Week 7: Poetry

 Activity: Words per line Fib poems about golfing.

Autumn:

Red

Orange

Leaves fall

Crisp air aroma

Hunt for balls amongst leaves

Early morning frost coats the soon dormant grass

Spring:

Brown

Gray

Leafless trees 

Lingering snow melt

Balls plunge into saturated fairways  

Feet and clubs become covered in wet soil 

Article: Can Zombies write mathematical poetry? Mathematical poetry as a model for humanistic mathematics. Karaali (2014). This article describes Gizem Karaali’s journey to teaching a course called “Can Zombies do Math?” and writing his first piece of mathematical poetry. 

In his early years Gizem wrote non-mathematical poetry in his native language, Turkish. However, he learned mathematics in English. He reflected, at this time “my mathematics and my poetry did not play together. They spoke different languages” (p. 40) 

Early in his career, after browsing works from the Humanistic Mathematics Network Journal (HMNJ), Gizem began to see how math, intrinsic to himself, could be explored and viewed in a humanistic fashion. This referred to either or both, teaching mathematics humanistically (as if students matter) and mathematics is a humanistic discipline (as if math is a human endeavor). He argued math shared three ingredients with what makes us human, cognition, consciousness and creativity. Inspired by HMNJ he and colleagues launched a new journal, Journal of Humanistic Mathematics (JHM). The goal of the publication was to “provide an open forum for both academic and informal discussions on all the various threads of mathematical inquiry.” (p. 42) 

From there came an invitation to participate in a creative writing workshop. This forced Gizem to ponder blending together his creative writing and love of mathematics for the first time in his life. In particular, it sparked a love for poetry which, he argued, shared the same three ingredients of what makes us human. A few years later, he taught a course, Can Zombies do Math? Students engaged with poetry that dealt with personal experiences and feelings with mathematics. 

For example: 

(p.43)

Here is Gizem’s first piece of mathematical poetry, oddly enough he wrote it after teaching the course in mathematical poetry. 

(p. 44)

In the Bridges Math Art video, Mike Naylor, spoke in zeros and ones, as if it were a poem. Indeed it rhythmically sounded like a poem as he stated. To me this showed how poems can be structured mathematically, just like the Fib poems (1, 2, 3, 5, 8 words or syllables). In such cases the poem did not need to be about a mathematical theme. Whereas, Gizem’s humanistic mathematical poetry did not need a mathematical structure but rather it needed a mathematical theme (personal experiences and emotions surrounding mathematics).

My questions this week are also my “stops”. Before reading and viewing the materials, what were your thoughts about math and poetry, … poetry that was mathematical structured …. poetry that was mathematical themed? 

What might poetry look like if it were both mathematically structured and themed? Maybe a poem like Gizem’s that is 1, 1, 2, 3, 5, and 8 words?

Math 

Dread

Soul sucking

Numbers cause numbness

Mind feels dumb and lost

Marks, grades, and report cards are the proof

Week 6: Math. Dance and Movement

This week’s introduction hinted at some fun and interesting mathematics, around imagining the infinite and infinitesimal. The article, Dancing Mathematics and the Mathematics of Dancing, by Sarah Belcastro and Karl Schaffer (2011), presented lots of interesting representations of mathematics. Both have Ph.D. 's in Mathematics and have created mathematical themed concerts. Sarah and Karl lay out the math that is in dance. Math such as, dividing music into counts, dance patterns arising from music rhythm, symmetry (of individual movements and movements of the people in a dance group). Symmetries include translations, mirror reflections, 180 degree rotations, and glide reflections. 

My stop this week is the seemingly high level math that Sarah and Karl also present. Math such as graph theory and topology. These math topics can be symbolically daunting. However, stepping away from the symbolic representations, these topics can prove quite interesting and fun. I recall one professor saying a doughnut and coffee mug are topologically equal. This was not a topology class, just conversation that popped up. Essentially, pretend each is made of clay. Preserving all the holes or loops, could you mold one into the other? (The hand grip and doughnut hole)

(Image created by ChatGPT)

We could get students to “act out”, like in drama class, to make themselves topologically equivalent to other objects. We could extend this to making human clay figures that have the child’s pose. They could be molded to whatever the original object was.

In the image above the person (with arms making a loop), the coffee mug, and doughnut are all topologically equal. A biologist would have to ignore the fact the digestive system is an open loop, lol. 

My question is what other objects could children make themselves topologically equal to? How would this look?

Activity - Rope Polygons (Regular)

Adapt the rope and knots to other math concepts:

Pythagorean triples. Example 3,4,5 Use the knots as a way to measure sides.

