Viewing:
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.
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.
Hi Grace,
ReplyDeleteYour shoelaces discussion is very thought provoking. Such a simple concept with so many possibilities! I like the idea of proving something is the best and testing it out, which lends itself very well to persuasive writing. You have me imagining some lessons on time and physical space in a primary class. Let's say there's a list of things we need to do to get ready to go outside for recess - which is the best order and why? Does it make sense to go back and forth between your desk and hook/cubby multiple times (put your boots on, put your pencil box away, put your hat on, push in your chair, put your jacket on, wipe your desk, etc.)? What happens if you put your mittens on first? Together we could explore different orders and decide on the most optimal option for our routine.
I appreciate your thorough summary of the Fisher article. It seems like there is an interesting connection between optical illusions and reality. (A personal favourite of mine are the neverending stairs pictures.) Is the only difference between an impossible triangle and a highly unlikely triangle the straightness and the 90 degree angles? I'm wondering how to connect optical illusions and mathematics in an elementary class - there's certainly potential for engagement! There are lots of opportunities for proofs and the mathematical thinking that encompasses the core competencies. Simply though, there are some opportunities for younger students to discuss perspectives. One example could be creating something with 5 cubes - what does this creation look like from different angles? Is it still the same 'thing' even though it looks different? Can you predict the other sides look like from this perspective? Hmmm. So much to think about. Thanks for all the ideas Grace!
Yes Grace this was a great summary of the readings and viewings.
ReplyDeleteI was thinking about the lacing activity and wondered at what determines the best lacing method. Did you agree with the definition of the best lacing method? For some of my students it might be more connected with how quickly they can get their shoes on and off. They are so used to slip on shoes that many grade 2 students are just learning how to tie or may not even know how to yet. If the shoe is laced too tightly they will stand on the back of their shoes. I wonder if they would have a different idea of what was considered the best lacing method?
Thanks for including the figures from your article, it is fascinating to see the "improbable" beaded version of the "impossible". It is interesting how adding a slight twist makes such a difference in these geometric objects as it does in the mobius strips. Plus the beading is aesthetically pleasing. I could see teachers wearing them as mathematical jewelry!
ReplyDeleteOne year the grade 12 class at my school bought white grad hoodies and tie-dyed them. It was really cool to see how different the patterns were. I can visualize how I think the cloth must have been folded to achieve square and triangular effects with orbifolds and will have to watch the video to see how close my guess is. This activity could be a good exercise in spatial reasoning!
I like the thought of playing with the idea of representations and the objects represented. It reminds me of the representation of infinity and the mobius bands I saw in my article from last week. Some questions that arise are: What is more important to capture in a representation, accuracy or essence? Or perhaps even something else? Does the answer change depending what the representation is used for?
Thanks Grace, I really like the connections you make among the videos, readings, and family life. I’d love to see photos of your daughters’ t-shirts and hear more about your dad’s unique shoe-lacing technique.
ReplyDeleteA lovely reading of Gwen Fisher’s article and a lively interplay of conversations and feelings, making for an interesting group discussion.
I hope you continue to explore ways in which art-making and math are a part of what you’re already doing and have yet to do!