Reading 8

 WRITING AND READING MULTIPLICITY IN THE UNI-VERSE: ENGAGEMENTS WITH MATHEMATICS THROUGH POETRY NENAD RADAKOVIC, SUSAN JAGGER, LIMIN JAO

In the article “Writing and Reading Multiplicity in the Uni-verse,” the ways in which poetry may be used to engage students with mathematics on a personal level were investigated. The article was inspired by Nanao Sakaki’s poem, which used expanding circles of scale, and the author challenged teacher education students to write their own poems that make personal connections to mathematics concepts such as distance, scale, and place value. At first, the instructors sought mathematical accuracy in the students' poems and were disappointed. However, after re-reading the students poems and drawing on the ideas of Derrida and Barthes, the instructors realized that the meaning of the poems was created by readers. Therefore, the instructors started to see the students' poems as authentic and personal. The article concluded that the use of poetry creates a safe and dialogic space for students to explore their understanding of mathematics and highlights the dynamic process of “knowing” mathematics.

Stop 1: Multiplicity of Meaning

I stopped reading when the authors discussed Derrida and Barthes and how meaning is not necessarily created in a text but by the reader. It made me think about how we are always looking for the correct mathematical meaning in a student’s work. In the article, the two instructors were initially disappointed because they did not see strong mathematics in the poems. However, they eventually realized that the students were engaged with mathematics in personal and metaphorical ways.I stopped reading at this part because it made me think about my own teaching practices as a mathematics educator. It’s not just about correctness in mathematics; it’s about how we make meaning as well. It’s closely related to my own beliefs about personal mathematics learning.

Stop 2

I also stopped at the section where students were given the opportunity to write their poetry related to mathematics. It was similar to the Fibonacci poems that the students wrote in the classroom. In the Fibonacci poems, the number of syllables is related to the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, and so on. It may not be the case that the student thinks to themselves, “I am using recursive number patterns,” but they are making connections to mathematics through the rhythm and creativity of their work.I stopped here because I realized that poetry related to mathematics, like the Fibonacci poems, helps make mathematics a safe place where students feel comfortable being creative and expressing themselves. It shows that mathematics is both logical and creative.

Question:

Do you have any experience teaching mathematics through poetry? What did you notice about students engagement and understanding?

Reading 7

 What Can We Say About “Math/Art”?-George Hart

The article “What Can We Say About Math/Art?” by George Hart explores the concept of math/art, artworks inspired by mathematical ideas. According to Hart, although math/art is a growing trend, there is no definitive way to define what constitutes mathematical art, partly because “art” is very hard to define. Rather than trying to establish boundaries, he proposes that math/art be seen as dynamic areas that develop through examples, interpretation, and discussion.

Hart also explores the role of math/art in relation to mathematics and fine art. He points out a thriving community of people who produce mathematical artworks, but notes that these are largely appreciated within the community rather than by mainstream fine art organizations. While many of these works could perhaps be better classified as craft, design, models, or visualization, this does not reduce their creativity or value.

Finally, Hart urges honesty and awareness in the understanding of math/art. He proposes it as a connection between analytical thinking and artistic expression, encouraging mathematicians and educators to explore creativity and think about the relationship between math and art.

Stop 1: I paused at Hart’s point about math/art being difficult to define. Hart says that even “art” itself is difficult to define, so it makes it even more difficult to define what constitutes mathematical art. This resonated with me because math is often seen as a precise subject with clear definitions, but Hart demonstrates that creativity doesn’t always need to be defined. It made me realize that knowledge can still be valid even if it’s not defined. This is also related to Nick’s interview, where math is said to be something we discover, not define.

Stop 2: I paused at Hart’s observation that many math/art pieces could perhaps be considered craft, design, models, or visualization rather than fine art. This observation seemed significant to me because Hart is not criticizing these pieces but urging a recognition of their purpose. It is easy to remember that value is not dependent upon being considered “fine art.” Visualization and models are very powerful tools in education for illustrating mathematical concepts.

Have you encountered an example where mathematics felt more like art or creativity than calculation? What shaped that experience?

Interview Reflection

 This interview with Nick Sayers explores how mathematics, art, and experience can intersect in unexpected ways. The insights offered here challenge the traditional understanding of mathematics and demonstrate how curiosity, materials, and imagination can inform both artistic expression and learning.