Three other ropes and knots could be used to make the squares of 3,4, and 5.

Circles - estimating the connection between diameter to circumference.

C = pi X d or circumference of any circle is a bit more than three times its diameter C - 3.14 x d. Let the distance between knots be a diameter then the circumference of the circle would

be three of these lengths plus about 15 percent of the way to the next knot.   

Link to My Final Project Draft

EDCP 553 Draft Final Project Outline

Week 5

 Week 5 Article Summary 

First off apologies to Amanda and Patrick for not replying to your posts last week. Life and work unexpectedly got away from me. 

Movement-based Mathematics: Enjoyment and Engagement without Compromising Learning through the EASY Minds Program. Riley et al. (2017).

Four grade 5 and 6 Australian classrooms participated in a six week physical and mathematical intervention program, Encouraging Activity to Stimulate Young Minds (EASY minds).  Two types of math lessons were used. One used physical activity as the platform to develop procedural fluency and the other focused on moving around and looking at the mathematics around the school. 

Researchers sought both student and teacher perceptions of the intervention. 6 of 66 students went on to participate in a detailed student focus group. Students particularly enjoyed rotating activities like hop-skip-jump and recording and determining averages. Student enjoyment was a common result, student comment “I like doing sport and being active and when you combine that with maths it makes it much more enjoyable” (p. 1660).

Here is one activity example (p. 1661): 

I had a pre-stop, before reading the article. Would there be a balance? As Susan Gerofsky says in the introduction,  don’t throw the baby out with the bathwater. After the intervention, do math lessons involve a mix of “regular” learning and learning similar to the EASY minds program? It appears so in some cases. “Many students reported more hands-on activities since involvement in the program, and many reported that their teacher was now more innovative using varied and interesting activities to improve their learning.” (p. 1662) 

Furthermore, engagement in math went up. Teachers were able to harness this engagement  during the more traditional learning. One teacher reported more students now attempting written and explicit work. Many students said they found math easier when they returned to the classroom. 

There were some negative comments, such as when the physical goal of the activity was hard to achieve. Example, throwing a bean bag into a hoop could prove difficult/frustrating and distract from the math. 

Week 5 Activity 

I decided to do base 4 as the extension. Then I wanted to explore perfect squares. First showing 4 and 16 in base 4. Which are 10 and 100 in base 10. The “1s” being red. Is it a coincidence that 4 and 16 are perfect squares and have one solid red ring? What about others?

Finally showing the product of identical factors in base 4 to see what a “perfect square” might look like. 36 and 49 both had a red ring but they also contained a white ring and the other color from the factors. 

Idea - Number can be represented in expanded exponential form. Ex: 342 = 2x100 + 4x101 + 3x102

Guiding Questions - How can we represent this in a more advanced place value chart?

Thousands 103	Hundreds - 102	Tens - 101	Ones - 100
	3	4	2

The Story - A place value chart is a linear/grid method to display a number. It aligns the same way we write numbers.  It shows powers of ten or ones, tens, hundreds. It is kind of arbitrary. We could use nested circles to display place value in base 10. 

Integrating art based activities - Color code the digits 0 to 9. The colors now represent the amount of one, tens, hundreds, etc… Choose one color and make as many numbers as you can. Ex: 2, 22, 222 would all be the same color but different number of shaded circles. 

Possible Extension - Extend this to base 9 (or powers of 9) What do your numbers look like now? Do the same thing for base 11. 

EWeek 4: Post one - Eve, T. (2019). Bridges Stockholm 2018 and this week’s Introduction

 Eve, T. (2019). Bridges Stockholm 2018 and this week’s Introduction

Eve Torrence is a mathematics professor at Randolph-Macon College, in Ashland, VA. Eve incorporates the arts into their teaching and designing mathematical sculptures. Eve provides an overview of the 2018 Bridges Conference in Stockholm. 

The conference takes place at the National Museum of Science and Technology. However, the museum is on a campus that is also shared by the Ethnographic Museum, Maritime Museum, Swedish Sports Museum and the Police Museum. In this particular year the proceedings included 44 papers, 55 short papers, and 21 workshops. 

Eve’s description of the museum makes it sound the perfect place for the conference, especially as day four honoured Nordic Day (marking the signing of the Helsinki Treaty) and Family Day. At the front of the museum is the Mathematical Garden. This playground contains but is not limited to a slide in the shape of a nautilus and a giant xylophone to explore the relation between fractions and tones. 

