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.)