Week 9: Math and Weaving

Reflective Reading 

from Åström, A., & Åström, C. (2021). The art and science of rope. https://doi.org/10.1007/978-3-319-57072-3_15

As an educator committed to providing a well-rounded and engaging curriculum for my grade 1 students, I often find inspiration in unexpected places. Recently, I delved into the article "Art and Science of Rope" by Alexander Åström and Christoffer Åström, which provided a fascinating exploration of the historical and archaeological aspects of rope making. While the content might seem advanced for young learners, the fundamental concepts and the intersection of art and science presented valuable insights that I could connect with my teaching experiences.

Stop Point 1: The Ancient Connection between Tools and Art

The article delves into the historical significance of tools, arguing that their usage was a crucial part of human evolution. This idea resonates strongly with my teaching philosophy, emphasizing the importance of hands-on experiences for young learners. I believe that providing students with tools, even simple ones like pencils and scissors, fosters their cognitive and motor skills development.

In my classroom, we often engage in art activities that involve using various tools, allowing students to explore their creativity while developing essential skills. Reflecting on the historical context presented in the article, I can draw parallels between our art projects and the early use of tools by our ancestors, showcasing the enduring connection between creativity and practicality.

Stop Point 2: Cordage and Rope as Essential Tools

The article highlights the crucial role of cordage, asserting that it is one of the most important tools ever used by humans. This revelation opens up a valuable opportunity to introduce the concept of tools in a broader sense to my young students. By simplifying the idea that rope and cordage are tools, I can emphasize their significance in various human activities.

Incorporating this knowledge into my teaching, I can design activities that involve teamwork and collaboration, simulating the communal aspects of using tools. This not only aligns with the historical context discussed in the article but also encourages social development among my grade 1 students.

Stop Point 3: Nature as Inspiration for Innovation

The article suggests that early cordage production might have been inspired by nature, specifically plants with ropelike structures. This notion provides an excellent segue to introduce the concept of innovation and problem-solving to young minds. By exploring the idea that early humans looked to nature for inspiration, I can encourage my students to observe and draw inspiration from their surroundings.

Incorporating nature-themed art projects and discussions about the ingenious ways in which humans have learned from the world around them can foster a sense of curiosity and environmental awareness in my grade 1 students.

In conclusion, the exploration of the "Art and Science of Rope" article has not only deepened my understanding of historical tools but has also offered valuable insights into connecting these concepts with my teaching practices. By weaving together the threads of history, art, and science, I aim to provide my grade 1 students with a holistic learning experience that sparks their curiosity and nurtures a love for exploration.

Three Reflective Questions

• 1) How can I integrate the concept of tools, inspired by the historical use of cordage and rope, into more hands-on and collaborative activities in my grade 1 classroom?

• 2) In what ways can I foster a sense of curiosity and environmental awareness in grade 1 students by drawing connections between nature's inspiration for cordage and their own creative endeavors?

• 3) How might I adapt my teaching methods to cater to different learning styles when introducing historical and archaeological concepts, ensuring that grade 1 students grasp the fundamental ideas without feeling overwhelmed?

Week 8: Knitting & Math

Reflecting on Knitting and Math: A Tapestry of Learning

Belcastro, S.-M. (2023). Adventures in mathematical knitting. American Scientist, 111(6), 426-429.

As a first-grade educator, I'm always on the lookout for innovative ways to engage young minds and make learning meaningful. 

Stop 1: An Unexpected Intersection
The article "Adventures in Mathematical Knitting," unveiled a fascinating connection between a seemingly traditional craft and complex mathematical concepts like manifolds. The article highlighted how basic knitting techniques, like increasing and decreasing stitches, can be used to represent the curvature of these abstract objects. This sparked a realization: knitting, with its tangible nature, could potentially bridge the gap for students struggling to grasp abstract mathematical concepts.

Stop 2: The Power of Making
This realization resonated deeply with my understanding of learning through making. When children are actively involved in creating something, they engage different areas of their brains, solidifying understanding and fostering a sense of ownership over their learning. Knitting, with its repetitive and rhythmic nature, can also promote focus and mindfulness, essential skills for young learners.

Stop 3: Weaving Learning Experiences
However, translating the intricacies of manifolds into first-grade classrooms might be a bridge too far. But that doesn't mean the core concept of using tangible representations can't be adapted. Here are some ways I envision incorporating the spirit of mathematical knitting into my lessons:

Shape Exploration: Students can use yarn to create basic shapes like squares, triangles, and circles. This activity not only reinforces shape recognition but also allows them to explore the concept of perimeter and area through hands-on manipulation.

