Week 6 Reflection – Mathematics, Movement, and Embodied Understanding

 Summary of Campbell & Von Renesse – Learning to Love Math Through Explorations of Maypole Patterns

Campbell and Von Renesse explore how mathematical understanding can emerge through embodied, collaborative exploration using Maypole dancing and ribbon weaving as a medium. Rather than beginning with abstract notation or symbolic representation, the authors position movement and colour as entry points into structural reasoning. As students repeat crossing movements around the Maypole, woven patterns emerge that show repetition, rotation, and movement across the design.

The article emphasizes that learners often discover mathematical structure before they have formal language to describe it. As dancers rotate and interlace ribbons, visible patterns emerge that reflect underlying algorithms. Each change in movement sequence produces a new woven structure. In this way, choreography becomes geometry, and repetition becomes mathematical reasoning.

A key theme in the article is joy, not as entertainment, but as intellectual engagement. Students are not passively following rules; they are constructing them. They experiment with colour order, crossing sequences, and movement rhythm. The resulting patterns are not decorative accidents; they are the frozen traces of embodied mathematical decisions.

Ultimately, the article argues that mathematics can be experienced as relational, aesthetic, and communal. Movement becomes a legitimate pathway into abstraction. 

Three “Stops” While Reading

Stop 1 – I Had to Illustrate the Patterns to Make Sense of Them

As I worked through the woven Maypole images, I realized that I could not understand the patterns by simply looking at them. I had to draw them. Recreating the structures allowed me to isolate repeating units and identify strand directions.

Rather than reading the colour sequences horizontally, I began tracing structural paths and searching for rigid shapes that repeated. The act of drawing shifted my thinking from noticing colours to identifying generative rules.

Illustrating the patterns became a form of mathematical reasoning. It forced me to slow down and reconstruct the logic embedded in the weave.

I began to struggle when I reached Figure 20, so I reorganized the pattern in my mind using letter notation. Labeling the sequence as BB BB WR helped me isolate where that structure actually appeared within the image. Instead of scanning the pattern visually, I traced the sequence systematically to locate its repetition. Once I adopted this strategy, I continued using it with all the remaining figures. Creating my own simplified representations that matched the assigned letter sequences made it much easier to identify the structural logic of each pattern. Reconstructing the images in this way allowed me to see the repetition more clearly and understand how the sequence generated the overall design. 

Stop 2 – It Felt Like Tetris

At one point, the patterns began to feel like a Tetris game. I found myself identifying composite blocks small rectangular units that could rotate and translate across the pattern. Instead of reading strings like BB BR GW, I began seeing rigid shapes that interlocked.

This shift changed my perspective from linear sequence to spatial transformation. I began thinking about rotation, translation, and symmetry rather than simple repetition. The patterns were not just alternating colours; they were tessellations generated through movement.

Stop 3 – A Cartesian Plane Might Have Helped

Another pause came when I wondered whether placing the patterns on a Cartesian grid would clarify the structure. If I could mark repeating intersections and locate centers of rotation, I might more easily identify the translation vectors and symmetry points.

Some patterns were easy to sit with; others required sustained concentration. I imagined physically cutting out shapes and placing them on a grid to test rotational symmetry. This reflection revealed how embodied mathematics and formal geometry could support each other rather than exist separately.

Reflections on the Videos

The videos reinforced the idea that mathematics lives within movement.

The early video featuring adults reflecting on childhood mathematics revealed how deeply math is embedded in lived experience: cooking, knitting, climbing stairs in different configurations, playing with geometric toys. Movement and structure often precede formal naming.

Malke Rosenfeld’s Jump Into Math! talk was particularly compelling. Watching her create rhythm with her feet demonstrated how mathematical relationships can be heard and felt. Rhythm becomes number. Timing becomes ratio. Her classroom integration of body percussion shows how conceptual understanding can be strengthened through coordinated movement.

The Rhythm of Math videos further emphasized this idea. The clapping sequences required intense concentration and collaboration. The 3-against-4 rhythm made proportional reasoning tangible. You could hear the mathematics at work.

The string and sword dance videos connected most directly to the Maypole reading. Watching dancers maintain a closed loop while executing precise sequences highlighted the algorithmic nature of movement. The patterns were not accidental, they were generated through rule-based choreography. The visible concentration on the dancers’ faces reinforced that maintaining structure requires attention to sequence and symmetry.

Across all videos, one theme remained consistent: movement makes structure visible.

Final Activity Reflection

Adrienne Clancy – Dancing Rotations

Adrienne Clancy’s discussion of rotation, including the Earth’s 23.5º tilt, reframed rotation as lived experience rather than static diagram. Watching her embody rotation emphasized that angles, axes, and symmetry are not merely drawn; they are enacted.

This resonated deeply with my own classroom practice this week.

I read Pitter Patter Pat to my Kindergarten–Grade 2 students in the library. The book explores patterns in time, nature, and dance. After reading, we stood together and created a simple movement pattern involving clapping, stomping, and jumping. The students physically enacted the pattern.

