Week 3: What Do We See Around Us?

This week, I took some of my students outside, and they were really excited, even though it was super cold, below -10 degrees!

To kick off our outdoor adventure, I instructed my students to find a spot and sketch anything they observed that was living or human-made. With materials like paper, pencils, and chalks from the classroom, they enthusiastically began drawing their surroundings. What surprised me was their focus on human-made structures in their sketch. Their sketches featured apartment buildings, our school campus, all defined by distinct lines and square shapes forming grids.

The sight of apartments and soccer nets immediately caught my attention, prompting me to join in the drawing. This experience resonated with the insights from this week's reading by Gerofsky & Ostertag (2018), highlighting how grids and building structures have served as powerful tools of territoriality and colonialism since the 15th century. The reading explained how grids compartmentalize spaces of thought into orderly, separate, and sealed boxes or cubicles (Gerofsky & Ostertag, 2018).

(My sketch of our school field)

Post-reading, I couldn't help but notice grids everywhere—floor patterns in photos, items on my classroom whiteboard, windows and doors of buildings, patterns on the school fence, and even the classroom itself, resembling a little grid box.

This experience triggered memories of a gardening activity I conducted last Spring with my former students at a school garden. I recalled attempting to control the garden by arranging it in rectangular or grid shapes, placing gardening paper in rows, and cutting it into rectangular shapes for seeds or planting.

Reflecting on this, I realized how we often find comfort in placing ourselves within rectangular shapes and grids, seeking a sense of control in our lives.

Returning to the outdoor activity, our students expressed disappointment at not finding any living things other than trees and humans. They explained that all the ants and other creatures (given the scarcity of bugs other than ants and spiders in our town) seemed to be in hibernation (why not?)

Prompted by this, I asked them to observe any patterns and lines they could identify. Their response emphasized rectangular and square shapes with straight lines. I posed another question:

"What if our buildings, soccer nets, and fences were not straight but irregular, and they didn't form rectangular shapes?"

They replied,

"That would be so weird, and maybe the buildings would collapse."

It was fascinating to hear their perspectives align with the insights from this week's reading—providing opportunities for students to explore different patterns, lines, and expressing the reasons behind them is crucial, especially in outdoor settings.

Here are some activities for experiencing lines and angles through whole-body movement or large body motions outdoors:

• 1. Utilize sidewalk chalk to draw various shapes and angles on the pavement. Encourage children to move along the lines or imitate the angles with their bodies. Incorporate games like hopscotch with geometric shapes or create a life-sized angle board where children match specific angles with their movements.

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• 2. Engage in nature-inspired art using natural materials. Arrange sticks or stones to form geometric patterns or shapes, discussing the angles created by their placement.

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• 3.Provide materials like sticks, stones, or branches for outdoor structure building. Discuss the angles formed by the arrangement of these materials, allowing children to visually understand how different angles contribute to the stability and design of their structures.

P.S I used to work with a outdoor space company to re-design the school playground area for early years. This reminds me of all the learning and playful opportunities for our students, but also makes me think about all the patterns and lines!

Reference

Gerofsky, S. & Ostertag, J. (2018). Dancing teachers into being with a garden, or how to swing or parkour the strict grid of schooling. Australian Journal of Environmental Education, 34/2, 172-188.

Week 2: Exploring Mathematical Patterns and Enhancing Learning Through Multisensory Experiences

This week, I read an interesting old text by Johannes Kepler from 1611. It's called "On the Six-pointed Snowflake: A New Year's Gift." I'll be honest, understanding it was tough, and it took me longer than I thought.

Basically, Kepler talks about why snowflakes always have six sides. He wonders why they're not four, five, or seven-sided.

He suggests that the hexagon shape (like a six-sided star) is the best way for snowflakes to fit together efficiently. He compares it to the hexagon cells in bee hives and honeycombs, as well as the way pomegranate seeds are tightly packed.

Kepler's idea is that the six-sided shape comes from how tiny bits of water arrange themselves to fill space most efficiently. He says it's similar to the structure inside honeycombs, which is like the space between ice crystals and snowflakes.

He also notices that some fruit trees, like apples and pears, have flowers with five corners. Kepler thinks this is special and connected to the soul of these plants.

This reading made me think of my first-grade students and how they get excited about snow. They have so many questions about how snow melts, why it turns into ice, and even why it sometimes turns black. Although they didn't ask about the shape of snowflakes in a geometrical way, I believe mathematicians like Kepler started exploring the world from their own experiences.

    

The next day, the weather got very cold in Korea, and I saw snowflakes on the classroom window. I encouraged my students to be like scientists and mathematicians. They drew what they saw and asked how long the snowflakes would stay on the window, focusing more on time than shapes.