I felt like I was really bad at it.(00:06:00)

The part of Nick’s story that resonated with me the most was his reflection on how he believed he was “bad at maths” as a kid. Because he struggled with mental calculations, he started to think of himself as someone who is not very good at maths. This is how school experiences in the early years can have a big impact on how students think about themselves. Students often associate being “good at math” with being able to calculate quickly, and when they struggle with this, they begin to feel like they are not good enough.

What struck me as particularly interesting is that Nick went on to be very passionate about geometry, programming, and mathematical art. Nick’s experience shows that our early experiences at school are not necessarily an accurate reflection of our abilities. Struggling with one area of maths does not mean that someone is not a mathematical thinker.

It also makes me think about how often schools reduce maths to numbers and speed, rather than creativity, visual thinking, and problem-solving.

 

it was kind of maths by stealth, like, it was, you know, programming and logic and all these sorts of things are…

00:06:49

Nick’s use of the phrase “maths by stealth” has really stuck with me, as it challenged me to think about my own experiences with math. I had always thought that success in math was inextricably linked with speed, accuracy, and number sense. However, programming as Nick describes it provides a completely different point of entry, one that is based in logic, pattern recognition, and visual thinking rather than calculation. It made me wonder: How many students might connect with mathematics if they encountered it this way first?

Nick’s experience also caused me to think about how mathematics is presented in the classroom. When students have difficulties with arithmetic, are we unintentionally telling them that they are “bad at math”? Nick’s later experiences with geometry and mathematical art completely contradict this notion. It is a difficult tension to balance: is mathematics being reduced to numbers when, in fact, it is so much more?

This reflection resonates very strongly with my developing view as a teacher. I find myself asking: What kinds of mathematical thinking are we failing to see when we emphasize only the symbolic and procedural ways of thinking mathematically? Maybe embodied, visual, and exploratory ways of thinking are not alternatives to mathematics, but are instead crucial paths into mathematics.

Bicycle Spirograph (~35:29)

What really fascinated me was the concept of varying speed and gear to create different patterns. It was a way of making something artistic and mathematical. I started thinking about how many mathematical concepts we are exposed to every day without even realizing it.

This stop also made me think about teaching. It is a good example of how math does not have to start with formulas or pictures. It can come from motion, play, and observation. The fact that geometry is created from something as simple as riding a bike is a great way to show how math can be interesting and dynamic.

Sunlight Pattern (~1:10:59)

I paused here because I was fascinated by the idea that something as ordinary as sunlight could be harnessed to “draw” mathematics. Nick talks about how the sun's changing position throughout the seasons creates patterns, almost like a natural history of movement. It made me think about how mathematics can be found in observation rather than calculation.

The “Morse code effect” of the clouds and sunshine alternating was fascinating. It illustrates how irregular and interrupted things, things we might think of as flaws, can create their own patterns. It made me think about how mathematics is full of variation and rhythm, not just perfect geometric shapes.

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?

Nick Sayers’ projects demonstrate to me that math and art are not disciplines to be learned in isolation but, in fact, interwoven approaches to understanding the world. By using a variety of designs and patterns, he illustrates how mathematical concepts such as pattern, symmetry, scale, and structure can be derived from observation. As a math or science educator, this inspires me to create more visual, kinaesthetic, and investigative learning experiences. It also inspires me to remember that students can learn math concepts through creativity, observation, and play, rather than just through equations and processes.

Project Outline

Rosmy EDCP 552 Project Outline

Reading 6

 Learning to love math through the exploration of maypole patterns

Julianna Campbell & Christine von Renesse

The article "Learning to Love Math through the Exploration of Maypole Patterns" examines how an inquiry-based, arts-integrated math course can change the way liberal arts students think about math. The article is based on a Mathematics for Liberal Arts class and focuses on maypole dancing as a way to introduce students to advanced mathematical thinking. Rather than being given formulas or procedures, students are encouraged to create their own questions, conjectures, representations, and proofs.

The article describes a number of models of ribbon interactions, primarily the tree model, letter model, and screen (Excel) model, which enable students to examine the over-under ribbon interactions mathematically. Using these models, the class defines equivalent ribbon patterns (rotations, reflections, translations, swaps, and color changes) and proves theorems about when two dances are the "same" pattern.

