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.

Week 5 Reading - Kelton & Ma (2018) Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration

I enjoyed the Kelton & Ma (2018) reading this week as it described a really interesting activity that I am going to take up in my classroom. I think this course has given me a ton of very simple activities to do in my classroom that connect with concepts, and I've really enjoyed that about the readings. The article focuses on a teacher who went away from the traditional math classroom and used the Whole & Half activity as a powerful way to learn about fractions. The activity required students to physically position themselves and engage in hand movements creating a new arrangement of their bodies in relation to each other and the environment. This use of space allowed students movements to become integral to their math understanding.

My first stop in the article was that the teacher had the students physically doing math, rather than learning math. This movement allowed them to explore fractional relationships through bodily movements and get creative with the physical space they occupied. 

At one point the article talks about Katie and Claire, who had trouble with the coordination of their bodies and Claire had to wait for Katie to become half. This breakdown (and I'm sure there were others) demonstrated some of the challenges of working with other people. I enjoyed reading about this case study because we are just about to start fractions in our classroom so I would be curious to try it in my classroom to see how the students do with it. 

A question to ponder: How might activities like "Whole and Half" reshape the traditional classroom setting and give students a new perspective on how math is "done" and how one "does" math? Would students make the deep connections necessary or would they think it's just a fun movement activity. What can you do as a teacher to ensure the conceptual understanding hits home?

Week 5 theme - Embodied, multi-sensory, and arts-based modalities

I found Sarah Chase's activity of dancing prime numbers (I feel like that's an oversimplification) to be really intriguing but I don't have the coordination to try it myself. I'd love to get some of the dancing students in my class up trying something like that though to demonstrate a different understanding of number and patterns. I tried a similar activity with my wife and have not recorded us doing it yet but we've made a few attempts.

Activity: Two partners clap on multiples of two different numbers, creating a rhythmic pattern. For simplicity sake, one partner claps on multiples of 3 and the other on multiples of 2. We experimented with multiples of various numbers and observed how it affected the complexity and rhythm of the clapping pattern.

We talked about the mathematical patterns created by different pairs of numbers and discussed why certain pairs produced different rhythms. 

Possible extension: Explore the impact of using prime numbers between 7 and 23 in the clapping activity and see how that influences the regularity or irregularity of the pattern.

Another possible extension: Collaborate with the music teacher to explore a cross-disciplinary connection with playing notes or some other way of finding common multiples by playing chords.

One more: Connect the clapping activity to traditional mathematical notation, with an effort to link the physical and abstract elements of the concept.

As we are just wrapping up some of our work on primes/multiples/factors now, I feel like this is a perfect time to try some of these specific movement activities with my class. So far they have been very receptive to my ideas and have engaged thoughtfully with them! 

Week 4 Reading - Dylan Thomas: Coast Salish artist

The article about Dylan Thomas traces his journey into mathematical art - sparked by his exposure to M.C. Escher in Grade 11 - which happens to be about the same time I was exposed to M.C. Escher, actually. Through some exploration of Escher's style mixed with traditional Salish designs, Thomas starts to see some similarities in the symmetry and rotation. Thomas' latest work, Infinity, was heavily influenced by M.C. Escher's Smaller and Smaller. It is based on dividing a square into smaller and smaller parts.

Salish art has always fascinated me. I was probably about 16 when I visited a Salish artist's studio in Gastown and learned about his work. My dad bought a series of his wood-carved pieces which still hangs in his living room 21 years later. Looking at Thomas' work through the lens of mathematical art, tessellations, and symmetry now as an experienced middle school math teacher is really captivating - I love the interplay of designs. Horizon on page 207 is such a cool piece of art, I am going to keep a screenshot of it to share with my students when we look at reflections later on this year.

There is limitless potential to combining math with art, and a student's interest in mathematical art can evolve into a rich cultural activity. Thomas' work serves as an example of the power of visualizing math in creative expression. I think his work will help my students to see math as a way to express cultural or other important ideas visually.

I don't really have a prompting question this week, just a consideration that the intersection of math and traditional and cultural art can inspire students to view math as an important part of cultural expression!

Week 4 theme - Mathematics and the Arts

This week's introduction resonated with me based on the challenges of teaching math to middle schoolers who have for so long seen it as a separate and rigid subject area. I've tried to incorporate activities all year long that allow students to see the mathematics in a variety of places and spaces, and see and experience mathematics as an interconnected subject. 

I love the idea of integrating math with artistic and cultural elements so I shared this week's activity of viewing the Bridges galleries and reproducing a piece of "math art" with my Grade 6's. Listening to the conversations and watching students explore the galleries I could tell that it was engaging and intriguing for students - many of them went on to explore some of the other years as well. 

The whole point of activities like these is to approach math through a more holistic and interconnected lens and I think in this case students were able to see something a little bit different. As you can see in picture 3 attached, one student even took the idea from the Bridges gallery and "extended" it, connecting his hexagons all the way to the edge of the page. 

Another student not pictured, because I ended up getting his face in the picture, drew his own version of the "pi maze" and then his friend added the digits of pi around the outside. This gave me a great idea of having one student start a piece of mathematical artwork and then randomly hand it off to someone else to have them extend and complete it. Math-Art Mash-Up Monday, perhaps?