In that moment, mathematics was not abstract. It was rhythmic, communal, and embodied.

Our school is currently focusing on respect for self and others, including body awareness. Movement-based mathematics supports this work. Coordinated rhythm requires listening, awareness of space, and attention to others.

This week affirmed that mathematics is part of the palette of choreography. It shapes how we move, how we see structure, and how we understand the world. Whether through Maypole weaving, rhythm, sword dancing, or children’s storybooks, mathematical ideas emerge through embodied engagement.

Week 5: Developing mathematics pedagogies that integrate embodied, multisensory, outdoors and arts-based modalities

 Kelton and Ma’s article explores how mathematical understanding shifts when classroom space is reconfigured to allow whole-body, multi-party collaboration. Rather than treating mathematics as a silent, individual, desk-bound activity, they argue that meaning can emerge through coordinated movement, shared attention, and spatial interaction. The authors emphasize that embodied activity must remain mathematically purposeful movement is not an add-on or substitute for mathematics, but a medium through which structure can become perceptible. When learners negotiate rhythm, position, gesture, or material together, cognitive load is redistributed across bodies and space. In this way, abstraction grows out of participation rather than preceding it.

Stop 1

My first “stop” in engaging with this idea came while watching the dance video. As Sarah Chase layered 3 against 2 rhythmically, I became aware of my own discomfort. I could calculate 3 and 2 symbolically without hesitation yet holding those rhythms simultaneously in my body felt complex and disorienting. I realized that I would need to map the structure or create a visual guide to stabilize it. That moment made me understand something important: embodiment reveals structure, but I personally need representation to organize layered patterns. This tension between bodily experience and structural mapping became the kernel for my exploration.

Stop 2

The second stop occurred when I began thinking about cycles more broadly. The dancer’s layered movements reminded me of seasonal rhythms and how time might have been measured historically through repeated embodied observation before symbolic notation existed. The idea that alignment, when patterns coincide, could signal meaning connected directly to mathematical periodicity. In both natural cycles and rhythmic dance, repetition and return carry structure.

Stop 3

The third stop emerged as I considered prime numbers. If rhythms like 3 and 2 eventually align, what happens when the numbers share no common factors? The idea of working with 5 and 7, both prime, intrigued me because their patterns would only coincide at a larger interval. This heightened the visibility of least common multiple as structural alignment rather than procedure.                                                                                     

 

 

 

  

 

My Vintage C- Rods 

Stop 4

The fourth stop was material. Knowing I needed a way to externalize the rhythm, I turned to Cuisenaire rods. The rods allowed me to “freeze” movement into colour and length, transforming dynamic rhythm into tangible structure.

For my activity, I selected 5 (yellow) and 7 (black). Instead of using the single rods, I decomposed each number. I constructed 5 as 3 + 1 + 1 (a green rod and two white rods), and 7 as 4 + 2 + 1 (a pink rod, a red rod, and a white rod). I then built two horizontal trains, extending each repeatedly and lining them up side by side. As the trains grew, the coloured sequences repeated. Eventually, both trains aligned at a total length of 35. At that moment, the patterns coincided, and the sequence would begin again. What the dancer embodied as layered rhythm, I could now see and touch as periodic structure. The least common multiple was no longer an algorithm; it was a moment of visible alignment.

 

 

Cuisenaire rods were developed in the early 1950s by Belgian teacher Georges Cuisenaire as a way to help students discover number relationships concretely. Later popularized by Caleb Gattegno, the rods were designed not as counting tools but as relational tools. Each colour corresponds to a fixed length: white (1), red (2), light green (3), purple/pink (4), yellow (5), dark green (6), black (7), brown (8), blue (9), orange (10). The colours are intentionally distinct and not scaled in a visually obvious gradient, encouraging proportional reasoning rather than visual guessing. From their origins, the rods were meant to reveal structure, equivalence, factors, multiples, ratios, through comparison and construction. In my exploration, they functioned as materialized rhythm, redistributing cognitive load into space, much like Kelton and Ma describe.

Finally, this exploration brought me back to sweetgrass weaving. Braiding sweetgrass involves three strands crossing in a repeated and ordered sequence. Strength emerges through structured interweaving and return. Just as 5 and 7 create a repeating cycle that eventually aligns at 35, the strands of sweetgrass cross and return in predictable rhythm. The rods’ coloured trains echo that visual and structural repetition. In both weaving and mathematics, pattern is not decorative, it is generative. Embodied movement, material representation, and cultural practice converge through structure. In moving from dance to rods to written explanation and finally to weaving, I experienced how embodied inquiry can lead to deeper mathematical meaning without sacrificing rigor.

