Week Nine: Mathematics & traditional and contemporary practices of making and doing

I chose to do the rope making activity and scavenged some dead grass from areas where the snow has melted off the hill behind my house. Lacking helpers, I chose to do the simple version where the grass was twisted into strands then wrapped back on itself in the opposite direction.

My z-twisted rope resembled a double-helix and was somewhat cylindrical. It was interesting to see the differences in process and product for multi-stranded braiding and rope making when watching the videos. The ropes were all cylindrical helices and each strand could be followed down the rope without going over or under another strand. In contrast, braids were flat and the alternating pattern of strands going over and under each other gave a more woven appearance.

 

 

 

I noticed that the grass still held the smell of summer despite having been dried and frozen for months. When making the grass rope I noticed a pattern of making three twists then wrapping the strand. The combination of twisting and the smell reminded me of when my sisters were young and used to make braided daisy chains and purple clover crowns in the summer. I also used to make hemp bracelets and the process was similar to the net making.

 

 

 

 

 

It was interesting to see such a similar perspective on the value of traditional knowledge and knowledge keepers from people in such different cultures. The videos showed Scandinavians (Closed by Hand), North Americans (Wildfibres), and South Americans (Weaving the Bridge at Q’eswachaka) all expressing the need to learn traditional methods from those who came before us. 

This quote from Undrum grabbed my attention, “There was no other way to learn. I had to learn from someone who knew how” (Ensby, 2016, 6:39). My husband's parents immigrated from Italy in the 1960s and they have a similar respect for traditional knowledge, including braiding garlic and onions for storage through the winter. 

 

 

 

 

 

 

The Astrom and Astrom (2021) article described the historical context and properties of rope. The mathematical description of rope has a lot of potential for a classroom, especially a physics class (which is just logic and applied mathematics in many ways). There could be discussions of the mathematical modelling used to describe the appearance of rope, or relate the diameter of the rope to the number of strands and their diameter. The authors also give equations used to approximate these values which could lead to a discussion of the assumptions made to create the models and equations. Their description of physical properties including linear density could also be used in a calculus course. When watching the video, "Weaving the bridge" I wondered how heavy the ropes would be and how much the final bridge weighed. The equations provided by Astrom and Astrom could be used to estimate the weight which could be compared to the weight of a more traditional steel construction. The woven bridge would also be a great exercise in all three areas of the Core Competencies. Communication, problem-solving, collaboration, positive cultural identity, and more.

Week Eight: Mathematics & fibre arts, fashion arts and culinary arts

My capstone project is going to be an exploration of factors that help keep girls engaged in mathematics through high school, so this week’s theme of challenging binaries and gender expectations resonated with me. I appreciated the acknowledgement in the introduction that men may be excluded from traditionally feminine endeavours, just as women can be excluded from traditionally masculine endeavours. My preliminary research and literature review indicates that women are underrepresented in STEM fields, especially computer science and engineering. Gendered stereotypes and expectations around STEM fields seem to play a significant role, but I wonder about the gendered stereotypes and expectations around “nurturing” fields like nursing and teaching. Men are very much underrepresented in those fields, and I wonder how many men rule out certain careers simply because they are considered feminine?

The introduction also mentioned social class stereotypes. My husband is a journeyman mechanic so the idea that trades people are lower class and/or unintelligent is familiar and annoying. While the specific math concepts encountered may not be extremely complex, there is an incredible amount of mathematical thinking and problem-solving involved in the trades. And yet, as the introduction suggests, the stigma persists and even pervades the school system. Students often view PreCalculus as “smart kid math” and Workplace math as “dumb kid math” despite its potential to be a really interesting and valuable course. But, I fear I digress…

On to the activity! I chose to do the origami because it is something that I am familiar with and enjoy doing. When working weekends in university I used to make little origami animals from post-it notes and hide them around my boss's office. I even made him a little zoo in an empty fruit tray container one time. 

The Miura-Ori pattern here is a relatively simple series of folds resulting in tessellations of parallelograms. It reminded me a little bit of a “magic ball” or “dragon’s egg” which is a slightly more complex pattern involving tessellations. 

 

 

 

 

 

 

 

 

 

In Quilts as Mathematical Objects, Gerda de Vries spent a significant portion of her presentation discussing tessellations, their properties, and their appearance in the art of quilting. The discussion of aperiodic tiling was quite interesting. In addition to tessellations, she also played with permutations and algorithmic design in her quilting. It was fascinating how many different patterns she could make with right isosceles triangles, three coloured fabrics, a bit of asymmetry, and an arbitrary set of rules for combining her triangles. 

 

 

It reminded me of the creativity that  arises from the tension between freedom and constraints which we explored through poetry last week. She talked about blindly following her rules then being surprised and delighted by the final product, which seems similar to the way PH4 poems unfold. Mathematical transformations, such as translations and reflections, and classifications of patterns were also analyzed using the context of quilting.

 

 

 

In the discussion of quilt design I thought there was a missed opportunity to talk about ratios and proportions as many patterns involved similar geometric shapes in different sizes. Ratios and proportions are also an important part of food preparation which is utilized in Hawksley’s article. She used coloured, layered beverages as a means of experiencing mathematics through the senses of sight and taste. Further claiming that “unlike most examples of food-based mathematical art, where the math is purely visual with no effect on the actual flavor and experience consuming the food, the math in our beverages is conveyed entirely by the ingredients and flavor” (p. 519). Ratios, proportions, and fractions can be explored by calculating the relative amounts of sugar or flavouring in each layer then comparing the differences in flavour when tasted. Hawksley also discusses the potential to use layered beverages to investigate arithmetic sequences, but this honestly feels like a stretch to me.

 

 

 

I teach the senior grades and this activity seems like it would be most appropriate for a math 8 class, but I could possibly see using it as a review activity in upper grades. Up to this point, I have only taught PreCalculus or Calculus courses and have been finding it difficult to apply much of what we have been learning to those courses. With the fairly specific yet assorted content to be covered, this has been a fairly consistent challenge throughout the program and my own investigations into more authentic learning activities. However, I am trying to remain open minded and make strong attempts to think of ways I could adapt the material. I need to keep reading Maria's blog for more "wonky math" ideas!

 

I wonder if this beverage activity could be adapted to look at rates of change or gradients if the layers were similar enough to slightly mix at the interface and/or have several layers? Another possibility is having students design quilt blocks, or copy an existing pattern, using mathematical functions in Desmos. Then they could use appropriate transformations to complete a full quilt design.