Karaali, G. (2014). Can zombies write mathematical poetry? Mathematical poetry as a model for humanistic mathematics. Journal of Mathematics and the Arts, 8(1–2), 38–45. https://doi.org/10.1080/17513472.2014.926685
This article engaged with the author’s personal experiences to introduce how he started to connect his interests in math with poetry, which he was not very familiar with at first. Karaali got interested in the ideas introduced by the Humanistic Mathematics Network Journal (HMNJ) and stepped out of his comfort zone to explore how poetry in English can be connected with math. He believes that mathematics and poetry share the three most important ingredients of what makes us human: cognition, consciousness and creativity. Thus, he developed a course titled “Can Zombies Do Math” to encourage students attempt to write mathematical poems with creativity.
STOP 1: “In my native language, Turkish, sentence structure is quite different from that in English. Correct grammatical forms exist, though they are not as rigid as one might expect. The speaker may and will often move the main parts of speech around in order to make a statement, emphasize a point, underline a concept or simply to convey the spontaneity of the particular conversation… But with poetry, I could only hear my voice in Turkish. Mathematics was different. My mathematical language was definitely English…”
This is a really interesting point, and I resonated with it a lot as a second language speaker. Same as Karaali, I use English to do math a lot, but I’m more comfortable in writing or reading poems in my first language (which is Chinese). I’m wondering if there is a reason why people feel more attached to their first language in poems. Probably it is because of the culture? Or how familiar you are with the poetry styles when you were kids, since lullabies and songs are all different variations of poetry. Karaali mentions that grammar in Turkish is not as rigid as English, so you can change the order of words to form a sentence. I guess this gives people more flexibility and creativity in writing poems. I found Chinese grammar has a similar nature as well, where we can arrange different characters to make new words each time without affecting the grammar or meaning of the sentences. This really makes me wonder whether multilingual people have more ideas for exploring poems and make more innovative connections in mathematical poems from various perspectives.
STOP 2: “Referring to our students’ course work, we can inquire explicitly: what does it mean to be creative in the mathematics classroom? The answer will come rather easily to most teachers of mathematics: students can think of novel ways of approaching problems. But what is novel is most often simply some idea or technique that they have seen elsewhere, now taken and used out of that original context. A concept that is often considered in tandem with creativity is divergent thinking, which captures thinking processes that lead to multiple possibilities. So it is fundamental to creativity in general, and to creativity in the mathematics classroom in particular, to be flexible and open to many interpretations and approaches.”
When I first thought about being creative in math, I had the same idea as Karaali mentioned here: to have more approaches to solving problems means you are creative. However, Karaali argues a new idea: that students may use different approaches because they have seen or learned the questions elsewhere. This may not reflect the students’ creativity, as the idea may not be original. This aligns with his statement in ‘zombie-learning’ about following the rules without any human creativity, interpretation, or flexibility. Karaali introduces the concept of divergent thinking, which means generating more possibilities. I can tell he tries to link this idea to poem-writing, since writing is very personal, and the idea of a poem can only come from your own mind, which aligns with the use of divergent and creative thinking.
Questions:
1. How do you support English Learning students in your class to try the mathematical poem activity? How can you make the poem-writing activity fun but not too challenging for students?
2. In your opinion, what makes a poem a mathematical poem? Besides structuring the poem by numbers or sequences, what other ways can you think of? Can geometry, function and graph also be used as part of the poetry? If so, what would that look like?
Week 8 Activity
I’m not really good at poem-writing. Poetry was always the unit that caused me the most headaches when I was in high school. However, I’d like to challenge myself this time to try the Fib poems.
Similar to what Karaali experienced in his article, I came to Canada in grade 10 and studied most of the math in English, but my first language is Chinese. I am definitely more comfortable in reading or writing poems in Chinese. In the Chinese language, one word (character) is one syllable, so we never distinguish words and syllables. This makes it extremely hard for me to write English poems when I have to be aware of the differences and count syllables in words.
I really like the flexibility of the Fib poems, which can be counted as syllables per line, or words per line, or lines per stanza, or any other countable thing connected with the poem. This offers more creative ideas. You also don’t have to be perfect at English or poem-writing, since it is easier to start by counting the number of words.
Since I’m working on my project this week on 2D-to-3D models, I had the idea for a geometry-themed poem.
Geometry (count by the number of words: 1,1,2,3,5,8)
Point
Line
An angle
Forms a surface
Enclose edges of a figure
New dimension is formed to create more possibilities
Element (count by the number of words: 1,1,2,3,5,8)
I
Am
An Element
Starts with H
Have one proton, no neutrons
Lightest element in the world—who am I
Sunny,
ReplyDeleteI really connected with this part of your post, especially the idea of divergent thinking. Like you, when I first think about creativity in math, I usually think about students finding different ways to solve a problem. But Karaali’s point that those approaches might just be strategies students have seen before is interesting. It made me think that creativity in math might actually come more from exploring ideas and making connections than just showing multiple solution methods.
Your Fibonacci poem made me think about this too. Even though it’s very structured, it still leaves room for creativity inside the pattern. I noticed something similar when I did the four-word poem activity. I actually liked having a clear structure because it gave me somewhere to start, and then I could play around with the words and see how the meaning shifted. In that way, both the Fibonacci poem and the four-word poem show how structure can actually support creativity rather than limit it.
For your first question about supporting English learners, I think structure might actually help. A framework like a Fibonacci or 4 word poem gives students a clear guide, so they can focus more on choosing words rather than worrying about how to build the whole poem.
For your second question, I think this week made me realize that a mathematical poem doesn’t necessarily have to talk directly about math. It could show mathematics through structure, patterns, or relationships. I also like your idea about geometry or graphs. I could imagine something like a poem shaped like a geometric figure, or lines that change length to represent a function or growth pattern.
I enjoyed your two poems:)
Sunny, I really appreciated your reflection about language and mathematical thinking. The experience of feeling more comfortable writing poetry in a first language while doing mathematics in English connects closely with Karaali’s discussion in Can Zombies Write Mathematical Poetry?, where Karaali explains hearing a poetic voice in Turkish while mathematical thinking developed in English. It highlights how language and culture shape the ways people express creativity. I also liked the connection to divergent thinking and how this idea appeared in the geometry Fib poem. The example nicely demonstrates Karaali’s argument that mathematics becomes more human when there is space for creativity and personal expression rather than what Karaali describes as “zombie learning.”
ReplyDeleteIt is a big challenge to write poetry in a language that is a newer one for us! You've done well. And perhaps give this a try: how would it be to write a Fib or PH4 poem in your most familiar language (and provide a word-by-word gloss for others that need it)? I'd love to hear you read a poem in Chinese and then give an approximate translation!
ReplyDeleteI know that for myself, writing poetry with the restricted structure of mathematical frameworks makes the process feel more approachable. I think this must also be helpful for second language learners. I actually am thinking mathematical poetry could help when doing the poetry units of english classes.
ReplyDeleteWhen I wrote my fib poem I used number of letters. I started by writing the numbers and then thinking of words that had that many letters. This would possibly reinforce spelling.
My own second language is Chinese, and writing a poem in Chinese feels impossible. The reason is the layers of meaning that are sometimes deep and quite challenging to understand. I have always heard that the most difficult activities in a second language are jokes, poetry, and prayer.
Another way to help second language students with poetry is to allow them to write it in their first language. Why not? It will be more meaningful for them this way. They could explain the meaning and how it fits the structure, which is the point after all.
I wonder, do you think that PH4 might work nicely in Chinese? Especially because the chéng yǔ is already a set of 4 characters.