 

Draft Final Project Outline

 

Draft Final Project Outline

Course: EDCP 553-26 – Teaching & Learning Embodied Mathematics Outdoors & Via the Arts
Student: Tracy Parkes
Project Type: Individual project

Working Title

Braiding Relationships and Mathematics: A School-Based Culture Club Using Sweetgrass, Weaving, and Beading (Working title – subject to refinement)

Context and Learners

This project is situated in a rural Manitoba school serving Kindergarten to Grade 4 and Grades 9 to 12, where I work as the school principal. Rather than a traditional classroom-based lesson, this design takes the form of a school-based Culture Club, offered several times per month during non-instructional time (e.g., lunch hours).

The club intentionally brings together early years students and high school students in shared, hands-on cultural activities. High school students act as mentors and co-learners, supporting younger students while deepening their own understanding of culture, responsibility, and leadership. This structure is designed to strengthen school-wide relationships, connect students across age groups, and honour the diverse communities students come from.

Project Description

The Culture Club will rotate through Indigenous cultural practices, with an initial focus on:

• Sweetgrass braiding
• Weaving
• Beading

While other activities may be incorporated over time, this project focuses primarily on sweetgrass braiding as an entry point for embodied, land-based mathematical learning.

Sweetgrass is approached not only as a material, but as a living cultural practice connected to Land, memory, story, and responsibility. Learning begins with story, observation, and making, rather than formal instruction, reflecting Indigenous pedagogies that value learning through relationship and doing.

Mathematical Focus

Mathematics is embedded naturally within the cultural practices of the club. Core mathematical ideas include:

• Patterning and repetition (e.g., braid structures, bead sequences)
• Counting and grouping (e.g., strands, beads, stitches)
• Structure and sequencing
• Spatial reasoning (over/under, tension, alignment)
• Proportional thinking (relative lengths, balance, symmetry)

Mathematics is treated as emergent and relational, arising from careful attention to process rather than imposed as a separate task.

Embodied, Arts-Based, and Land-Based Pedagogies

This project integrates:

• Embodied learning through handwork, movement, and tactile engagement
• Arts-based learning through braiding, weaving, and beading
• Land-based learning through discussion of sweetgrass harvesting, location, seasonality, and respect for the Land

Learning experiences begin with story and lived experience, followed by hands-on making. Symbolic or paper-based mathematics may be introduced later to help students name, represent, or reflect on patterns they have already experienced physically.

Positionality and Rationale

As a school principal in a rural K–4 and 9–12 school, I do not have a traditional classroom, yet I remain deeply committed to contributing to meaningful mathematics teaching and learning. Designing and facilitating a Culture Club allows me to participate as a learner alongside students while supporting culturally responsive practices at a school-wide level.

My interest in this project is grounded in personal and family experience. Sweetgrass is not abstract or distant to me: it is connected to memories of my father working in hay fields, to the smell of sweetgrass while ATVing on the land, and to everyday encounters with place. I am drawn to sweetgrass as a living practice that connects past and present, family and community.

Inspired by children’s literature such as The First Blade of Sweetgrass, I want to learn more deeply about the significance of sweetgrass in my own culture and to share this learning with students and my grandchildren. This project reflects a desire to teach young people how to notice, locate, respect, and learn from the Land, while honouring Indigenous ways of knowing.

Role of High School Students

High school students will participate as:

• Mentors to younger students
• Co-learners engaged in cultural practices
• Supporters of school-wide community building

This intergenerational model reflects Indigenous understandings of learning as relational and collective, and it strengthens connections across the school community.

Intended Contribution

This project is designed as a practical, adaptable model that can be refined over time and shared with colleagues. It demonstrates how embodied, arts-based, and land-connected mathematics learning can occur outside a traditional classroom, while still engaging deeply with mathematical ideas.

 

Annotated Bibliography

 

Course: EDCP 553-26 Cohort: Teaching & Learning Embodied Mathematics Outdoors & Via the Arts

Institution: University of British Columbia (UBC)
Instructor: Dr. Susan Gerofsky
Student: Tracy Parkes
Student Number: 51695494

This annotated bibliography supports the design of an embodied, land-based mathematics learning experience centred on sweetgrass braiding and related weaving practices. The work is intentionally situated within my role as principal of a school serving both Kindergarten to Grade 4 and Grades 9 to 12 learners. This unique configuration requires pedagogical approaches that honour early years’ sensory, play-based, and story-driven learning, while also offering depth, continuity, and leadership opportunities for older students.

Sweetgrass braiding provides a powerful cross-grade context for mathematical exploration, inviting learners to engage with pattern, repetition, structure, spatial reasoning, proportional thinking, and careful attention to process. At the same time, it functions as a living Indigenous practice grounded in relationship to Land, community, and responsibility. Beyond classroom instruction, this work informs the development of culturally meaningful spaces, such as a lunchtime cultural club, here students across age groups can engage in intergenerational learning, mentorship, and shared making.

The sources included in this bibliography were selected to provide ethical, theoretical, and pedagogical grounding for this work. Together, they draw from Indigenous education, land-based learning, and holistic approaches to curriculum, supporting the creation of learning environments that honour Indigenous knowledges while fostering meaningful mathematical engagement across developmental stages.

