Week 7 - Critical Reflection - Mathematics & poetry and novels

 Before reading further, if you haven’t read my reading summary, please read at least the summary poem “Poems are made by erasing.”

    This may have been my favourite week of the course so far; at least that is what the hours I have spent playing with and writing poetry this week tell me. It might be tied with the week were we re-created art and I got sucked into flow with tessellating trapezoids. My brain (and body) is a bit exhausted from late nights not noticing the clock but still needing to get up in the morning. Please forgive me if my writing is discombobulated in this post.

    When I reflect on my classroom practice with poetry, I see that I connected math at least implicitly, if not explicitly. I admit I was somewhat neglectful of having kids engage with reading poetry (but when I had teaching partners, they were good at that), but loved exploring the writing of poetry with them. I had a book from Scholastic that I used a bunch that taught different forms (haiku, cinquain, limerick, acrostic, ballad, and others) through examining a few examples and then scaffolding the writing (then I had students develop a book of their own poetry with at least one example of each of these and a bunch more of their choice). We were mostly counting and noticing patterns – of lines, syllables, stress, rhythm. So, I can see the mathematics connected to poetry through these experiences but this week opened up my understanding to more ways that math and poetry live together in this world.

9x9square poem by JoAnne Growney
cited in Glaz, 2019

    I appreciated how Susan, in the introduction this week, laid out three ways that “mathematics inspires poetry and novels” (p. 1): they might be about mathematics or mathematicians, they might connect mathematical ideas/concepts and human experiences (analogies, metaphor), or mathematics might be used to create/shape the writing or to analyze it. Without this guidance, I may have needed more time to figure out what mathematical poetry (my focus, I didn’t examine other literature this week) is or is not. I am not sure I have it completely figured out but Susan’s ideas helped with listening to and reading (and creating) poetry this week. I found some examples of these in my reading/viewing/creating this week. The understanding that the subject matter is what can make a poem mathematical is demonstrated in Sarah Glaz’s poems on the Bridges Math and Art 2021 Virtual Poetry Reading website. The two poems Death of Euclid and Archimedes are about the title mathematicians. (I suspect there is something mathematical about the structure of these poems as well, but I didn’t examine them that way.) Amy Uyematsu’s poem Countdown brings together counting and numbers to ‘deal with more serious political issues’, specifically shootings in the U.S. To me this is connecting mathematics and human experiences. I think the final idea, that of mathematics informing the structure of poems, is what I enjoyed exploring most through my own poetry but also finding it in others (when it was obvious). Daniel May used the Fibonacci sequence to structure his poem A Fibonacci Poem for the After where the poem grew in syllables and then contracted again based on that mathematical pattern. In the interview by Sarah Glaz of JoAnne Growney, there are a few square poems where the number of syllables on each line is matched by the total number of lines (e.g., 5x5square or 9x9square). I enjoyed creating Fibs and played with having a pattern of Pascal’s triangle structure a poem of my own creating. When creating found poems as my reading summary, I tired a 9x9square poem for the Romania section (as the poem in that section was of the same type) and it was really difficult (I had the added constraint of using someone else’s words) and time constraints had me abandon it. I am sure if I had dedicated more time to examine other poems, I would have uncovered intriguing ways mathematics structure them.

My poem structured on Pascal's Triangle

    It seems like we can define mathematical poetry pretty broadly (though some people want more constraints than others – I felt JoAnne Growney and Sarah Glaz differ on what is and isn’t mathematical poetry). So, to that end, my question is:

What is NOT mathematical poetry?

Notes for the 'stop' at 
"Poems are made by erasing" in Glaz 2019

    One of my biggest stops, big enough to involve a whole page of stops and scribbles, was when I read the section in Glaz’s interview with Growney titled “Poems are made by erasing.”  Before I had read more than the title I had scribbled “I erased so much or scratched out --> connection to math – draft solutions, back up, try something different – then make elegant.” The poem this section is framed around is called How Did It Come to This? and references Picasso’s art as “notions of a bull…in the end a few lines” (Glaz, 2019, p. 251). In the interview, Growney talks of a writing prof who shared her own draft in class and said, “’That poem has one-third too many words’” (p. 251). Here I scribbled, “Like Mozart – Eugene Oschady.” Eugene was a cellist in the VSO and a member of a local string quartet. At a quartet performance, he talked to the audience about how Mozart’s music was criticized for too many notes but Eugene argued that Mozart’s genius was knowing when he had the exact right number of notes. He played a motif from Mozart’s Symphony No. 40 and added just one extra note in the middle and end of the motif and it made the audience chuckle because sounded silly. Ironically, when I composed the found poem for this section of Glaz’s interview, I had way too many words and was going to add more. I stopped, thought about it, and scratched things down to the minimum that would get the message across.

Editing down "Poems are made by erasing" found poem

    The connection to math education here is the idea of math drafts.  We allow students first, second, third, or more drafts in writing. When do we do that in math class? I was introduced to the idea of math drafts in an NCTM webinar that I only caught the end of and haven’t gone back to watch the whole thing. However, the part I did see gave me a good idea about the concept. The idea is that students take a break from a problem and circulate the room looking at other students’ incomplete work, offering feedback and gathering inspiration for their own work. They may go back to their own work and scratch things out, start again, or have a new idea that breaks them out of being stuck.

    We can also give feedback to students on being more elegant or efficient. I don’t think elegance or efficiency should be the first goal when students are learning a concept, but as they are ready, they can develop this. For an example, I had a student who understood division using the partial quotient strategy but would only divide by 2, 5, or 10 (as I remember it – anyway, the numbers were small) even if dividing by 100 or 200 or 500 might have been more efficient. She didn’t mind working through long columns to get to her answer. I could tell she understood the concept and was able to slowly nudge her to increasing her initial numbers to be more efficient. I think this is like erasing words in writing poetry – getting rid of the extraneous to get at the essence. (If I had the inclination, I’d edit this blog post back by 1/3!)

Questions to ponder

What is NOT mathematical poetry?

What similarities do you notice between the creation of poetry or other writing and working with mathematical problems and solutions?

I’m curious to know what possibilities primary teachers see in writing mathematical poetry with students who have, generally, a smaller lexicon to draw from and relatively limited experience with math patterns and concepts compared to older students.