Week 7 Mathematics & poetry and novels

 

Reading

As I delved into the reading on Surfing the Möbius Band, a couple of significant 'stops' captured my attention, sparking a reflective journey into the intersection of art and mathematics.

The first 'stop' arises when the authors discuss the formal experiment in issue 11 of the Silver Surfer series, titled "The Moebius Madness of Silver Surfer." The decision by Dan Slott and Mike Allred to structure the storytelling using the form of a Möbius band is intriguing. The Möbius band, known for its representation of change and renewal, becomes a metaphor within the comic, symbolizing the cyclical nature of time and space in the Marvel universe. This integration of mathematical concepts into the narrative is a unique storytelling device and prompts a deeper reflection on the character's existential journey. The Möbius band becomes a visual cue, guiding readers through Silver Surfer's temporal loop and emphasizing the importance of free will in breaking the cycle.

Another 'stop' occurs when the reading explores the broader cultural impact of the Möbius band in fiction. The Möbius band, with its odd topological properties, has been utilized in various stories to symbolize either an endless loop or a mysterious transition to 'the other side.' Examples from Star Trek to an Argentinean film illustrate the diverse ways in which this mathematical figure has been woven into the fabric of storytelling. The reading suggests that the Möbius band, beyond its mathematical accuracy, holds a powerful place in the collective imagination, serving as a symbol for the unending and the cyclical in literature and art.

As I reflect on these 'stops,' I wonder how readers perceive the integration of mathematical concepts into the visual storytelling of comics. Does this enhance or detract from their engagement with the narrative?

In conclusion, the reading not only explores the creative use of mathematical concepts in comics but also raises questions about the accuracy of these representations. The fascinating interplay between art and mathematics in Silver Surfer's story prompts me to appreciate the beauty of their union while recognizing the occasional discrepancies that arise when mathematical symbols enter popular culture.

Activity

As I immersed myself in Sarah Glaz's introduction to the Fibonacci poems for Bridges 2021, a pivotal moment emerged in the creative process and collaborative spirit behind the collection.

Indeed, it is the origin story of the Fib poems within the Bridges poetry community. The virtual setting of the Bridges 2021 conference, designed as the town of Königsberg with its seven bridges, became the catalyst for the poetry gathering in the Glade. The challenge of limited time for over thirty poets led to the ingenious idea of blink-poems, specifically Fibs. This creative solution, sparked by Alice Major and refined through collaboration, not only facilitated a quick read-around but also paved the way for forming a unique collection. It highlights the adaptability and inventiveness that can arise when artistic minds come together to navigate challenges.

Another noteworthy 'stop' explains the Fibonacci sequence and how it translates into Fib poems. Glaz provides a concise and clear understanding of the mathematical underpinning of Fibs, tracing their syllable count back to the Fibonacci numbers. However, I struggle to complete my poems below and will continue the work when I feel more rested and inspired. This intersection of mathematics and poetry adds depth to the creative process, emphasizing the harmonious blend of two seemingly disparate disciplines. The structured nature of Fib poems, derived from the Fibonacci sequence, presents a fascinating framework for poets to explore and express their ideas.

Now, as I reflect on these 'stops,' I wonder how the poetic form derived from the Fibonacci sequence influences the thematic choices made by the poets. How do they navigate the constraints of the form to convey their ideas effectively?

Algebraic Equations

X

plus

Y makes Z

Solving for the unknown

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Geometric Points

Circles

spin

around points

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Explanation:

For the first Fib poem, "Algebraic Equations," I explored the realm of algebra and the process of solving equations. The Fibonacci sequence determined the syllable count in each line (1, 1, 2, 3, 5, 8), guiding the poem's structure.

In the second Fib poem, "Geometric Points," I delved into the world of geometry. The Fibonacci sequence dictated the syllable count in each line (1, 1, 2, 3, 5, 8), shaping the poem's progression. The lines aim to capture the elegance and precision of geometric shapes.

Poetry in the Glade: Bridges 2021 Fib CollectionTop of Form

 

Viewing

Exploring the diverse landscape of mathematical poetry through the lenses of various poets has been an enriching experience. With their unique background and perspective, each poet brings a distinctive flavor to the intersection of mathematics and art.