I think it's important for students to experience things and use all their senses to learn about math. This week's readings discussed "multisensory," which means using our senses like touch, sight, hearing, and sometimes taste to understand math. It's helpful for students to touch, feel, see, listen, and even taste things to learn about 3D shapes in their lives.

As a teacher, student, and someone who loves math, I learned a lot by exploring with my food. I started by collecting fruits like apples, bell peppers, tangerines, and spicy peppers. When I cut the apple, I found a five-pointed star pattern in the center, just like Kepler said about apples having five corners. The bell pepper had four corners, and I'm pretty sure there are bell peppers with three corners, too!

I also had fun making a tetrahedron (a 3D shape) using two pieces of paper at home. While making it, I used my senses to notice patterns and shapes following the instructions.

(I recorded myself struggling with the paper folding😆)

After these activities, I realized how important it is for students to touch, feel, see, listen, and sometimes taste things to learn about math daily. For students who can't use all their senses, like those with disabilities, it's best to use the senses they can to help them learn and stay curious. In my school, we have some students with disabilities, and they always engage in sensory activities, touching and feeling objects as a big part of their learning.
Reference
 Excerpts from Johannes Kepler (1611/ 2010) On the Six-pointed Snowflake: A New Year's Gift.

Week #1 Post: Embodied Mathematics: Exploring Gestures and Body Measurements in Teaching and Learning

 Part 1: The Power of Gestures in Teaching Mathematics

Embarking on Gerofsky's (2011) exploration of "Seeing the graph and being the graph," the concept of using gestures in mathematical instruction felt uncharted. The word "gesture" sparked connections to my role as a teacher working with English Language Learners (ELL) and memories of students expressing themselves through intricate body language.

The study delves into the impact of teachers' gestures on students' understanding of mathematical concepts. A compelling example involved the class gesturing the shape of a graph for the function y=4. The diversity in students' gestures, ranging from subtle hand movements to whole-body engagement, highlighted the multifaceted nature of conveying mathematical ideas through gestures.

I couldn't help but relate this to a recent experience with a student. While not directly related to mathematics, the term "gesture" reminded me of a science experiment conducted by a student involving corn starch and water. Struggling to verbally explain the gooey texture, she used her entire body to demonstrate how it flowed and moved—a vivid illustration of the power of embodied expression (see photo).

The study recognized that gesturing in mathematics goes beyond demonstrating knowledge and skills; it becomes a multimodal resource for learners. Experimenting with gestures while visualizing graphs underscored the power of embodying mathematical concepts. The study suggested incorporating gestural approaches in teaching graphs and functions resonated, particularly as I consider its applicability to my grade one students, especially in upcoming lessons on measurement using non-standard units.

Questions arose concerning English language learners:

1. How would they express understanding in the new unit?

2. How could gestures enhance their comprehension of mathematical concepts?

These inquiries underscore the importance of making learning engaging and meaningful for young learners.

Reference: Gerofsky, S. (2011). Seeing the graph and being the graph. Educational Studies in Mathematics, 76(3), 245-256.

Part 2: Body Measurement Adventures

In body measurements, I embarked on a fun activity using my partner as a measurement tool. Comparing our measurements to those in the Math and Measurement in the Garden handout revealed surprising correlations, sparking curiosity about factors influencing the results.

Cultural differences emerged, notably my unfamiliarity with inches due to a centimeter-centric upbringing in Korea. The discomfort prompted contemplation on the arbitrary nature of measurement units. We measured our kitchen island using my partner's hand length, creating a practical application of the body measurement exercise.

Differing preferences surfaced – my partner leaned toward inches, while I favored centimeters and handspan. The ensuing discussion explored convenience and underscored the versatility of using both measurement systems, ultimately appreciating the value of having a measuring tape.

This body measurement exercise extended beyond the playful aspect, providing insights into practical applications. Considering a new wine cooler purchase, the exercise informed us about available space and compatibility with the kitchen island. The interplay of preferences and considerations enriched our understanding of measurements.

In conclusion, the week's exploration encompassed the influential role of gestures in teaching mathematics and the practicality of body measurements. As I integrate these insights into my teaching approach, I look forward to fostering a dynamic, engaging, and inclusive learning environment for my students.

Hello, Math Inquirers!

 

Hello, everyone!

I'm Sue Park, a Grade One teacher at Chadwick International in South Korea. My passion lies in cultivating open-ended mathematics and inquiry-based learning in my classroom. Join me in this concise blog, where I'll share insights, experiences, and discoveries from my journey in transforming the learning landscape for our youngest minds.

Let's delve into the world of open-ended mathematics together!

Best, Sue