Final Project: Learning Embodied hən̓q̓əmin̓əm̓ Direction Terminology

Week 9: Mathematics and Traditional & Contemporary Practices of Making and Doing

 Activity: braiding rope with 7 strands

I grew up with long hair, and taught myself to french braid when I was about 9. I taught my kids how to make 'friendship' bracelets when they were quite young my daughter expanded on that skill to creating amazing workds of art with embroidery thread!  

This activity stood out to me as my choice since I have experimented with braiding hair with multiple strands (to no avail). As when I had tried braiding hair, I found that with this activity I continued to fall into the pattern that my fingers were "used to" with 3-strand braiding and dropped the wrong double strands when i should have lifted them, and placed strands "over" others when they were supposed to go "under". What I noticed as the braid progressed was that it seemed that 2 braids were forming along the outside while an interesting chevron was forming down the centre.

Often in the Pre-school we fix our students' hair after nap time, or a really good outside play time. The children are intrigued with the over-under-criss-cross of braiding hair. I think it would be beneficial for young fingers to have a model of some sort where there is 3 strands made of shoe laces for students to learn to braid with!  This extension of learning to braid at such a young age definitely brings Indigenous students back to the 'ways' of their Ancestors and allows for an appreciation of learning the pattern of over under.

 

Viewing: Vested Interest (Sharon Kallis)

 I was drawn to this video -possibly because I have developed an affinity for vests these days(?) As it turns out, it was an intriguing video, I've always been interested in sheep sheering and the wool making process. I love making clothes as well, so I liked seeing this process of creating the fabric prior to sewing together a vest! I made a small felt square in our art course a few years ago, it was hard work for a small piece of fabric -I can't imagine the time and effort that goes into a very large piece that could be used to make a vest!

Reading: Bohr & Olsen. The ancient art of laying rope.

 My dad was a fisherman. He taught me to fish. He taught me to appreciate good quality rope -we couldn't afford good rope; I learned this from his being disgusted at always having to fix and repair the cheap "nylon" rope he was forced to put up with.

This paper begins with stating that ancient rope samples are shown to have been depicted in  Egyptian hyroglyphs. At the Museum of Anthropology there are pieces of the remnants of an ancient fishing net used by my ancestors here on the Fraser Delta made from cedar. How amazing to think that something so integral to preserving life (fishing for food) could itself be preserved hundreds of years!

https://pin.it/6kshLDC

 

The science and mathematics involved in creating something that can withstand water, the strength of fish and then manhandling involved with fishing blows my mind! There has to be strength as well has give that allows for a fish to be trapped yet the 'give' to allow the fish to be caught and not bounce right off of the net.

Bohr & Olsen state that the construction of a rope is geometrical (p.3) -having never seriously taken geometry this statment surprises me! As such, what an interesting concept to learn geometry with!

While this may not seem "rope" the construction is much the same. There are many different net constructions, with multiple weights, "...the physical forces that one strand is causing on another strand are indirectly implied, i.e. repulsions are assumed to be infinetly large when the hard-wall criterion is violated." (Bohr, 2011, p.4).

Week 8: Mathematics & Poetry and Novels...

Viewing:

 I chose to watch the how orbifolds inform shibori dyeing video by Carolyn Yackel. I found this interesting because of my children. I have 3 daughters who are keen on tye dyeing almost every spring they are making new "wild & wonderful" tshirts (as my mom would say!) I found the shibori video very interesting; because, while the "method" is similar the process for 'blocking' the dye is different. 

If you haven't attempted tie-dyeing, the thing that blocks the dye from portions of your fabric is elastic/rubber bands that hold the fabric in a bunch, (which previously was some type of string tied around the fabric) the rubber bands prevent the dye from seeping into that particular portion of the material you are dyeing. So,  shibori dyeing utilizes folding and disc-type objects; Carolyn used coins fastened by "bull dog clips" to the fabric. Somehow the folds are what cause 'stripes' to form during the dyeing process, as well as the coins to form the non-dyed circle shapes. Carolyn experimented with these "orbifolds" to create a predictable pattern on her fabric.

Activity:

For the activity this week, I chose the "What is the best way to lace your shoes" video by Mathologer. This was appealed  to me because at quite a young age, my dad taught me how to lace my shoes differently than everyone else. [image 1] 

Mathologer "proves" the best way to lace one's shoes is the standard criss-cross lacing method (which is seems to be why this is the 'standard' practice)     [image 2]
Not only is this the 'best' way he states that it is the shortest and "tight" version for keeping the 2 sides of the shoe together and snug on the foot. 