About my learning and wonders	About the Poets
Stephanie Strickland's "The infinity stops between our fingers." Strickland's work, marked by a lifetime achievement award, introduces me to the intriguing realm of digital literature. The poem suggests an exploration of the infinite within the finite, perhaps within the context of human connection. The use of digital media adds a layer of complexity, urging me to explore how technology amplifies the poetic narrative.	Website: https://en.wikipedia.org/wiki/Stephanie_Strickland Sample poem: The infinity stops between our fingers
Kaz Maslanka's "Hwadu" Maslanka's journey from a BFA in Sculpture to pioneering mathematical visual poetry fascinates me. “Enigmas are to Ontology as The Song of Ancient Dreams are to The Sound of the Ocean”. "Hwadu" not only highlights his artistic prowess but also brings me into a world where mathematical concepts transform into visual art. The connection between mathematics and poetry, elucidated through his work, prompts me to ponder the intricate beauty of numbers and aesthetics.	Website: http://mathematicalpoetry.blogspot.com/  Sample poem: Hwadu
Susan Gerofsky's "Glided, gilded and Barely, bleary." Gerofsky's commitment to a multidisciplinary approach is evident, blending mathematics, arts, and environmental education seamlessly. The poem, employing the constraints of a Fib and adding the layer of anagrams, creates a nuanced exploration of contrasting states. Using anagrams, like "Glided/gilded" and "canoe/ocean," adds an extra layer of complexity, reflecting the intertwining nature of mathematics and language. The choice to structure the twenty syllables into two iambic pentameters adds a rhythmic quality, echoing the cadence of a mathematical heartbeat. I wonder what sensory experiences might have inspired Gerofsky's exploration of contrasting states in this Fib poem.	Website: https://edcp.educ.ubc.ca/susan-gerofsky/ Sample poem: Glided, gilded and Barely, bleary
Dan May's "Eight Minutes" May's exploration of connections between mathematics and poetry within the teaching context offers a unique perspective. "Eight Minutes" sparks my interest in how he navigates the intersections of musicology, mathematics education, and poetry. The poem suggests a concise yet impactful exploration of a mathematical concept, leaving me intrigued about the depth within simplicity.	Website: https://talkingwriting.com/daniel-may-poem Sample poem: Eight minutes
Larry Lesser's "E(X)" As a distinguished teaching professor, Lesser's engagement in mathematical poetry and songwriting resonates with me. "E(X), the expected value, is the mean of all possible outcomes of a statistical experiment where each outcome is weighted by its probability." Indeed, it hints at a statistical exploration, and I am curious about how he weaves statistical concepts into poetic narratives. Also, his prolific presence in various literary and mathematical platforms prompts me to reflect on the broader impact of such interdisciplinary endeavors.	Website: https://larrylesser.com/poet-larry-ate/ Sample poem: E(X)

 

In delving into the works of these poets, I find myself on a journey where mathematical ideas intertwine with diverse artistic expressions. The poets' distinct styles and approaches invite further exploration into the multifaceted relationship between mathematics and poetry. How do these poets uniquely bridge the gap between mathematical precision and poetic expression? 

 Bridges Math and Art 2024 Virtual Poetry Reading website

 

Final Project Proposal: Tony Domina

 Here is the link

Outline Prosal Final Feb 12.docx - Google Docs

Week 6: Mathematics & dance, movement, drama and film

 This week's reading on mathematical learning through the reenactment of choreographed performance analyses of three cases in which groups of four (quartets) worked with video recordings of the 2016 Rio Olympic Games opening ceremony. Exploring how collaborative actions can foster mathematical understanding and artistic expression is fascinating. Two noteworthy "stops" in the text stand out for reflection.

First Stop: Integration of Physical Props and Collective Action: one critical aspect is emphasizing the physical engagement of quartets with the shiny plastic sheet, or Mylar, as a prop. Indeed, the quartets actively dissect and reenact movements, exploring the prop's physical possibilities. This collective manipulation of the prop becomes a medium for learning, creating geometric shapes and structures at various levels, from quartet to assembly to the entire performance. Also, integrating physical props adds a tactile dimension to the learning process, making it more immersive and engaging. The connection between physical actions and mathematical concepts, such as rotations, reflections, and translations, highlights the embodied nature of learning.