Pattern Play: Introducing simple knitting patterns, like alternating colors or creating stripes, can introduce students to the concept of patterns in mathematics. They can practice identifying, replicating, and even creating their own patterns, building foundational skills in sequencing and logic.

Counting and Addition: Yarn can be used to create visual representations of addition and subtraction problems. Students can manipulate the yarn to add or remove strands, making the process of abstract calculation more concrete and engaging.

While these are just a few initial ideas, the possibilities are vast. Collaborating with art or crafts teachers could unlock further creative avenues, like weaving geometric shapes or creating yarn sculptures representing various mathematical concepts. The key takeaway is this: embracing the unexpected connections between seemingly disparate subjects like knitting and math can spark curiosity, foster a love for learning, and ultimately create a richer tapestry of understanding for our students.

It has reminded me of the power of creativity, exploration, and cross-curricular connections in fostering a love of learning in young minds. As I continue to explore these possibilities, I am confident that the lessons learned will far exceed the boundaries of the classroom, leaving a lasting impact on both my students and me.

Video: Origami Fashion with Uyen Nguyen Part 1

Uyen Nguyen's video demonstrates the transformation of origami paper into a form of fashion. She delves into aspects like direction, patterns, and shapes, including curves, diagonals, diamond patterns, and more. This serves as a compelling illustration of the diverse connections that can be forged between origami and mathematics.

This Week's Activity:curricular work with Coast Salish weaving and mathematics.

Over the weekend, I spent time with my niece engaging in hand weaving activities. Together, we measured the required amount of yarn, practiced various patterns, focused on the right direction, and determined when to flip our hands for the next layer. It was a delightful experience to intertwine mathematical considerations with the enjoyment of creative play.

Week 7: Mathematics and Poetry

 This Week's Reading: 

Karaali, G. (2014). Can zombies write mathematical poetry? Mathematical poetry as a model for humanistic mathematics. Educational Studies in Mathematics, 86(1), 38-45. https://doi.org/10.1007/s10649-014-9544-4

Gizen Karaali's article, "Can Zombies Write Mathematical Poetry? Mathematical Poetry as a Model for Humanistic Mathematics," talks about math in a new way. Instead of just numbers and rules, the author says math is connected to what makes us human – thinking, being aware, and being creative. While reading, I found three important things to think about. First, the idea that math and poetry can go together, making math more relatable. Second, that math isn't just about rules, but can be beautiful too, like art. And third, that being creative is an important part of doing math.

My First Stop:

The first important thing to think about is how math can be like poetry. Karaali says that just as poetry is a way to express feelings and ideas, math can be too. It's like using words and numbers to tell a story. As a teacher, this makes me think about how I can make math more fun for my grade 1 students. Maybe I can use simple rhymes, stories, or games to help them understand numbers and shapes better, making math more interesting and easy to understand.

My Second Stop:

The second thing is about finding beauty in math. The author talks about how math can be like art, with patterns and shapes that are pleasing to the eye. This makes me think about how I can show the beauty of math to my grade 1 students. Maybe I can use colorful things or games to help them see that math is not just about rules, but can be really cool and pretty.

The second important thing is about finding the beauty in math. Karaali talks about how math is not just about rules but can also be really pretty, like art. This makes me wonder how I can show the beauty of math to my grade 1 students. Maybe I can use colorful things or fun games to help them see that math is not boring but can be exciting and nice to look at.

My Third Stop:

The third point is about being creative in math. The author says that being creative is an important part of doing math. This makes me think about how I can encourage my grade 1 students to be creative when they are learning math. Instead of just following rules, maybe I can let them come up with different ways to solve problems, making it more fun and interesting for them.

As a teacher, these thoughts make me want to make math more exciting for my grade 1 students. I want to show them that math is not just about numbers and rules, but it can be like a fun game or a beautiful picture. I also want to encourage them to be creative in math, to come up with their own ideas and solutions. This way, they can enjoy learning math and see it as something interesting and cool.

Finding Five Mathematical Poems From Mathematical Poetry at Bridges 2021

1. Stephanie Strickland

New York City, New York, USA
http://stephaniestrickland.com

Poem: The Infinite Stops Between Our Fingers

2. Amy Uyematsu
http://www.poetryfoundation.org/bio/amy-uyematsu
Poem:  This Thing Called Infinity

My personal interpretation:

"I think she talks about the idea of infinity, which means something that goes on forever and is impossible to fully understand. She mentions how nature, like a passion flower or snowflakes, makes her feel the presence of infinity. The poem also touches on some tricky math ideas about infinity and how it can be confusing. I think the poet reflects on how time can feel very long during sad moments and very short during happy ones."

