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.