Second Stop: Ensemble Learning as a Coherent Unity: another significant aspect is the layered nature of ensemble learning, where the quartet, assembly, and whole performance levels interact dynamically. Indeed, the quartet level serves as a manageable entry point for participants, allowing them to enact critical aspects of the performance. This leads to exploring mid-level assemblies, creating geometric figures, and propagating waves. Finally, the highest-level performance unfolds with crystalline structures, liquid waves, and vortex motion. Therefore, the high level of coordination emphasizes the coherent integral unity of the performance. The quartet's engagement is not isolated; it contributes to the ensemble's significance and impact, showcasing the learning experience's collective nature.

Questions for further exploration include how physical prop interactions enhance mathematical understanding and the potential applications of this ensemble learning approach beyond dance and mathematics.

Questions for Discussion:

1. How does integrating physical props, such as the Mylar sheet, enhance the learning experience for the quartets? Can you think of other examples where tangible objects contribute to mathematical understanding?
2. In what ways does the layered structure of ensemble learning, from quartet to assembly to the whole performance, reflect the interconnectedness of mathematical concepts? How might this approach be applied to other disciplines beyond dance and mathematics?

Vogelstein, Brady, and Hall (2019) Reenacting mathematical concepts in large-scale dance performance

 

Reflection on the "Rope Polygons" Lesson:

The "Rope Polygons" lesson provides a unique and engaging approach to teaching geometry concepts, mainly focusing on measurement, reasoning with shapes, and understanding polygon properties. Indeed, I have not tried this activity. However, I would ask students to explore the properties of different polygons, such as triangles, quadrilaterals, pentagons, and hexagons. Using a twelve-foot knotted rope adds a kinesthetic and collaborative element to the learning process, making geometry come alive in a new context. The main task, challenging groups to create regular polygons with their bodies and the rope, is a hands-on and dynamic way to bridge the gap between abstract geometric concepts and real-world applications. Moreover, facilitating a whole-group conversation after the activity allows students to articulate their thought processes, share challenges, and learn from each other.

Also, I would suggest extensions for further exploration, such as investigating angle measures, side lengths, diagonals, and relationships between surface area and perimeter. This will allow for differentiation based on student readiness and interest. These extensions would encourage students to think beyond the initial challenge and deepen their understanding of geometry.

Moreover, I like allowing confusion and intervention when consensus cannot be reached. This pedagogical approach acknowledges the value of struggle in the learning process. It aligns with the idea that confusion can be a stepping stone to learning, fostering resilience and problem-solving skills. Finally, the reflective component, where students draw a picture to map out and showcase their group's approach to the challenge, is a valuable assessment tool. It reinforces their understanding and provides a visual representation of their learning journey.

http://www.malkerosenfeld.com/lesson-plans.html

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

 Part 1: Reading

In this week's reading, two key points stand out to me. The first is the acknowledgment of the interconnectedness of physical movement, interaction, and mathematical learning. The article highlights the significance of opportunities for physical movement and expression in shaping how we think, learn, and communicate about mathematics. The notion that mathematical thinking cannot be separated from the settings in which it occurs resonates with me, emphasizing the dynamic relationship between the body, the environment, and mathematical activities.

The second remarkable 'stop' is the theoretical framing of the study, which brings together perspectives on the social production of learning spaces and embodied interaction. Theoretical frameworks often serve as guiding lenses, and in this case, combining ideas about the social spaces of learning with the importance of embodied action in mathematics education creates a rich foundation for understanding how whole-body collaboration can influence the spatiality of learning environments.

The research method involves pictures of learners participating in whole-body, multi-party activities, specifically focusing on walking scale number lines (WSNL) and whole and half (W + H). To illustrate, the WSNL participants incorporate classroom-based practices, using arithmetic computations on the gymnasium number line. In contrast, W + H participants perceive the activity as a departure from traditional methods, emphasizing the enjoyment of the embodied experience. This divergence prompts questions about the potential of transforming school mathematics through body-based design.

The study underscores the importance of considering the theory of place in understanding the embodied self within a total environment. At a socio-theoretic level, the research seeks to redefine embodiment in mathematics education by highlighting the interconnectedness of corporeality, inter-corporeality, and space. Recognizing the need to comprehend these complex relationships, the findings stress the significance of understanding the consequences and potential of expansive learning designs. Ultimately, the research advocates acknowledging the nuanced nature of embodied, emplaced, and interactive aspects in mathematical thinking and learning, opening up possibilities for creative leverage in the field.