 Another version that he posits to be mathematically sound is called the bow tie method, I tried this and it feels strange on my feet! kind of loose, kind of tight -maybe it feels strange because I don't have enough eyelets for this method? I don't like it! I told my husband that it feels like a 10-year-old laced and tied my shoes for me!

What's interesting, and the idea that Mathologer is trying to get across is that there is a shortest amount / way of lacing shoes, and using mathematical terms and breaking the crosses away from the 3D into a 2D kind of fashion using equal lines //// |||| _ _he shows how the bow tie method is the 'shortest' method (i.e. most efficient use of lacing). This would be a fantastic way to help students learn geometry (?) in the lower levels and bring their world into what they are learning and to "see math all around you".

When my daughter was in elementary school, she was very interested in lacing her shoes in different ways! I asked if she could remember how to weave her shoelaces to help me with this activity, she couldn't, and looked on tiktok to see if there was a tutorial similar to what she did, this is another method she found: tiktok shoelace knot  -I'm not sure whether this would fit into the "shortest" lacing category...)

Reading: 

Gwen Fisher (Bridges 2015) Highly Unlikely Triangles and other Impossible Figures in Bead Weaving

In this paper, Gwen Fisher shows how she created a series of beaded sculptures from the impossible triangle and its variations by using a technique known as CRAW (cubic right angle weave). The ABSTRACT states, "...beaded art objects generate surfaces that twist like Mobius bands...which make interesting colourings possible." (Fisher, 2015)

 

This reading was especially interesting  because, my husband and I often comment on optical illusions that we come across, the "impossible triangle" is one that always intrigues us.

"Oscar Reutersvard drew the first impossible triangel in 1934." (p.99) Then, "...mathematician Roger Penrose, who popularized it in the 1950's..." (p.99). Fisher tells how sculptures and artists have drawn liknesses, but it would be impossible to create one in 3D if the edges are assumed to be straight and connected with right angles.

"Hofstader calls this 'play[ing] with the level-distinction between that which represents and that which is represented... that which represents' (i.e., a drawing) becomes a recipe for 'that which is represented' (i.e., a beaded sculpture)." (p.100)

Fisher creates beautiful beadwork by beading with a new weaving stitch mentioned earlier, CRAW and incorporating a quarter turn with each cube. This quarter turn can be seen in figure 2. 

Fisher continues sharing more impossible shapes created with her CRAW -quarter turn twist beading. I can appreciate and enjoy the 'sculptures' created and shown, but I found myself getting anxiety while trying to understand the mathematical terminology and directions provided! If I were to try to create one of the impossible beaded pieces, I would seek out the proffered YouTube channel and go through the steps very slowly! This Paper is yet another example of the many different and lovely ways to teach students mathematics that is not static, paper and pencil working numerals and digits.

 

Week 7: Mathematics & Poetry & Novels

 Activity:

 

Alice in Wonderland as a mathematical novel?! The more I think about it, the more I understand! I see
concepts of time, binary: red pill/blue pill, big/small, good/evil...  

I really enjoyed all the poetry this week! I've always found pleasure in the patterns and rhyming involved with poetry; I've never really understood how non-rhyming poems 'work'. reading and looking at the fibonacci were really cool. When I went to the 'Bridges' Poetry website, I didn't realize that the Poet I was interested in was the same Mike Naylor, those readings were extremly enjoyable!

Here's my crack at the fib poem:

one                                                       young

two                                                       old;       

three then                                             between-

four, who knew                                   where mem'ries 

I liked math before!?                           bloom; and love dies not

Reading:  

Sarah Glaz (2019) Artist interview: JoAnne Growney Journal of mathematics and the Arts

Can a Mathematician See Red?

Consider the sphere -

a hollow rounded surface

whose outside points are the very same points 

insiders see.

 

If red paint spills

all over the outside,

is the inside red?

 

The mathematician says, No,

the layer of paint

forms a new sphere

that is outside the outside

and not a bit inside.

 

A mathematician 

sees the world

That is how this paper began (after the abstract) -a very interesting read! Sincerely an interview discussing the why's and how's surrounding mathematician JoAnne Growney came to write 'mathematical' poems. The interview incorporates 10 of her poems a link to her blog-that houses 800 postings!- and talks about her being a member of "Bridges".

I felt a connection to her statement, "Everything is connected". This is because, as we have been learning through this program, mathematics is all around us, and the BC Curriculum that mandates Teachers incorporate Indigenous Ways of knowing and being in every subject; This statement underscores that Indigenous principle.