Applications of Indigenous Knowledges in the 21st Century

Shava, S., & Togo, C. (2019)
Chapter in Traditional and Indigenous Knowledge for the Modern Era

Summary
Shava and Togo examine the continued relevance of Indigenous knowledges across contemporary contexts, including environmental stewardship, food systems, technology, aesthetics, governance, and education. They argue that Indigenous knowledge systems are often marginalized within formal education while simultaneously being appropriated and reframed through Western lenses without acknowledgement of their origins or epistemological foundations. The authors emphasize the need to reclaim Indigenous knowledges as coherent, evidence-based, and dynamic systems that continue to evolve in response to modern challenges.

Relevance to This Project
This chapter provides an essential theoretical foundation for positioning sweetgrass braiding as a legitimate knowledge system rather than a supplemental or “craft-based” activity. For a K–4 context, it supports the framing of braiding as a meaningful way for young learners to encounter pattern, repetition, and structure through embodied engagement. For Grades 9–12, it strengthens the rationale for examining Indigenous practices as sophisticated systems connected to sustainability, technology, and design. From a leadership perspective, this source supports curriculum decisions that challenge deficit-based narratives and affirm Indigenous knowledge as intellectually rigorous and pedagogically rich across grade levels.

The First Blade of Sweetgrass

Greenlaw, S., & Frey, G. (2020)
Children’s picture book

Summary
The First Blade of Sweetgrass introduces readers to the cultural, spiritual, and relational significance of sweetgrass through the story of a young child learning about its careful harvesting. The narrative emphasizes respect for the Land, gratitude, patience, and responsibility, highlighting practices such as taking only what is needed and offering thanks. Sweetgrass is presented as a living gift and teacher, situated within seasonal cycles and intergenerational knowledge.

Relevance to This Project
This text demonstrates how story functions as legitimate pedagogy in land-based and culturally responsive learning contexts. In K–4 classrooms, the book serves as an accessible entry point for exploring pattern, counting, sequencing, measurement, and cycles through narrative and discussion. In a K–12 school context, it also models how Indigenous stories can ground more complex conversations about stewardship, ethics, and relational accountability. Including this text affirms children’s literature as curriculum and positions Indigenous storytelling as a valid and powerful source of knowledge within mathematics education.

Cree Elders’ Perspectives on Land-Based Education: A Case Study

Hansen, J. G. (2018)
Brock Education Journal

Summary
Hansen explores Cree Elders’ perspectives on land-based education as a relational framework for learning, childrearing, and cultural continuity. Using participatory and arts-based research methods, the study highlights the role of Elders and grandparents in knowledge transmission while emphasizing children’s agency, curiosity, and independence. Knowledge is understood as braided across generations, places, and practices, challenging settler-colonial assumptions that frame tradition as static or historical.

Relevance to This Project
This article provides a conceptual foundation for understanding braiding as both metaphor and lived educational practice. For K–4 learners, it supports the design of learning experiences that honour children as capable knowledge holders engaged in relational, hands-on learning. For older students, it offers a framework for understanding intergenerational knowledge, mentorship, and responsibility. As a school leader, this source informs the creation of learning spaces, such as cultural clubs or shared projects, where students across grades can engage collaboratively in embodied, land-connected mathematical inquiry.

Implementing a First-Year Experience Curriculum: Voices of Faculty

Nichols, L. D. (2019)
Canadian Journal of Higher Education

Summary
Nichols examines faculty experiences implementing First-Year Experience curricula, emphasizing the importance of relationship-based, holistic approaches to student belonging and engagement. Faculty participants describe tensions between institutional structures and pedagogical values, noting that meaningful curriculum change requires shared vision, collaboration, and recognition of teaching as relational work.

Relevance to This Project
Although situated in post-secondary education, this article reinforces principles that are highly relevant in K–12 contexts, particularly within a combined early years and secondary school. The emphasis on belonging, coherence, and intentional curriculum design parallels the challenges of integrating Indigenous and land-based practices in schools. From a leadership perspective, this source supports the need for structural alignment, such as scheduling, space, and staff support, to ensure that embodied, culturally grounded learning experiences like sweetgrass braiding are sustainable and meaningful rather than tokenistic.

A Wholistic Vision of Academic Success

Brant, J. (2023)

Summary
Brant presents a strength-based, wholistic understanding of academic success grounded in Indigenous maternal pedagogies. Through sharing circles with Indigenous women, the study highlights success as relational, identity-affirming, and connected to community, rather than measured solely through grades or standardized outcomes. The work emphasizes story, care, and the Four Rs: respect, relevance, reciprocity, and responsibility.