The students then use combinatorial thinking to determine the number of non-equivalent ribbon configurations for six ribbons based on various color constraints. In addition to the mathematical content, the article highlights the role of inquiry-based learning in overcoming the fear of error, increasing ownership of ideas, and changing the perception of math from rigid and procedural to creative and exploratory. The article also features a student experience that clearly shows how curiosity and struggle lead to confidence and joy in learning math.

Stop 1: For the first time… I was encouraged to ask questions.

I stopped here because it brought back memories of my experience as a learner. For a long time, math was about following procedures, memorizing formulas, and avoiding errors. Asking too many questions sometimes meant holding the class back or appearing weak. Reading how the student in the article felt safe to wonder made me reflect on how powerful that feeling is. When learners are encouraged to question rather than simply answer, math becomes an investigation rather than a survival experience.

As a teacher, this stop is very relevant to my practice. I see now how easily learners can become disengaged when math is presented as a fixed and procedural subject. Providing a space for curiosity, confusion, and conversation is not a soft addition – it is essential.

Stop 2: Representing the dance mathematically

I stopped at the point where the students were having difficulty representing the maypole dance. The students did not readily come up with the “correct” representation; instead, they tried, failed, and finally came up with representations. This caught my attention because I have noticed this in my own learning and teaching: understanding comes after struggling, not before.

In my own learning, I used to think that struggling meant that I was “not good at math.” But now I realize that struggling is actually a part of doing math. As a teacher, this experience reminds me to be more patient with students when they are struggling with concepts such as graphs, functions, or geometry.

Questions for discussion:

·       Inquiry-based learning asks students to explore, question, and justify ideas instead of just following procedures.
What challenges might teachers face when using this approach in real classrooms?

·       Have you ever had a learning experience that changed how you saw the subject? What made the difference?

Reading 4

 

Reconfiguring mathematical settings and activity  through multi-party, whole-body collaboration-  Molly L. Kelton • Jasmine Y. Ma

This article examined how multi-party whole-body collaboration can reshape mathematics learning by reconfiguring the body/spaces/mathematics relationships. Based on theories of embodied cognition and the social production of learning spaces, the authors contended that mathematics learning is not only cognitive and symbolic but also physical, social, and spatial.

Through two case studies of students’ mathematical experiences, a walking scale number line activity at a gym and a Whole and Half ratio and proportion activity at a classroom, the study illustrates the role of students’ bodies during the production of mathematical objects. The role of students’ bodily movements, their interactions with peers, and their positioning incorporate mathematical meaning, as disruptions to these movements highlight the impossibility of separating the social and the mathematical.

The results indicate that intentionally using designs that engage the whole body and collaborative movement hold promise for expanding our notions of mathematical activity. Whole body collaborations that generate productive friction within traditional spaces of school mathematics can lead to new possibilities for "sense-making," "creativity," and "engagement."

Stop1: When bodies became mathematical objects

I stopped, particularly when the authors talked about situations when “the students' own bodies became mathematical objects, for example, by standing on a number line or forming whole and half intervals with their hands.” What struck me, however, was that these concepts of movement, space, and coordination were not just informing or supporting mathematical concepts; they were actually the mathematics itself. That is, when the students bumped into each other or had to stop and wait for a partner before they could proceed, mathematics was disrupted. This stop helped me see mathematics as something that emerges through interaction, not just through symbols on paper.

Stop 2: When classroom space was “edited” for learning

I stopped when, in the Whole and Half activity, students started using unexpected parts of the classroom-the floor, Smart Board, and open spaces between desks-to build and extend mathematical intervals. This was a striking moment because it shows how learning spaces are not fixed entities; they are mobilized by how students move and act within them. I stopped here because this made me think of how often classroom routines restrict movement and reduce creativity. In this activity, students reimagined the classroom and used their bodies to investigate increasingly complex ideas. At this stop, I wondered how many mathematical opportunities are lost each day when classrooms are built to keep bodies still rather than allowing movement to support thinking.

Question:

I wonder what new possibilities for inclusion and sense-making might emerge if students are encouraged to edit spaces on the floor, on the walls, and in open areas as part of their mathematical activity, and what supports teachers might need to make this workable.