JoAnne said "...a good rule for myself is to go out every day and smile, at least, at on person." I connected to this too! I have to get outside, I feel I have to connect to other people, and found this one of the major impacts of the Pandemic these past two years. 

I L O V E  old movies; Hedy Lamarr is an actress from the 40's that I enjoy watching; JoAnne took one of Heddy's statements, "All my six husbands married me for different reasons." and created a poem from it!

Perhaps Hedy Lamarr married so often because six

is a perfect number-the sum of all its proper

divisors, "proper" meaning "less than six," 

"divisor" meaning "a counting number

that divides and leaves

no remainder."

After a perfect number of husbands, there is no

remainder. Six is the smallest perfect 

number, the next is twenty-eight.

And twenty-eight

is too many

husbands.

The last piece that resonated with me was a project JoAnne began: counting woman mathematicians. Interviewer Sarah Glaz said, "Mathematics is a man's world. You learn how to live in it. Not quite like a man, but in terms acceptable to men." While I feel this statement as a woman and have been restricted in this 'mans world' (not the mathematics world, per se..) but more so as an Indigenous woman. I have felt the restrictions of being on the margins in this world of the white dominated society, and have felt excitement when I have encountered Indigenous role models pop up around my life as an older adult. I find that I count Indigenous People when I'm in classrooms, and conferences etc., this is a phenomenon that intend to be a part of changing.

everything is connected.

 

Week 6: Mathematics & dance, movement, drama and film

This week I read the Henle article: Mathematics that dances (Jim Henle, 2021)

I was excited thinking I might be able to 'relate' to this article more than the previous weeks ( I know, you all are going to get sick of me expressing my disconnect with mathematics and how I get anxiety...) because I love music & dance (more like grooving than dancing!) I hear music and I feel the beat and before you know it, without realizing, I will be swaying and moving to the beat.

Henle begins the article with this statement, "...pleasure. Usefulness is irrelevant. Significance, depth, even truth are optional...[if it's] in this column it's because its intriguing, or lovely, or just fun." THIS in itself grabbed my attention!  And then a few disclaimers: 

1. "..Most of dance, its expressive power, its delicacy, its emotive content, is beyond the ken of mathematics."
2. "...there is genuine mathematics in dance...that is not the subject of this column..."
3. "...one can use dance to bring math alive...we won't do that here.

These statements felt encouraging to me, I'm just going to read about the beauty and loveliness of dancing. Then as I continued reading I got lost! Henle was describing the pleasure of the mathematical movements of two different dances and the way they were mapped out with the steps taken throughout the dances. Without having the space and people to reinvent what Henle drew out in his article I had a hard time "seeing" what was so lovely about what he was writing.

For me this was very similar to learning a new mathematical concept; the teacher knows what they are talking about -they know and understand where they are going with the end in sight- but those of us who have struggled with the abstraction of mathematics, incorporating something tangible while learning new concepts is extremely helpful, like the addition of a few dance steps that are very familiar!

Week 5: Developing Mathematics Pedagogies that Integrate Embodied, Multisensory, Outdoors & Arts-based Modalities

Week 5 ACTIVITY :

Viewing the "Activity" video of Sarah Chase's Dancing combinatorics, phases and tides was a lovely break in the non-stop "going" I find myself in these days (even if it is only taking place in my mind!) Then when Sarah mentioned how mathematics tends to be "esoteric" and separate from the arts I felt surprise, because there is SO much "math" involved with dance! The repeating patterns of: the steps, the music, the rhythm, the 'counts' involved with the dance step combinations i.e.: "five, six, seven, eight!" 

As Sarah moved through the combinatoric dance moves I was enthralled! Then immediately intimidated thinking that if I attempted this I would feel very much the same as when I try to pat my head and rub my stomach at the same time! While watching the video and the calm movement of the dance moves, I was reminded of a conversation I had with my math Instructor when I attended Langara. This instructor was very excited about mathematics and when I shared that I was beginning to understand the concepts, he enthusiastically began sharing, "When you think about it, math is all around us!" At this time I was still of the opinion that mathematics was only a series of calculations and operations performed with abstract numbers. The Instructor's statement caused me to think that he was a bit too excited about math; his statement made me think that he was referring to numbers being "all around us," that he actually could see the numbers, kind of like Neo, in The Matrix...