Relevance to This Project
This article supports framing sweetgrass braiding as living pedagogy that engages heart, mind, body, and spirit. For K–4 learners, it reinforces the importance of relational safety, play, and story-based learning. For Grades 9–12, it provides language for valuing leadership, identity development, and community contribution. As a principal, this source strengthens the ethical grounding for designing learning environments that prioritize belonging, cultural continuity, and meaningful engagement over narrow academic performance.

 

References

Brant, J. (2023). A wholistic vision of academic success: Indigenous maternal pedagogies and strength-based education. Canadian Journal of Higher Education, 53(2), 45–62. https://doi.org/10.xxxx/cjhe.v53i2.xxxx
(Replace DOI if required or remove if not available.)

Greenlaw, S., & Frey, G. (2020). The first blade of sweetgrass. Nimbus Publishing.

Hansen, J. G. (2018). Cree Elders’ perspectives on land-based education: A case study. Brock Education Journal, 28(1), 74–92. https://doi.org/10.xxxx/brocked.v28i1.xxxx
(Replace DOI if required or remove if not available.)

Newberry, J., & Pace-Crosschild, T. (2020). Braiding sweetgrass families: A transmedia project on parenting in Blackfoot Territory. Families, Relationships and Societies, 9(3), 411–427. https://doi.org/10.1332/204674319X15754614021266

Nichols, L. D. (2019). Implementing a first-year experience curriculum: Voices of faculty. Canadian Journal of Higher Education, 49(2), 1–17. https://doi.org/10.xxxx/cjhe.v49i2.xxxx
(Replace DOI if required or remove if not available.)

Shava, S., & Togo, C. (2019). Applications of Indigenous knowledges in the 21st century. In S. Shava & C. Togo (Eds.), Traditional and Indigenous knowledge for the modern era (pp. xx–xx). IGI Global. https://doi.org/10.4018/978-1-5225-8900-0

 

 

 

 https://gallery.bridgesmathart.org/exhibitions/2022-joint-mathematics-meetings/kate-jones

Artwork Summary 

Imagine It and Build It by Kate Jones explores the remarkable combinative diversity that can emerge from just five geometric pieces called octiamond shapes composed of eight equilateral triangles. By rearranging these five identical building blocks, the artist creates recognizable forms such as birds, animals, and human figures. The result is a visual representation for the imagination, and constraint, where mathematical structure becomes a source of creativity rather than limitation.

Art Replication

To replicate Imagine It and Build It, I focused on the underlying mathematics of, geometry, and transformation by physically constructing and rearranging five octiamonds. Each octiamond is composed of eight equilateral triangles, and the mathematical challenge lies in exploring how many recognizable forms can emerge under strict constraint, using the same five pieces, without overlap, and with very limited opportunities for symmetry. I used the free resources and diagrams from MathPuzzle.com (https://www.mathpuzzle.com/octiamond.html) to support  my understanding of the octiamond and this site also showed me more possibilities to use these shapes with.

To create the pieces, I printed triangular graph paper from Incompetech and used this tool to set the parameters for the size of the triangular graph paper.

	https://incompetech.com/graphpaper/triangle/) I then used different colours of paper to assemble  each octiamond  making it more visible during construction. I began placing and gluing them together mimicking the five shapes used in the original artwork. Having the opportunity to work with physical materials made the mathematics tangible: through trial and error plus the shapes did not turn out perfectly.  After constructing the octiamonds, I attempted to assemble them into figures that resembled those shown in the artwork. This process highlighted how constraint generates creativity, recognizable forms emerged not in spite of the limitations, but because of them. The activity reinforced that mathematical structure does not limit imagination; instead, it invites play, experimentation, and problem solving. This was called the Sampan Ride Elephant Hen and Egg Bird on a Tree Disco Dancer This task also lends itself naturally to classroom use. Students could construct equilateral triangles using a compass and straightedge, emphasizing precision and geometric reasoning before moving into combinatorial exploration. A clear demonstration of how to construct equilateral triangles with a compass can be found here: https://www.youtube.com/watch?v=XBgwGROzzzk. From there, students could build octiamonds, investigate symmetry and transformation, and explore how many figures can be created from the same fixed set of shapes. In this way, the activity bridges geometry, art, and inquiry, making mathematics both visible and meaningful

Week 4: Mathematics and the Arts — Noticing Patterns Across Sound, Movement, and Behaviour

 

Summary

Week 4 invited us to challenge the long-standing separation between mathematics and the arts. Drawing on C.P. Snow’s idea of the “Two Cultures,” the course introduction highlighted how mathematics and artistic ways of knowing have often been positioned as opposites, despite their shared history. Historically, disciplines such as music, geometry, astronomy, and arithmetic were deeply connected, forming part of the classical liberal arts. Many non-Western knowledge systems, including Indigenous ways of knowing such as Two-Eyed Seeing, continue to resist this divide by holding scientific, artistic, and spiritual understandings together.

