Week 2: Multisensory Mathematics - Summary and Response (post 2 of 2)

 Summary of Kepler’s (2010) reading

This selection reads like poetry, where Kepler seems to describe the wonders of six-sided shapes, particularly the perplexity of snow or “six-corned stars” (p.35). The article highlights the fascination of different 3D structures forming, such as the “keel of cells”. They discuss rhombuses and compare angles, such as obtuse angles, of beehive cells, which on paper or in words, can be difficult to describe. I can see why the tactile practice of forming or building these shapes is so significant as you need to go through trial and error to see which sides can line up and if they are able to meet and conjoin with precision. The orientation can play a significant factor in how the cells appear and the 2D shapes that form the 3D composition (I found this video as an added visual support, I’m a visual learner myself: Matematicasvisuales: Honeycomb)  

The article then goes on to explore pomegranates and the configuration of their seeds. That they too have this rhombic structure as the fruit matures. The article portrays the story of how the seeds begin small, round, but as they grow, there is less sufficient room. And as the “rind stiffens and the seeds continue to grow, they become crowded and pressed together” (p.53). A great question would be for students to explore, where else may they see this phenomenon? How can they compare volume and surface area, like cells? There are so many excellent extensions students can explore: ratio of the cell's surface area to volume, types of cells in the human body, why are we multicellular organisms versus single-celled, what type of cells do plants have, and how does that impact their rigidity? (Sorry, the biology teacher in me is coming out)! But its application of mathematics and 3D configuration can be extended.

Overall, I appreciate how this article shows the fascination of these platonic structures and how their composition is derived from 2D polygons or shapes.

Reflection of Kepler’s reading and assigned videos:

There is a difference in observing real-life objects and feeling them rather than simply observing them in images or photos. For example, when peeling an orange, you start to notice that some of the pieces may not necessarily be the exact size, which can affect the symmetry if you were to have cross-sectioned the fruit. When my student (who has verbal challenges) tried making the icosahedron, she struggled to connect some of the sides. If she had more time, she may have been able to complete the puzzle but oftentimes, we need to rotate, maneuver or manipulate the pieces to gain a better understanding of the configuration. This can be shown through an image but not everyone has the visual processing skills to grasp these mentally. For many students, hearing to feeling items or sounds enhances the comprehension of a concept. Like young babies, they learn through sense through their hands and mouth, and this contributes to a way to grasp their world. Wortman (1988) notes: “The function of the brain is to sort out the information gained from the senses into meaningful learning.” This is especially important as theories from Piaget note that we don’t all learn math at the same rate. Having additional information inputs can provide an enriched learning environment. Why should this not continue as children progress into adolescence or adults as mathematical learners?