate science and mathematics is a great way to embrace the First Peoples’ learning principle: “Learning is holistic, reflexive, reflective, experiential, and relational (focused on connectedness, on reciprocal relationships, and a sense of place)( First Nations Education Steering Committee, n.d.).” By having the students explore the land and learning from it, trying to figure out how different places offer different types of pictures and by having them produce art from their land is a holistic experience able to connect them with the land.

Stop 3: “I realized that when I took my camera low down, it looked like a sort of ancient, sort of a ruined city of castles like a ruined empire, like an empire of dust (1h 49min).”

This made me stop for two reasons. First, it is interesting that the different scale (lowering the camera) offered a different view on the artwork. It confirms that working with different scales can offer different perspectives and allow learners to develop new ideas (Chronaki et al., 2025). Also, it shows that creating artwork is a process where you try an idea, create some of it, verify your work, create a little more, verify again, look at it under a different perspective, and then decide if the artwork is good or not. This process is very similar to guess and check we use in mathematics! Now, I can see how creating mathematical artworks could help students become more risk takers in mathematics tasks.

Secondly, I thought this was a good example of how mathematics can be used to represent data. This is a good example of what D’Ignazio & Klein (2020) call data visceralization; a data representation that the body can experience both emotionally and physically.

What does this artist's work offer you in terms of understanding math-art connections, and what does it offer you as a math or science teacher?

Other than what I discussed in my stops, this artist’s work made me see with concrete examples how arts can open up different perspectives, offer new engaging learning activities, can offer different scales to work with certain mathematics concepts, and can help us re-think our relationships with the Earth and the living things.

Questions:

When you presented/created your projects with learners, what were their reactions? Did they enjoy it? Were they aware they were doing math/science?

Did you ever have to convince someone that your work was mathematical? If so, what did you tell them?

References

Chronaki, A., Gerofsky, S., Nemirovsky, R., Ryan, U., Lazaridour, E., Letsiou, M., Torretta, N. B. & Hillgren, P. (2025). Circular movements of healing with maths, arts and craft: Reimagining disciplinary transversals for learning. In Proceedings of MACAS 2025, University of Moncton, NB.

D'Ignazio, C., & Klein, L. F. (2020). Data feminism. MIT Libraries Experimental Collections Fund. https://doi.org/10.7551/mitpress/11805.001.0001

First Nations Education Steering Committee. (n.d.) First Peoples Principals of Learning [poster]. Retrived from https://www.fnesc.ca/first-peoples-principles-of-learning/

Circular movements of healing with maths, arts and craft: Empowerment

Circular Movements of Healing with Maths, Arts and Craft: Reimagining disciplinary transversals for learning recounts experiences where the authors tried to cross over disciplinary boundaries found in science and mathematics. Susan Gerofsky’s project details how adults re-storied their relations with mathematics while investigating the mathematics of mazes. Ricardo Nemirovsky explains how sculpting (especially passing from 2D figures to 3D shapes) can develop new knowledge on geometry, even for adults who are familiar with geometry. Anna Chronaki and Ulrika Ryan show the tensions student teachers can feel while exploring geometry with their body and making connections between the geometry and curriculum content. Maria Letsou describes how ceramic sculpture can support the development of risk-taking and the use of serendipity across disciplines. Anna Chronaki and Eirini Lazaridou show how to counter hierarchies by bringing children and adults to learn together while creating crafts. Nicholas B. Torretta details the lessons institutions should learn from capoeira: respectfully challenging what is already in place and re-connecting with the past and ancestral knowledge to give opportunities to re-continue. Overall, Circular Movements of Healing with Maths, Arts, and Craft argues for the need of mathematics and science disciplines with a slower pace, that transcend the hierarchies and boundaries usually present in the field, and re-connect the disciplines to the living things, the planet, and humanity.

“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.”

This passage was an important learning moment for me. In my school, the lack of risk-taking and resilience is a problem that is commonly identified by our mathematics teacher from grade 1 to 11. In my groups, the most successful students are those who are willing to take risks: try out an idea even if they are not sure that it is the right way to solve the problem. I needed to take risks to be able to be successful in Cegep, where I started being more challenged by STEM courses. Although, it seems that the way we teach mathematics now is doing the opposite of encouraging risk-taking. Each year, I get more students with math anxiety and refusing to put some work down if they are not 100% sure how to do it. It seems that they are so afraid of not getting the final answer right that it is not worth trying anything. Thus, I agree with the article’s arguments for the need of transversing disciplinary boundaries and re-thinking some of our systems. If the way we teach mathematics was perfect, we would see students being confident in taking risks. And if transversing disciplinary support positive attitudes towards risk-taking, then we definitely need more or those activities in our classes. It could also help students see that they have strengths in mathematics they were not aware they have. For example, Nick Sayers mentioned at the beginning of the interview that he thought he was bad at math (Gerofsky, 2026). I am sure our classrooms are full of students like Nick Sayers, who are exceptional artists, scientists, and mathematicians, but are not aware of it because of the boundaries present in science and mathematics.

”The task was integrating, relaxing, and empowering the participants.”

After I read this quote, I started wondering how this activity or using the body and the arts to explore mathematics in general can empower learners. Paolo Freire wrote that a radical person is someone who does not get imprisoned by the circles of security, but rather work to deconstruct those circles (1968/2021). The boundaries present in sciences and mathematics can be seen as those circles of security, circles we have been reproducing without questioning their relevance in our time. Transversing the boundaries and the hierarchies allows more people to enjoy mathematics, promote risk-taking, creates new ideas and new ways of seeing mathematics concepts, to redefine our relationships with the world and the living things (Chronaki et al. 2025; Gerofsky 2026), and to be critical about what we learn and how we learn it (Chronaki et al. 2025). Transversing the boundaries aligns with all of the values of mathematics for human flourishing defined by Su (2020). Thus, transversing the boundaries empower learners by allowing them to question the methods that have always been used and by showing to more people they can be mathematicians as well, and that their ideas, even if different, are valuable. In my classroom, using the body and the arts to teach mathematics empower my students by allowing them access to mathematics. It shows them that they can be part of the mathematics community without having to leave a part of themselves behind. It gives them the power to want to struggle, to continue mathematics after high school and pursue STEM careers, which is an important need in the community.

Questions:

How is teaching mathematics through the arts and the body empowering the students in your classroom? Do you notice using the arts and the body improves your students’ willingness to take risks?

References:

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.

Freire, P. (2021). Pedagogia do oprimado. (É. Dupau & M. Kerhoas, Trans). Éditions de la rue Dorion. (Original work published 1968)

Gerofsky, S. (2026, February 18th). Nick Sayers interview. [Video]. Vimeo. https://vimeo.com/1166172275/3a7a243bce?share=copy&fl=sv&fe=ci

Su, F. (2020). Mathematics for human flourishing. Yale University Press. https://doi.org/10.2307/j.ctvt1sgss