This week also introduced the Bridges Math + Art community as a contemporary example of this integration, showcasing how mathematics can be expressed through visual art, music, movement, and play. My reading, Make Music Visible, Play Mathematics by Capozucca and Fermani, reinforced this perspective by showing how mathematical and musical understanding emerges through hands-on, multisensory experiences. Rather than focusing solely on counting or ratios, the authors emphasize geometry, structure, and transformation, noting that “mathematics is about structure and pattern.” This framing resonated strongly with my experiences in classrooms and school leadership, where learning is often most powerful when it is embodied and relational. 

Stop 1: Sound and Movement as the First Patterns

As I read about the music-geometry workshop described in the article, I was reminded of an early years lesson I taught with a group of Kindergarten and Grade 1 students during an introductory patterning unit. Instead of beginning with visual patterns, we started with sound and movement patterns. We explored repeating sequences using clapping and stomping, gradually building more complex patterns together.

What we noticed was that when the whole group participated simultaneously, the classroom began to sound like music. The students were not labeling AB or ABB patterns, but they were experiencing rhythm, repetition, and structure in an embodied way. This experience closely mirrors Capozucca and Fermani’s approach, where understanding emerges through listening, movement, and collective participation. It reinforced for me that mathematical thinking does not need to begin with symbols or definitions; it can begin with the body. 

Stop 2: Playful Mathematics Through Sound and Drawing (Vi Hart)

The short Vi Hart videos, Möbius Music Box, Sound Braid, and Doodle Music, extended this idea of embodied mathematical play. These videos present mathematics through doodling, looping, rhythm, and sound, allowing patterns to emerge organically rather than through formal instruction. What stood out to me was how mathematical ideas such as repetition, symmetry, transformation, and variation were experienced rather than explained.

In Sound Braid and Doodle Music, simple visual marks transform into rhythmic structures, blurring the boundaries between drawing, music, and mathematics. This playful exploration aligns strongly with the reading, which argues that learners develop deeper understanding when they are given space to experiment and discover patterns for themselves. Watching these videos reinforced my belief that curiosity and play are powerful entry points into mathematical thinking, especially when learners are allowed to engage multiple senses at once.

Stop 3: Multiple Perspectives and Making Numbers Audible

My third stop connected back to the TED Talk from Week 1, where the speaker demonstrated multiple ways of representing the fraction 4/3, including using sound. At the time, I shared this idea with my school staff during a discussion about perspectives. What resonated most with them was how a single number could be understood in many different ways depending on how it was represented.

Revisiting this idea through the lens of Week 4 strengthened my understanding of why representation matters. Just as music, geometry, and movement can offer new ways to understand mathematical ideas, taking multiple perspectives allows us to see the “whole” more clearly. My staff appreciated how this metaphor extended beyond mathematics and into our work with students. To truly understand learners, we must be willing to consider different viewpoints rather than relying on a single narrative.

 Stop 4: Patterns in Human Behaviour and the Role of Movement

My final stop this week came from noticing patterns in everyday school life. One Friday felt particularly intense, behaviourally, the day resembled what staff often jokingly refer to as a “full moon.” I spent much of the day managing situations in the office, which left little time for anything else. One Grade 3 student in particular stood out, a student with autism who is high-functioning and able to communicate even when experiencing heightened frustration.

Over time, I have noticed clear patterns when working with this student. If I can introduce movement,  walking, pacing, or physical activity, his emotional state begins to shift. Recognizing this pattern led our school to purchase two small pieces of exercise equipment: a stationary bike and a rowing machine. This decision was grounded in the understanding that movement supports impulse control and emotional regulation, not only for this student but likely for others in the future.

This experience echoed the central message of Week 4. Whether we are observing patterns in mathematics, music, student behaviour, or nature, noticing patterns equips us to respond more effectively. When patterns are recognized, they become tools for problem-solving rather than challenges to manage. 

Closing Reflection

Week 4 reinforced for me that pattern is a unifying concept across disciplines and lived experiences. Mathematics, music, learning, and behaviour are all shaped by our ability to notice structure, rhythm, and repetition. When we attend to these patterns,  through sound, movement, geometry, or observation , we are better equipped to support learners, design responsive environments, and make thoughtful decisions. Mathematics as art, music as structure, and behaviour as pattern all remind me that learning is not confined to subject areas, but woven through the everyday moments of teaching and leadership.

Resources – Week 4: Mathematics and the Arts

Course & Theoretical Framing

• Snow, C. P. (1959). The Two Cultures and the Scientific Revolution. Cambridge University Press.

Bridges Math + Art

• Bridges Organization. (2022). Joint Mathematics Meetings Art Exhibition.
  https://gallery.bridgesmathart.org/exhibitions/2022-joint-mathematics-meetings

Reading

• Capozucca, A., & Fermani, M. (2019). Make Music Visible, Play Mathematics. In Bridges 2019 Conference Proceedings.
  https://bridgesmathart.org/bridges-2019/

Videos

• Hart, V. (n.d.). Möbius Music Box.
• Hart, V. (n.d.). Sound Braid.
• Hart, V. (n.d.). Doodle Music.
  (Vi Hart videos, available online)

TED Talk

• Strogatz, S. (2014). The joy of x [TED Talk].
  https://www.ted.com/talks/steven_strogatz_the_joy_of_x

(This is the talk commonly used to explore multiple representations of mathematical ideas, including using sound, rhythm, and visual metaphors to rethink familiar concepts.)

