Week 2 Activities + Connections

A highlight this week has been thinking about disability in a new way: a cultural/societal problem, not an individual one. In the introduction of the weekly topic, Dr. Gerofsky made a very compelling argument that perhaps the social and built environment is what is disabling. When we design more inclusive lessons that target multiple senses - it benefits everyone! 

Watching Vi Hart this week helped to remind me of the math that can be found in everyday life. 
I managed to document ways to take Rocket candies and demonstrate concepts of permutations + combinations, statistics, graphing, graph theory, and geometry.

Then, after viewing the hexaflexagon video, I constructed my own transforming snowflake. I find this use of the hexaflexagon the most intriguing. 

The mathematical fruit yielded some interesting patterns:

The horizontal apple slices yielded five point radial symmetry. This is very similar in structure to the apple blossom (below) mimicking the five-point radial symmetry, and similar to the symmetry of Phylum Echinodermata ("Spiny-skin" like starfish). 

I wondered what the dots above each peak and trough of the star represented, so cutting vertically I found they connected the stem to where the flower would have had its petals at the base of the apple creating a ten-bundle cage around the central star-shape containing the seeds. I would imagine that all apples are constructed in a similar fashion, but I might be over-reliant on my one sense of vision to determine this. 

Source: https://chelanranch.com/cdn/shop/articles/apple_blossom.jpg?v=1697583102

Also cutting into the stem of lettuce, I noticed an entirely different pattern as this isn't a fruit, but a shortened stem with large leaves. 

This arrangement of leaves reminded me of the golden ratio video from Vi Hart, and her explanation on 137.5 degrees as the optimal angle for leaf arrangement to maximize sun exposure without self-sabotage! Down a small rabbit hole on phyllotaxis I stumbled upon this website that teaches you how to use the golden ratio to draw flowers using R ("an open-source programming language and environment designed specifically for statistical computing, data analysis, and graphics," says Google).

Reflection questions: 

I did not construct the paper shapes when reading about Kepler, it was tremendously difficult to visualize what he was trying to communicate. I feel quite confident in my 3D spatial orientation capacity, but I still felt lost here. Instead, I built his descriptions of space-economy using playdoh to facilitate my own understanding of his concepts and it was a night-&-day difference. 

In his book, The Six-Cornered Snow Flake: A New Year's Gift, Kepler (2010) described rotating a pyramid of balls such that the side rather than the apex was uppermost to reveal a special orientation... I couldn't visualize this, then I made it out of playdoh and STILL I struggled (my wife documented this process), then when I correctly oriented the pyramid and removed the sphere revealing the four balls below, I was shrieking with joy (my wife documented this, too). 

The difference between knowing and understanding can be minimized by learning from 3D living things and/or objects with shape, texture, smell, taste, etc. instead of a 2D printed image. 

For individuals with sensory impairment, this might be the only accessible way for students to experience an analogous first-order experience of a phenomena. As stated in our weekly introduction by Dr. Gerofsky, "if we reframe 'disability' as a driver for innovation and creativity, rather than as a deficiency, there is the potential to benefit the population at large, in education as in business."

This coming semester, I know I have students with severe dyslexia, test anxiety and the like. I am going to see if I can approach all subjects with this new frame of mind and model the accessibility that I want to see in our society and built environment. 

 

Links to the videos we watched copy-pasted from Week 2 resources: 

1. Vi Hart: Math improv Smarties (note that what she calls 'Smarties' is what we in Canada might call Rocket candies) and Supersmarties

2. Vi Hart 4 short Hexaflexagon films: Hexaflexagons part 1 --  Hexaflexagons part 2 -- How to make a Hexaflexagon --  Hexaflexagon Safety Guide --- and the ultimate, edible hexaflexagon, Flex Mex!!-  (For some additional optional Vi Hart edible math viewing, you can also check out the Green Bean Matherole &  Borromean Onion Rings)

3. George Hart: Mathematically correct breakfast (instructions) with video link at the bottom