WEEK 2: Kepler explores the geometric and physical principles underlying the formation of snowflakes and other natural phenomena. He draws parallels between the hexagonal patterns found in snowflakes, honeycombs, and pomegranate seeds, suggesting these shapes are efficient solutions to packing problems in nature. Kepler ponders the philosophical implications of these natural patterns, reflecting on the inherent mathematical intelligence within nature's design. He considered the material necessity and the innate tendencies of natural bodies to assume particular forms that optimize space and function. Kepler integrated geometry, physics, and philosophy to understand the principles that govern the natural world. STOP 1： " For a thing has a shape of its own when it is bounded by itself, since boundaries determine shapes. "(p.37) This quote resonates with the concept that the identity of an object, concept, or entity is largely framed by where it ends—where the line is dr
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WEEK 2: Activity
Activity Reflection: The patterns or markings seen in a gourd when cut open likely result from natural growth processes. In botany and biophysics, many plants' growth is influenced by genetic factors and environmental conditions, which determine the distribution and shape of plant tissues. Similar to the natural patterns Kepler studied, the patterns inside a gourd may be a consequence of how cells divide and grow, governed by specific biochemical and physical laws. This internal patterning could be a natural manifestation of resource allocation, structural support, or physiological needs during growth. As Kepler noted in his work, many phenomena in nature can be understood by exploring fundamental mathematical and physical principles.
WEEK 1 : Reflections The article I have read is Nathan, M. (2021) Excerpt from Foundations of Embodied Learning pp. 3-7 and 147-151. Briefly summary: What I have reading can be divided into 2 parts: 1. The first part is about the way of learning: embodied learning is a natural human activity, and it is possible to design for it in ways that can inform educational practices and policies in order to usher in a new era of educating the embodied mind. And it set up 2 examples: ⑴ students actually have very good intuitions about how to think about unknown quantities and generalized relationships between quantities prior to formal instructions. ⑵ society does not value embodied forms of knowing; educators seldom encourage students to engage in any of physical activities to get understanding of subjects. 2. The second part is about grounding metaphor used in mathematics education. It mentioned 3 examples (numbers and operations, algebraic equations, geometry) of mat