Week 3: Mathematics outdoors activities

 

As I looked more closely at the birds around my feeder, I began to notice how much mathematics lives in their movement and choices. I was especially drawn to the birds in flight. When their wings fanned out, the feathers spread in a way that felt almost perfectly symmetrical. Each wing mirrored the other, and the spacing of the feathers created repeating patterns that shifted smoothly as the bird moved through the air. What looked effortless was actually a precise balance of shape, angle, and motion.

I also took several images of birds on the ground and perched on trees, feeders, and the orange metal hanger. The birds constantly adjusted their angles depending on the surface they landed on. On tree branches, their bodies aligned naturally with the slope of the branch. On the feeders, especially the plastic birdhouse, their posture changed again. The plastic surface is smooth and rigid, and I noticed that birds could not stay on it for very long. It does not behave like the natural surfaces around it.

This contrast made size and scale very visible. Smaller birds, like chickadees, managed the plastic feeder more easily. Their lighter bodies and smaller feet allowed them to grip and balance in ways that larger birds could not. The blue jays struggled more. They often used a different strategy altogether, using their beaks to throw seed onto the ground, where the flat surface made it easier for them to retrieve food. This felt like problem solving in action, adjusting strategies based on body size, surface, and efficiency.

The placement of our bird station is also intentional. It sits beside an ornamental apple tree so the birds can quickly escape into cover if needed. I have only witnessed a hawk attack once, and it was a chickadee that was taken. Since then, the tree has grown even more, offering additional layers of safety. The tree creates a kind of spatial network—branches at different heights and angles, that birds use to move quickly and protect themselves.

The materials we choose for feeding birds also carry mathematical consequences. Plastic feeders are easy to clean, but they offer very little grip. Wooden feeders are harder to maintain, but their rough surfaces behave more like tree bark and branches. Even when the feeder swings in the wind, the natural textures help the birds stabilize themselves. In a place where wind is constant and temperatures drop to –45, these details matter. It still amazes me that such tiny bodies survive conditions like this, constantly adjusting position, balance, and movement.

The metal hanger itself is another story of geometry and reuse. It wasn’t bought, it was made by my dad when we moved away and built our house on our own property. He used a hollow metal pipe and bent old rake teeth from a dump rake into arches. Those curves now hold the feeder steady. The structure has never needed repair, only a coat of paint, one of my favourite colours, orange. What I see now is a combination of straight lines, curves, symmetry, and tension working together, shaped by both human design and practical need.

Watching birds has always brought me joy. But watching them with the mindset of a mathematician adds another layer. I see balance, adaptation, scale, symmetry, angles, and problem solving playing out constantly. Mathematics is not something imposed on this scene, it is already there, alive in movement, material, and relationship.

Tracy's Sketch of bird feeding.

Week 3 – Sustainable Mathematics in and with the Living World

Introduction: Learning Mathematics Outdoors and with the Land

Most mathematics learning still happens indoors, inside classrooms shaped by desks, schedules, and expectations that quietly influence how we think about knowledge. This week’s focus invites us to pause and ask a different question: What happens when mathematics learning moves outdoors and happens in relationship with the living world? The introduction for this week challenges the idea of the mathematics classroom as a static, silent space. Instead, it invites learning that is embodied, sensory, and relational, learning that happens on and with the Land. Outdoor spaces like gardens, fields, forests, riverbanks, or schoolyards are not just alternate locations for lessons. They can act as co-teachers. The living world responds, changes, resists control, and invites attention in ways that cannot be fully planned or contained. This is not a call to abandon indoor learning, notation, or structure. Rather, it is about balance. When mathematics is taught only through symbols on paper, it can drift away from meaning. Learning outdoors can help reconnect mathematical thinking to lived experience. It can support curiosity, lower anxiety, and invite deeper noticing, especially when learning is designed to honour place rather than treat it as a backdrop.

Reading Reflections: The Grid, Balance, and Living Beside Structure

This week’s readings also helped me reflect on the “grid” of schooling. The grid shows up everywhere: in timetables, curriculum documents, assessment tools, classroom layouts, and even in how we organize our thinking. The grid can feel comforting. It helps manage the complexity of teaching and learning. But it also limits what is possible. What resonated with me was the idea that we don’t need to fully escape the grid to teach differently. Instead, we can learn to live beside it. Sometimes we work within it. Sometimes we loosen it. Sometimes we resist it. This way of thinking feels more honest than pretending we can step completely outside systems that shape us.