Now, I find myself pondering how these theoretical considerations translate into practice.

1) How can educators integrate whole-body, multi-party activities to enhance mathematical learning experiences?

2) How do students perceive and engage with these activities?

3) How might students' understanding of mathematical concepts evolve through embodied interaction?

 

Part 2: Activity: I still wonder how to integrate this week's activity into my teaching!

Week 4: Mathematics and the Arts Reflection on the Bridges Conference Reading

 

I delved into the vibrant and interdisciplinary realm of the Bridges Conference. Three distinct stops in the text caught my attention, each offering a unique perspective on the convergence of mathematics and art.

Stop 1: The Mathematical Garden and Polyhedral Climbing Structure (Fig. 1)

The Mathematical Garden, with its interactive features like puzzles, mazes, and a giant xylophone, is a testament to the immersive nature of the Bridges Conference. The polyhedral climbing structure, depicted in Fig. 1, not only symbolizes the interconnectedness of mathematical concepts but also exemplifies the playful integration of math into physical experiences. As a participant, I can only imagine the joy and intellectual stimulation of engaging in such a creative and educational environment. How does incorporating interactive installations in the Mathematical Garden enhance the conference experience for attendees?

 

Stop 2: Marjorie Rice's Pentagonal Tilings (Fig. 2)

 

Fig. 2 showcases a pentagonal tessellation on the ramp leading to the museum's entrance, setting the stage for the Reza Sarhangi Memorial Lecture. Marjorie Rice's story, a self-taught mathematician passionate about pentagonal tilings, is inspiring and intriguing. This episode highlights mathematical discovery's democratization and emphasizes the mathematical community's collaborative spirit. The use of unconventional notation and Marjorie's journey in discovering new pentagonal tilings sparks curiosity. How does Marjorie Rice's story contribute to reshaping the narrative around who can be a mathematician? In what ways do unconventional approaches to notation impact the exploration of mathematical concepts?

 

Stop 3: Hedy Hempe's "H-spiral" (Fig. 5)

 

Fig. 5 introduces us to Hedy Hempe's "H-spiral," an artwork crafted from carefully arranged eggshells, earning an Honorable Mention for 3-dimensional Artwork. As embodied in this piece, the fusion of mathematical concepts and artistic expression prompts contemplation on the diverse forms through which mathematical ideas can be communicated. How does the "H-spiral" exemplify the intersection of art and mathematics? In what ways does the inclusion of 3-dimensional artwork contribute to the broader narrative of the Bridges Conference?

In conclusion, this week’s reading has been a profound eye-opener for me, reshaping my perspective on the interconnected worlds of mathematics and art. Reflecting on the Mathematical Garden, Marjorie Rice's Pentagonal Tilings, and Hedy Hempe's "H-spiral," I am inspired by the seamless convergence of these disciplines at the Bridges Conference.

This newfound awareness extends beyond the conference walls. Last night, as I dined at a restaurant, I could not help but see the art in the subtle play of light, noticing the elegance of a sphere shape. It has become clear that exploring mathematical concepts is not confined to academic settings but extends into our daily experiences.

This realization prompts me to ponder: How do these seemingly ordinary encounters with mathematical aesthetics in our surroundings contribute to a broader appreciation of the intersection between mathematics and art?

Eve Torrance (2019), Bridges 2018, Nexus Journal

 Picture from the restaurant in North Vancouver

This week's activity:

Engaging with the Bridges Math Art Gallery, I explored a captivating Möbius band carved in Somerset Alabaster.

https://gallery.bridgesmathart.org/exhibitions/2011-bridges-conference/nickdurnan

 

While appreciating the accessible mathematics behind the piece, I ventured to understand its intricacies, striking a balance between familiarity and pushing my boundaries.

 The YouTube video on cutting Möbius strips provided additional insights, making the mathematical aspects more tangible and intriguing.

Why is cutting a Möbius strip so weird?

 https://www.youtube.com/watch?v=Qy0FSfEPBic

 I tried and got this: