Kepler, J. (2010). The six-cornered snowflake: A New Year’s gift (C. C. Rodrigáñez, Illus.). (Original work published 1611).
Stop 1: My first stop occurred right at the beginning when Kepler describes searching for a gift and mentions "prodigiously puny creatures." This immediately brought me back to my Grade 4 classroom. When we made those 3D symmetrical snowflakes, the children weren't just doing a craft; they were holding a mathematical marvel. Kepler’s focus on the "puny" is a stop for me because it challenges our academic habit of only looking for "big" ideas. As a math educator, it reminds me that the most profound truths are often hidden in things we usually walk right over. We often move too fast past the small things in our curriculum that actually deserve our attention.
Stop 2: I stopped again on page 65, where Kepler distinguishes between the "material necessity" that shapes pomegranate seeds (physical pressure) and the "formative" nature of flowers and snowflakes. This was a dense section that forced me to slow down. In math education, we often teach the how - how to measure a shape or identify a pattern, but we rarely stop to ask why nature chooses one geometry over another. Kepler’s struggle to find a "different kind of thinking-cap" for this anomaly is exactly the kind of intellectual "itch" I want my students to feel. It’s a reminder that true mathematical thinking happens when the simple explanations stop working.
Stop 3: The final stop was Kepler’s "mortification" at arriving without a gift, which actually sparked his entire inquiry. As teachers, we are often terrified of not having the perfect answer or lesson ready for our students. Kepler’s lack of a physical gift led to a gift of intellectual discovery. This changed my perspective: I realized that sometimes the best thing I can bring to my students is an unanswered question and the vulnerability of being "empty-handed" alongside them.
A Question I Wonder: Kepler spent this entire treatise trying to solve the mystery of "Why six?" and eventually admitted he hadn't fully answered it, yet his curiosity laid the groundwork for modern science. How can we, as educators, create "stops" in our math lessons that prioritize this kind of unresolved wondering over the quick, correct answer, especially when we are under pressure to move through the curriculum at a continuous pace?
"I realized that sometimes the best thing I can bring to my students is an unanswered question and the vulnerability of being "empty-handed" alongside them."
ReplyDeleteBeautifully put!
"In math education, we often teach the how - how to measure a shape or identify a pattern, but we rarely stop to ask why nature chooses one geometry over another. Kepler’s struggle to find a "different kind of thinking-cap" for this anomaly is exactly the kind of intellectual "itch" I want my students to feel."
I think this connects to our concerns that math (and science) is approached through narrow analytical lens limiting the scope of what we can learn and that should prompt critical introspection on the kind of knowledges and wisdom we seek to uncover and through what ways of cognition and awareness.
"Kepler’s focus on the "puny" is a stop for me because it challenges our academic habit of only looking for "big" ideas. As a math educator, it reminds me that the most profound truths are often hidden in things we usually walk right over. We often move too fast past the small things in our curriculum that actually deserve our attention."
Reminded me of Blake's poetry:
To see a world in a grain of sand
And a heaven in a wild flower,
Hold infinity in the palm of your hand
And eternity in an hour.
Thanks a lot for sharing these thoughts, Kabula!!
Beautiful musings and observations here, Kabula and Aun! I just love Kepler's writing for its close-up view of finding awe and wonder in the close observation of the living world. Isn't it great to get to know this famous scientist in such a humble and at the same time awe-inspiring way? "Be like Kepler!"
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