3. Carol Dorf

http://talkingwriting.com/why-poets-sometimes-think-in-numbers/

Poem: Ask for a universe and what do you get?

My Personal Interpretation:

"I think the poet talks about space travel and how scientists once thought about using wormholes to go to other worlds. The poem imagines a future where artificial intelligence (AI) might explore space before humans and send us updates. It also considers the challenges of space exploration, like dealing with intense heat and losing the sense of night when close to bright lights."

4. Marian Christie

https://marianchristiepoetry.net

Poem: Elevenses

My Personal Interpretation:

I think Marian reflects on the number 11, which stands out as an odd one between the neatness of 10 and the convenience of 12. The poem highlights the uncommon nature of 11 in our daily lives — we don't have 11 fingers or toes, buy 11 items, or choose 11 for things like rolls or eggs. Christie uses a terrace scene with three people enjoying coffee, scones, and a sunny day to capture the uniqueness of 11. The binary notation of 11 is linked to the poet and two others, creating a moment of connection under the open sky with the backdrop of June's birdsong and a cricket match on the radio. The poem appreciates the distinctiveness of 11 in the simplicity of shared moments.

5. Tom Petsinis

http://tompetsinis.com/

Poem: Mathematician

Now it's my turn to become a mathematics poet!

 My Fibonacci Poems:

1. Fibonacci Buddies

Count with us, the Fibonacci crew,

One, one, two, three, oh, it's true!

Rabbits hopping, a joyful view,

Growing numbers, join the queue.

Start with one, then add one more,

Each new friend, we adore.

Counting onward, never a bore,

Fibonacci's friends, let's explore.

In a sequence, like a song,

Numbers dance and play along.

Spiraling up, oh, so strong,

Fibonacci's rhythm, all day long.

2. Magical Fibonacci Garden

In a magical garden, a number delight,

Fibonacci's secret, shining bright.

One and one, start the flight,

Add them up, what a sight!

Two rabbits play in the sun,

Three join in, oh, such fun!

Numbers dancing, one by one,

Fibonacci's garden, second to none.

The flowers bloom in a spiral grace,

Following numbers, embrace.

Magical patterns, a math trace,

In Fibonacci's garden, find your place.

Final Project Proposal - Art Mosaic And Mathematics

 

Final Project Proposal

Week 6: Let's Dance To Learn Mathematics!

This week's Article: sarah-marie belcastro & Karl Shaffer (2011). Dancing mathematics and the mathematics of dance. 

I enjoyed watching Malke Rosenfeld's TedX video, "Jump into Math," where she discussed the importance of patterns in math, highlighting the strong connection between mathematics and dance. While learning to dance, individuals not only develop physical skills but also gain insights into mathematical concepts, particularly in geometry. Rosenfeld's emphasis on ensuring dance synchronization with a partner to understand transformations and symmetry resonated with me as a valuable approach to make mathematics more tangible.

In the article by Sarah-Marie Belcastro and Carl Shaffer (2011), they underscored the parallels between dance movements and mathematical concepts. My first stop in this article was when many dancers performed symmetrical patterns in movements. This resonated with Rosenfeld's emphasis on symmetry in dance. My second stop was exploring the strong relationship between geometry and dance, where dancers utilized various tools like ropes or ribbons to form shapes. By observing dancers moving their bodies in different directions, it became evident how these movements connected to the principles of geometry. This article provided practical activities and challenges for integrating body movements into mathematics learning, becoming my second stop in this insightful exploration.

Reflecting on our first graders, who thrive on physical engagement, I recalled an activity where we transformed the playground into a giant number line, fostering their interest and participation in addition and subtraction. The dynamic blend of movement and mathematics proved more engaging than traditional paper-based approaches.

After absorbing insights from the video and article, I'm pondering questions about incorporating more movement-based approaches, like dance, into our math lessons. Considering my upcoming math inquiry on time, I'm exploring activities that merge movement with temporal concepts. Additionally, I'm contemplating ways to be mindful in connecting mathematics and dance, seeking simple and practical steps for immediate implementation.

Reflective Questions:

1. How can I implement more movement-based approaches, such as dance, in mathematics learning?
2. What are some possible activities to explore in my next math inquiry on time?
3. How can I be more mindful in making connections between mathematics and dance?
4. What are simple and easy steps I can take immediately to enhance the integration of movement in math lessons?
5. 
   

For this week's engaging activity, I introduced the Clap Hands body-rhythm pattern game to my first graders during our morning meeting. Regrettably, I couldn't capture the lively moments as I didn't have my co-teacher present for recording or photos. Nevertheless, the experience was thoroughly enjoyable and fascinating as I observed the students' diverse movements challenging one another. While some required additional guidance to grasp the rules, the overall engagement and focus were noteworthy.