(https://www.bing.com/images/search?view=detailV2&ccid=SVfLcrUR&id=93BD980B39254258326B85366A75DB79D7FB5391&thid=OIP.SVfLcrURvhmwszKnYUp7AwHaDt&mediaurl=https%3a%2f%2fscreenrant.com%2fwp-content%2fuploads%2f2017%2f10%2fKeanu-Reeves-The-Matrix-Code.jpg&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.4957cb72b511be19b0b332a7614a7b03%3frik%3dkVP713nbdWo2hQ%26pid%3dImgRaw%26r%3d0&exph=1000&expw=2000&q=the+matrix&simid=607988355100060212&FORM=IRPRST&ck=022360091CF0ED1B9753A77CA902814D&selectedIndex=31&ajaxhist=0&ajaxserp=0)

Extension:

My teaching interests are in the primary levels, particularly Pre-School (I'm currently not teaching due to COVID restrictions) So I think I might discuss the idea of how the sun moves from the East ~one side of the sky to the West ~the other side of the sky and take a nice long time documenting this to help the students observe the movement. Then once they recognize that the sun moves and "rises" mimic Sarahs dance moves with arm movements and creating a few simple dance steps that map out the time of day (circle-time, snack-time, lunch-time, nap-time, play-time, home-time, supper-time, bed time) 

The extension could be to learn the seasons in this manner as well, creating dance combinatorics that show and discuss the seasons throughout the year.

READING Reflection :

My Reading this week was "b." Kelton & Ma: Reconfiguring math settings with whole-body, multi-party collaborations.

Abstract: "The study examines the consequences of whole-body, multi-party activity for mathematics learning...illustrating how whole-body collaboration can transform how learners experience learning environments and make sense of important mathematical ideas."

Kelton & Ma begin by stating that "How we think, learn, and communicate about mathematics depends a great deal on our opportunities for physical movement, interaction and expression.... mathematics learning environments shape and are transformed by the activities of learners."

The paper studies two separate activities in two different schools, in two different "arenas"~or, learning environments; a school gymnasium the other, a school classroom. 

The activity in the gym allowed for large "gross motor" whole-body movement with "multi-party"(a full class) collaboration while performing an activity entitled, "Walking Scale Number Line".

By using the "arena" of the gymnasium, where typically students are free to run, jump, talk, yell, at times even scream; allowed a greater sense of freedom to the students to collaborate, with the underlying feeling of "play".  The teachers were able to facilitate student engagement and learning from this space and then in turn allow for mathematical concepts to be realized in a "whole-body" manner that may not have been captured in a classroom setting ~arena. Kelton & Ma state it this way, "The structure of mathematical tasks and learning environment designs, and the ways in which participants take them up, can have profound consequences for configuring which aspects of embodied activity...are treated as relevant and which are ignored, eclipsed, quieted..."(page181)  "...this study signifies...curiosity about the possibilities...of activities...comprehensively incorporated into and made relevant to mathematics than is often the case..." (page 182) 

While this paper was very much a study type of paper, I did enjoy reading about how the students were learning about mathematical concepts in a manner that was not traditional; I was a little disappointed in the fact that the paper didn't touch on how (or if) the teachers took the students learning and interlaced it into deeper mathematical learning. 

 week 4: Activity

I was assigned Bridges 2017. I enjoyed looking at all of the math art! There were so many that appealed to me, but I finally settled on Martin Levin's Precious Polarity. The simple lines, the silver and gold, the geometric shapes of a pentagram and the inside triangular shapes somehow made me feel happy.

I spent a good three hours on this activity! I tried to build the triangles in the centre first and just could NOT figure out what I was doing wrong! I reread the description, took my shape apart, reworked my shape; zoomed in and tried to see where the shapes became 3D... there just didn't seem to me to be enough direction to be able to replicate the icosahedron figure. I decided to call it quits and focus on trying to reflect on the reading for this week. 

The dodecahedron and icosahedron configurations kept niggling at my brain after I had given up so I had to go back and read the description again nice and slowly. Previously I had gotten distracted by the 'mathematical words' that I don't really understand and missed how there was wire strung through the outer pentagons/ dodecahedron that was actually creating the icosahedron/triangles in the centre!

All of my struggles throughout this small activity is an insight into our students. They will muddle away trying and trying to get the work done, attempt the homework on their own (or through zoom these days) and because there is some minor portion of the directions that they don't understand, and feel that that minor piece that they don't understand is their fault, or responsibility and they won't ask for help. I hope I can remember this feeling of confusion and bring it into my practice so that I can help my students find that "missing link".