For Nordic Day 4 lectures on creative education occurred in the morning. Family Day opened in the afternoon with Susan Gerofsky’s world premier of her play “Witches of Agnesi”. Here is a link to a video of “Witches of Agnesi” ,https://vimeo.com/339892315. The play brings together three different mathematicians who all faced obstacles in their careers because they were women. (Maria Agnesi (1718–1799), Sofya Kovalevskaya (1850–1891), and Emmy Noether (1882–1935))

Some of the activities of Family Day reminded me of our virtual Family Math Day we did in Cynthia’s course. However, the virtual aspect lacks some of the personal connections that an in-person event has. Family Day included over 20 workshops featuring - making paper geometric models, spirographs, and origami. Family Day ended with a Music Night and a Bridges Fashion Show. 

Reading about the binaries of arts and math, from the Introduction, had me thinking about examples of art/math crossovers that I could readily recall. The works of Dutch graphic artist Maurits Cornelis Escher came to mind first. I see from some Bridges entries, his tessellations are inspirations for the work of others. As for science, the Element song came to mind. (https://www.youtube.com/watch?v=U2cfju6GTNs) 

The readings also mentioned how the divide is American/European. My questions this week are: What art/math crossovers first came to your mind? 

Thinking back to your Virtual Family Day activity, did it incorporate any art crossovers? 

Also, as the NWT switches to the BC curriculum, there is a high school course called the History of Mathematics. I’m quite interested in teaching this course and I wonder if doing so would provide both historical and modern  examples of arts/math crossovers from different cultures.

 

Week Three : Post 2 Article, Introduction, and Video

 Williams urges us to move away from a schooling model characterized by discipline silos and mechanistic, technocratic worldviews. She advocates for a shift towards an educational approach that promotes a sustainable world, incorporating systems thinking and holistic learning. For example, she notes that living systems are not hierarchical but are networks nested within other networks, where the whole is more than the sum of its parts. She emphasizes the need for greater ecological literacy, arguing that pedagogy should be grounded in place to better understand patterns and relationships.

Williams then details a program in a Portland, Oregon school district focused on food and garden-based programming. This initiative involved 3,500 K-8 students across eight schools, as well as multiple sites for school-based learning gardens and environmental and nutritional farms. The program fostered numerous partnerships, with university students forming a learning garden committee that included parents, community members, students, and school staff.

The program addressed local issues: the rising number of hungry children in Oregon, increasing rates of obesity and diabetes, urban students' diminishing connection to nature, and the widening achievement gap between white and ethnic minority students.

Learning about patterns and relationships was deeply integrated into seasonal learning, emphasizing care for oneself, the land, and the community. This approach extended beyond traditional curricular math connections like patterns of time, size, and quantity. These insights from deep student engagement is my first stop. I was blown away when a 12 year old had deep insights to the patterns and relationships of caring for land and nature. “It is strange that people can take pride in large lawns and waste their land by simply growing and cutting grass. If we plant gardens instead, we can also grow food, we can bring wildlife and at the same time eat healthy fresh food.” (p. 47)

My second stop is from this week’s video and the first week’s TEd Talk video. Seeing Dancing Proofs reminded me of week one - changing perspective is understanding. Viewing the body in motion, from above, is a change in the perspective of sight. Therefore, understanding of proofs has occurred. From a ground view to an aerial view.

My question for week three extends from my second stop and learning more about engaging the body and all of its senses. We can change perspectives within the sense of sight, ground view to aerial view. So could it be possible to change perspectives within another sense, say smell? And would such a change in perspective also result in understanding as put forth in week one’s TEd Talk? 

I used AI to generate an image of hearing on land and underwater. 

Week Three Post 1 - Activity

 Week Three Post 1 - Activity (article and video post coming on Saturday)

I am currently in Paulatuk NT and as you can see I’m not going to be sitting or standing outside for long. Also, in terms of living things (plants and animals) right now there are only a few ravens, dogs, bushes, and humans. So this week, I am taking some liberty and drawing lettuce chunks from a salad, a banana, and an apple. The outdoor human made structures are being drawn from the comfort of looking out my window. 

In living things there were no right angles whereas human made structures were riddled with them. Living things had curved or arched lines whereas human made structures had straight lines. Human made structures are probably this way for both simplicity's sake and structural strength. I found it interesting that the banana formed a pair and a set of approximately equal angles. Then I Googled banana blossoms to see if I could determine a relationship between lines and the blossom/flower. However, the image of a banana blossom only confused me further!!!!!

****EDIT banana angles 60/60/80/80/80

I think that close observation and drawing would strengthen the understanding of angles and lines as it combines two senses for the same concept. The student would be highly attentive to sight and feel. This would be especially the case if, as this week’s introduction states, “we work to create a balanced program of mathematics” that is both outdoor and indoor (nature and sensory balanced with traditional methods).