March 11th - Term Assignment Draft 2

 Please find my draft slides here, as well as my updated draft proposal here.

Week 9 - Mathematics and traditional and contemporary practices of making and doing

This week's introduction touched on a few points that got me thinking about math and making. I am the last person you might find weaving or twine-making but some of the more modern technologies do appeal to me (laser-cutting, 3D printing, etc.,)

I think if there is one thing this course has exposed me to and really got me thinking more about is the diversity of mathematical practices. This course has explored a ton of traditional and contemporary practices, with a goal of getting me (and more importantly, my students) experimenting with these practices as a way to make connections to mathematical principles. While I can appreciate the mathematics within the technologies of rope-making, loomed textiles, and natural dye processes, the honest fact of the matter is that it is unlikely that I will engage in many of these given the materials and time necessary - they simply feel so far away from my comfort zone. I do enjoy watching this hands-on approach, though. I am much more likely to engage in some of the more modern approaches, like upcycling waste materials for creative re-use. 

Bohr & Olsen (2011) The ancient art of laying rope

Bohr & Olsen (2011) take a look at the historical significance of rope-making, and draw attention to the symbolic importance. The authors identify examples from various cultures which emphasize the historical and cultural significance of rope-making practices. The discussion within the article extends to scenes depicting advanced rope-making techniques in ancient Egyptian tombs. The authors further take a look at the geometrical properties of ropes, and discuss the similarity in the structure of ropes made from different fibrous materials. I've never really thought about it too deeply, but there is a universal relationship between the interlocked nature of a helix and the number of rotations in a helix. Bohr & Olsen (2011) reveal some universal behaviour of helix structures.

Secondly, the article examines zero-twist structures, which is a rope that is rigid and inextensible. I've never really thought much about ropes as geometric structures but it makes sense when put within this context. If I could connect it directly to our curriculum, I wouldn't mind the idea of exploring the relationship between rope-making and geometry with my students, but I think the ideas of rigidity and extensibility are more in tune with other curriculums than the Alberta Grade 6 curriculum that I am working with. I think about tensile, compressive, shear, and torsional strengths and loads and high school curriculum when I think about those kinds of things. If I were taking this up with younger students it might have more to do with the symbolic and traditional nature of rope-making than the mathematics.

Week 8 - Mathematics & fibre arts, fashion arts, and culinary arts & Belcastro (2013)

Flashback this week as I read the materials to 2009 Malcolm deciding whether to become a teacher or go to culinary school. If I wasn't a teacher right now I'd most likely be a chef, and as someone who has spent/does spend a lot of time in the kitchen I can appreciate the mathematics inherent in the craft of preparing food. I grew up making recipes with my grandma, most of which she had memorized, and I scrambled in my adult life to gather them from her and write them down somewhere. My grandma was diagnosed with lung cancer in June of 2021 and between then and November of that year when she passed away she wrote all of her recipes down for me. Something that I will keep and one day pass along to my own kids. As a kid I didn't appreciate the mathematical thinking or patterns in these recipes but I can certainly see them now.

Knitting, crocheting, cooking, and other practices involve a lot of mathematical thinking in terms of proportions, logic, geometry, and others. The key takeaway of this week's introduction is the change in attitude required to recognize the inherent mathematics in these skills. This is the message that I try to pass on to my students when we do math - that by keeping an open mind and acknowledging the interconnectedness of math in life and in most things we do, there is a way to deepen your understanding. My students are very into finger weaving the last few weeks as one of the teachers in my school started a club, so I encouraged them this week to work those skills and make some interesting things.

Belcastro's (2013) article, Adventures in Mathematical Knitting, details her long-standing passion for knitting and crafting mathematical objects, namely Klein bottles. Belcastro argues that crafting these objects enhances understanding because it requires a deep comprehension of the abstractions that are being created. 

My first stop in the article was the challenge Belcastro faced early on in the designs of mathematical knitting. As someone who is not and has never been a knitter, I can't imagine the difficulty in planning out the twists and surface texture needed in designing something like a Klein bottle. The design has to fit together mathematically as well as aesthetically, as Belcastro explains, so there are multiple layers of challenges inherent in a task such as this one.

It's not overtly there but is fairly easy to make the connection to math when you look at fibre arts such as weaving, knitting, crocheting. The geometry and the patterns are evident in any beautiful piece of work. Cooking and knitting were both mathematical hobbies of my grandma, one of which I picked up and the other I didn't, but it's clear that she had a mathematical mind for these things. Her third hobby was drinking coffee, which I've also taken a liking to, and is rich with mathematics on its own. Weighing beans, heating water to a specific temperature, measuring pour rate; there are mathematical concepts in many hobbies that we don't think of.

Week 7 - Writing mathematically-structured poems & Radakovic, Jagger & Jao (2018)

 

I made an attempt at a braided bellringing PH4 poem this week, as discussed in Gerofsky (2020), and really enjoyed the process. Coming up with the four initial words was a little bit tricky, so I just went with what was in front of me - a steaming cup of coffee - something that has been a consistent staple of mine through all the big life changes of the last four years. Reliably and consistently, I can sit at the table and enjoy a cup of coffee every morning.

I loved the interplay of the four words as they weaved through the page, and how I could intersperse punctuation or emphasize different words to take different meaning out of each line. Line 6, morning ritual, caffeine-fueled is just slightly different than line 1, caffeine-fueled morning ritual, but gets the exact same point across. 