Clap Hands Body-Rhythm Pattern Game (photo from the website)

This activity brought to mind a game from my past experiences in Korea known as "Di-Be-Di-Be-Deep." In this game, participants engage in three specific body movements, with the player and the "it" selecting one movement after the chant "Di-Be-Di-Be-Deep!"—similar to the concept of rock, paper, scissors. If the player matches the chosen movement of the "it," they lose. This game not only adds a fun element but also encourages students to think strategically about their movements to outsmart the "it."

Photos of the game, "Di-Be-Di-Be-Deep"

Reference

Belcastro, S.-M., & Shaffer, K. (2011). Dancing mathematics and the mathematics of dance.

Week 5: Stories in Mathematics

Video Activity - Binary Numbers Represented as Concentric Circles

I selected an activity presented by Ali and Colin that creatively illustrated binary numbers using concentric circles, incorporating coloring and arithmetic. Initially, I found the concept of binary numbers confusing, but it became intriguing to witness how Ali and Colin transformed this intricate idea into concentric circles, drawing inspiration from Kandinsky.

Inspired by Ali and Colin's approach, I adapted the activity for my first-grade students who are currently developing the concepts of addition and subtraction within 20. I put different colors to each number and devised Math Riddles, prompting students to analyze the colorful concentric circles and compute the sum of the associated numbers.

For example, in the first circle of sample 1, colors like yellow, blue, and orange represent 2+1+0, totaling 3. The next circle, displaying linen and green, corresponds to 5+3, resulting in 8. Hence, the answer is 3+8, equating to 11.

In another sample, students are challenged to work backward, starting with the final number and deducing possible combinations. For instance, the initial circle with red, yellow, and linen corresponds to 4+2+3, summing up to 9. The subsequent one, featuring two orange and one yellow, represents 1+2+1, totaling 4. Consequently, 13 is expressed as 9+4.

Another sample with different shapes.

I also tried to crate an artistic piece using colors representing birthdays within our classroom community. After identifying birthdays and assigning colors to each month, I colored concentric circles, repeating layers for multiple individuals born in specific months. The final result revealed the colorful patterns.

Lesson Plan on Addition within 20
Issue	Some students lack creative thinking and connections between math and art despite having fluency in adding and subtracting within 20.
Guiding Questions	1. What do you see? What do you think we are learning right now? 2. What do circles and colors represent? 3. What else can we represent using colors and concentric circles? 4. What is the relationship between numbers and patterns (or colors)?
Integrated Learning with Outdoor Education	Let students make patterns using different materials from outside and come up with their own problems.
Possible Extension	Share their work with each other and collaboratively solve the problems.

Reading from Dietiker: What math education can learn from art:

Stop 1: The Separation of Math, Science, and Art Dietiker highlights the common separation of math, science, and art, emphasizing misconceptions about the nature of science and art. This resonated with my classroom experiences, where discussions often revolve around integrating math with science and literature. For instance, our recent exploration of scientists' thinking and the scientific method involved an experiment on states of matter with baking. This activity seamlessly integrated measurement and time, leading some students to even produce procedural writing about their baking experiences.

Stop 2: Untidying Mathematical Experiences Dietiker's assertion that creating aesthetically rich mathematical classrooms requires untidying students' mathematical experiences struck a chord with me. Reflecting on my own practices, I recognize the importance of visual prompts, especially for English Language Learners in my class. Visual presentations significantly enhance their engagement and participation in solving math problems.

I found a strong connection with Dietiker's concept of math as a story. Many students express negativity towards mathematics due to its perceived difficulty. However, framing mathematical problems as stories has proven effective in cultivating a more positive attitude. When problems transform into relatable stories, students are more willing to share their thoughts and ideas verbally. Moreover, realistic and relatable "stories" prompt students to challenge themselves and engage in problem-solving. The use of manipulatives and drawing strategies further enhances their involvement in the process.

Questions Arising from the Reading:

1. Encouraging Student-Created Math Stories:

   • How can I inspire my students to generate their own stories within the realm of mathematics? What creative prompts or approaches can be employed to nurture this storytelling aspect?

2. Integrated Curriculum Design:

   • How can we ensure that our educational program or curriculum seamlessly integrates mathematics, art, and science? What initial steps should be taken to promote a cohesive and interconnected learning experience for students?

This reflection prompts me to consider ways to empower students as storytellers in mathematics and underscores the importance of a well-integrated curriculum that incorporates art, science, and mathematics harmoniously.