Draft Project Link

Slides for final project

Week 9: Traditional Practices

Apologies for the format - I can't figure out Blogger this week. My input screen looks like html code for some reaason and I'm not a coder lol. Videos: I must say the videos this week were personally inspiring. I had day-dreams of leaving my job and becoming a rope maker or something of the like. From age 12 to 25 my job was a farmer. From 25 to now, 38 I’ve been a teacher. I have a friend who has become a part time blacksmith, which arose from a hobby. He has his own forge and classes come to take part and learn. Dancing braids is definitely something I’d like to do someday with students. Personally, I’d like to investigate the math a bit deeper. Watching the Vest-ed Interest video about sheep wool and making clothing seemed like a nice way to address the environmental impacts of the modern clothing industry. That being one of the math for social justice issues in our previous course. I find it relates to traditional kamik and mitt making in the NWT. From experience handmade mitts are much warmer and flexible than their industry made counterparts. I remember a simple pair of rabbit fur mittens being the most comfortable way to keep my hands warm walking around town in temps that went to the negative forties. So from my experience I tend to use handmade items for winter as practicality and as an added benefit it has less environmental impacts. Activity: I must say, I learned a lot just ripping strips from old fabrics. I figured I’d need to use scissors to get nice straight even widths but I only needed my hands.

I found the braiding process quite soothing. It would be something I could do to let my mind unwind. The act of ripping the strips from the fabric was also a bit of a stress reliever. I thought about how there could be so many science experiments that could come from rope making and braiding. For instance, how does the strength of one fabric strip compare to three strips braided together? Is the relation linear or something else? Other investigable question could be: How does friction between strands contribute to the overall strength of a braided rope? What is the relationship between the diameter of a rope and its load-bearing capacity? What mathematical models can describe the braiding patterns and their impact on rope strength? Article: This week I read the APTN article ‘The spirit of the medicine will lead us back’: How Avis O’Brien is guiding Elders to weave their first cedar hats By Anna McKenzie. It describes Avis ‘Nalaga’ O’Brien’s journey to and experience with teaching We Wai Kai and We Wai Kum elders how to weave their first cedar hats. Twelve years prior Avis was feeling disconnected from her culture but started learning how to weave from her sister. At the start of her weaving journey she still wanted nothing to do with it or her culture. However, the healing power of the cedar began to make her interested in her culture. Today she describes, “It’s like we’re giving back these Elders something that was taken to them, taken from them through our history,” she says. “It’s pretty magical.” One elder, Wasden, “says she believes cedar is “who we are and where we come from. It’s entwined in everything we do — from birth on a cedar mat, to death in a cedar box. It’s used for potlatches, for skirts, wreaths, head pieces. It was used for storage, cooking, blankets, mats, and even personal hygiene.” My question this week is: What science questions do you see coming from exploring these traditional practices like weaving?

Week 8

 This week's activity engaged me in a predictable struggle lol. I have difficulties with orienting the paper correctly. I wish the people in such videos didn’t hold up their paper and turn it all around for us to see until they are done. Simply, fold then flip or rotate in the most efficient way possible. This would leave me guessing less. Although I did get the Miura Ora Origami folds after the third attempt. Interesting math here might be how efficient the new structure is at compacting the surface area. 

I read Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving by Fisher, G. (2015). Gwen’s inspiration for her woven beaded sculptures came from Oscar Reutersvard’s 1934 Impossible Triangle. Impossible triangles are a “two-dimensional drawing that represents three straight beams with square cross sections, and the beams appear to meet at right angles.” (p. 99) Impossible polygons are a natural extension of this optical illusion. 

(Fisher, 2015, p. 99)

Gwen notes that the flexibility of weaving beads removes the optical illusion of the 2D drawings. This is why she refers to her creations as unlikely triangles and polygons instead of impossible. The beading medium allows for techniques like turns and twists or varying sizes and directions. As well as curvature which removes the straight edges of the 2D drawings. Other techniques with this medium include strategic use of bead size, colors, and placements. Bead color can be used to show paths, lines, faces, and vertices. 

(Fisher, 2015, p. 102)

A stop that came to me was caused by the uniqueness of the medium and the techniques which allowed for a different take on the impossible triangle versus the 2D paper. As well, as when Gwen mentioned how graphic designer M.C. Escher used the impossible triangle in some of his drawings. The contrast between 2D paper and 3D woven bead sculptures cause me to think of Marshall McLuhan's “the medium is the message”. “Each medium, independent of the content it mediates, has its own intrinsic effects which are its unique message.” (McLuhan, E) The beading medium allows for a new take on what paper says are impossible constructions. 

This kind of flows to Gwen’s desire to make a highly unlikely dodecahedron that shows the ten distinct paths (loops) that occur when moving through the twists and turns of the medium. She referred to this as passing through levels of hierarchy. 

(Fisher, 2015, p. 105)

I also was drawn to the uniqueness of the mediums, and the possible messages that come from each, when I watched the videos. In particular Yackel, who said “wallpaper patterns are realized through the dyeing process”. I appreciated the uniqueness of techniques and limitations that come with the medium, 2D paper is not infinite like the patterns it is trying to capture. Her use of the words constraints and resists - the tightness/clamping of the cloth prevents the dye from entering the cloth - both highlight the uniqueness of the medium. It is also fun to think of the folds as allowing a 2D paper to briefly enter the 3D world, which was similar to Gwen’s mention of passing through levels of hierarchy. 

(Yackel, 2020)

References:

McLuhan, E. (2024). Commonly asked questions about McLuhan – the estate of Marshall McLuhan. Ginkgo Press. https://www.marshallmcluhan.com/common-questions/ 

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.