I like the idea of putting something like this on a coffee cup, maybe with some alterations, punctuation, or maybe a different word that works better in certain lines - does anyone have any suggestions? I showed my wife my work as she does sublimation onto ceramic mugs and she said she "didn't get it"... haha.

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Radakovic and Jagger engage with a poem by Sakaki, which has a structure built around concentric circles and increasing scale (1 - 10 - 100 - 1000 - 10 000). Mathematical poetry is an interesting intersection that I've never explicitly thought of before, but makes total sense. Any time I've examined poetry with my students, our work and attention is rooted in the math of the poem; how many stanzas in this poem? How many syllables in this haiku? Poems are a great way to see the relationship between literary works and math.

The authors recognize an important personal connection between authentic mathematics and poetry. Personal expression, routine, and playing with the words contributed to the authenticity and relatability of the work. This approach challenges the formal approach to poetry interpretation, which allows for a differing perspective on students' work. 

I shared some mathematical poetry with my students this week and we had fun picking out the words and phrases that we recognized from math. There was one poem, in particular, that tied together some of our work around fractions, which I'll share here. 

At lunchtime, Thomas had to share,

with a friend a juicy pear.

He cut it using extra care,

and left two pieces - that seemed fair.

When he was done, he had to laugh,

now each boy had exactly half.

The next day Thomas went to tea,

with two others - that made three.

They wanted to share evenly, 

the biggest sandwich they could see.

It was cut without a word,

and each boy saw they had a third.

Thomas and three friends dropped by,

hungry for a pizza pie.

They decided they would try,

equal pieces for each guy.

Thomas happily reports,

that each boy got a perfect fourth.

- Author unknown

Florian Mass, a data engineer who runs the blog at https://www.fpgmaas.com/ has a series on poetry and data which is fascinating, where he analyzes poetic meter of one of Reddit's "top" poets. Check it out if you're interested! 

Question for thought: How might the inclusion of poetry and specifically mathematical poetry impact the teaching of math in a diverse setting?

Week 6 reading - Henle (2021) - Mathematics that dances

Henle's article focuses on the mathematical elements of dance and how they can be related to mathematical concepts. The primary goal of this comparison is not necessarily to teach math but identify aspects within dance that are intriguing. I think this is an important thing to highlight as sometimes the exploration and play and movement is what prompts mathematical thinking, and approaching dance with math in mind might stifle creativity, whereas approaching with creativity in mind might encourage mathematical realizations.

One stop I had while reading the article was the specific examples of the Binasuan and dance with the four dancers; Henle discusses the idea that specific dance movements can be analyzed mathematically. The use of real-world dances to illustrate math principles adds some relatability to the discussion. Even though I'm not a dancer, I can see some of the ties to movement. Henle encourages separating the educational aspect of dance and math to focus on the inherent beauty and complexity of the dances themselves.

Henle also invites students to invent dances, which enhances the exploratory message of the article and encourages readers to appreciate the art and beauty of dance. I like this idea of having students invent movement and have explored this in the past few weeks - particularly with the idea of symmetry and reflection. I'm definitely going to try to incorporate some more creative movement in my class going forward as we explore new mathematical concepts. 

The second stop I had was the Locomotion game on page 77. In this game, participants spread out and silently choose two partners in their head. The movement begins, and each person moves around the room in an effort to create equilateral triangles with their two partners. Of course, other people are trying to create equilateral triangles with them, so things get a little bit complicated. At some point, the movement more or less ends and everyone is in equilateral triangles with their partners. I can't wait to try this in my class with the students and am going to try get them into the gym this week to do this in a large open space. 

I encourage you if you're able this week to try the locomotion game, or to try and invent a dance with your family or students, and try to identify any mathematical elements you can think of.

Week 6 theme - Mathematics, dance, movement, drama, and film

This week I took up the Clap Hands game in my classroom with my grade 6's and I would say they engaged with a bit of reluctant compliance, rather than enthusiasm. Many kind of went through the motions and I lost some of them, but a few did immerse themselves in the pattern-based aspects of the game. It was a challenging week to take up this activity in my classroom, and so far not representative of my students' willingness to participate. It made for a difficult dynamic and I saw some difficulty in sustaining focus for the students. As the activity went on, a few students became distracted which impacted their ability to contribute and process some of the patterns that were occurring. I think this game would work well with younger students or within a music class, but many of mine had difficulty seeing the connections to math. 

I enjoyed George Hart's traditional longsword dancing video and would love to try this with my students when we are engaged in geometry or angle work - right now we're looking at fractions so I'm focusing more on visual tasks that tie to parts of a whole and combining that with my class project. I love the idea with using popsicle sticks to manipulate angles and then trying to recreate the popsicle stick 'routine' with longer and larger pieces of wood that resemble swords. It would be a great movement challenge for the students. 

Another thing from this week's work that stood out to me is the value of working together with others - only so much math can be learned in a silo alone, it is crucial to expand our work to include other people and get and give ideas. So many mathematical ideas were born out of bored people just hanging out with others and trying things out. With the requirements of the curriculum and the broad scope of things I need to teach in my class, I find there's never enough time for unstructured exploration. I'd like to make more space for that, as kids learn a lot through play.

553 Assignment Proposal

Please click here to access my assignment proposal.