Connections to Indigenous Ways of Knowing

Learning mathematics in and with the living world also connects strongly to Indigenous ways of knowing. It brings attention to relationship, story, responsibility, and reciprocity. In this framing, mathematics becomes a way of relating to the world, not just measuring or controlling it. That feels especially important in a time of ecological crisis, when education has a role to play in how young people learn to care for the world they are part of. The idea of “dancing teachers into being with a garden” stayed with me. It offers a different image of teaching, one that values listening, noticing, movement, and even stillness. Teaching does not always have to mean talking, directing, or managing. Sometimes it can mean making space for learning to emerge through experience. This week reminded me that mathematics does not have to be separate from culture, story, or Land. When learning happens in relationship, mathematics can carry meaning that lasts far beyond the classroom.

Stop One: Sweetgrass, Story, and Carrying Knowledge Forward.

My thinking begins with sweetgrass and the stories it carries. One place this begins for me is the children’s book The First Blade of Sweetgrass by Suzanne Greenlaw and Gabriel Frey, illustrated by Nancy Baker. This story offers an accessible way to understand the history and importance of sweetgrass, not just as a plant, but as a living teacher and relative. Alongside this, I find myself drawn to Braiding Sweetgrass by Robin Wall Kimmerer. I have not read it yet, but I am aware of its focus on relationships between people, plants, and responsibility to the Land, and it feels like a book I am ready to spend time with. Together, these texts will help me learn more about sweetgrass as something living and relational, rather than something to be studied at a distance. Sweetgrass also connects closely to my own family story. I carry memories of my dad talking about the smell of sweetgrass while processing hay to feed animals on the ranch where I grew up. That land has been in our family for seven generations. It will remain in our family, as it is being willed to my grandchildren with clear expectations around care and responsibility. I am the grandma now, and that matters. I didn’t grow up with these teachings. My grandparents couldn’t talk openly about who they were. Their generation had to hide their identity, and that silence carried into my dad’s generation and then into mine. I have stopped it there. I will make no apologies and no concealment of my culture anymore. I see it as my responsibility to make sure the next generation grows up knowing who they are, where they come from, and how knowledge lives in relationship with the Land. When I think about sweetgrass this way, mathematics is already present—in cycles, in continuity across generations, and in systems of care and stewardship.

children’s book The First Blade of Sweetgrass by Suzanne Greenlaw and Gabriel Frey, illustrated by Nancy Baker

Stop Two: Rewilding Schooling Through Sweetgrass and the Senses.

I love the idea of rewilding schooling, and this week helped me imagine what that could look like more clearly. When I think about sweetgrass, I imagine learning that brings many senses together. I picture being out in the fields with students, smelling the sweetgrass, feeling it in our hands as we gather it, noticing the texture of the blades as we prepare them for braiding. There is movement in this work, and patience, and attention. There would be conversation too. Stories shared between students and teacher. Questions that arise naturally. And there would be sound, the wind moving through the grass, the quiet rhythm of hands working, the calls of birds or other creatures nearby. Learning would not be silent, but it also wouldn’t be rushed. Thinking about this makes me realize that I could create learning experiences that hold all of these senses together. I just haven’t fully done that yet. The pull of schedules, curriculum pacing, and classroom expectations is strong. For me, rewilding schooling doesn’t mean removing structure altogether. It means loosening it enough to make space for learning like this to happen. Sweetgrass feels like an invitation to slow down, to notice, and to learn with the Land rather than simply about it.

Stop Three: Between Two Trees

I once saw a short video showing a family weaving between two trees. I wasn’t able to track down the original video, but later found an image that helped me return to the idea: backstrap weaving anchored to living trees. That image stayed with me. The trees are part of the learning system. The body becomes part of the loom. The environment matters. Weaving in this way challenges the idea that learning must be framed by classroom walls or fixed structures. Mathematics shows up here through pattern, tension, repetition, and direction, but it does so in a way that is alive and responsive.

https://backstrapweaving.wordpress.com/2013/04/03/backstrap-weaving-where-the-yarn-grows-on-trees/

Stop Four: Weaving, the Métis Sash, and Passing Stories Forward

I have done this type of weaving with students. My students created friendship bracelets while learning about the Red River Métis sash. The colours carry meaning connected to community. The patterns range from simple to complex and include directionality that tells stories. For many students, especially Métis students—this work was about more than art or mathematics. It was about connection. These are stories that have been interrupted by disconnection from culture, shaped by political pressures and the need to survive. That loss matters. It also makes the work of returning to these stories even more important for future generations.

Example of weaving with my students 

Image of a loom, that was used in a course I took. 

Here we are making the Arrowhead Metis Sash

Arrowhead Sash Pattern

My Final Reflection: Why This Matters

This week invited me to rethink mathematics as something that can be learned in relationship with the living world. Outdoor learning, Indigenous perspectives, and embodied experiences offer ways to loosen the grid of schooling and make space for learning rooted in place, story, and responsibility. Rather than trying to escape structure, I am learning to live beside it, creating room for mathematics that is meaningful, relational, and alive.