Assignment #2 Reflection

Hello twins.

Below are some thoughts on Assignment 2 and how the presentation went in class.

When I was researching coordinate systems, I initially didn't think I could cover enough information for a 10-minute presentation. However, once I read the story about how Descartes created the coordinate system based on a fly on his ceiling, I knew I had to proceed with my choice. I found that having different slides for Chinese, Islamic, and other perspectives was influenced by my BEd readings and our discussions in class. It can be so easy to simply reference that one historical figure who is the most well-known or who the idea is named after. It requires more work to look into its development in other places around the world which may have coincided with or often predate the work. It was definitely a learning experience for me as I hadn't made the connection between Descartes being the Latin root for Cartesian. I also found it really interesting to see how a French man named Oresme created the way of graphing that still makes up a good portion of our high school math curriculum. I certainly found some good anecdotes to share with my future students when introducing said topics. Lastly, I really enjoyed learning about Babylonians and the connections between the 12 months and the 30-degree segments of a circle. Horoscopes are another very popular topic in modern society and so to trace it back to its original roots was a valuable insight.

I thought the class presentation went pretty well. I decided to start with my activity because we had just listened to around 30 minutes of math history and thought the class could benefit from a change of pace. My fellow classmates seemed to like the activity as much as I did and I'm glad that we were able to have a collective moment of achievement on the last puzzle. It was a resource that I learned during one of my Whistler Pro-D workshops. I remember being excited on that day to implement it in my classes and so I'm really glad that it worked out well today. My presentation provided more of an overview of how different parties contributed to the modern coordinate system and what the applications might have looked like in that time period. I particularly enjoyed telling the Descartes story although whether or not it actually happened remains to be considered. Lastly, I always enjoy incorporating some of my own interests into my lessons with the fashion graphic I discussed at the end. During class presentations, I enjoy seeing how unique our teaching styles are and how our personalities manifest in how we teach. During my short practicum, I found that when teaching the lesson, I was most able to connect with the students as they got to see my personality a bit more. I have found that the less we have to pretend or put on a show as a teacher, the more rewarding and authentic the experience is.

Thanks for reading,

Josh

Thanks for reading,

Josh

Dancing Euclidean Proofs

 Hello twins.

The following is a response to the Dancing Euclidean Proofs film we watched in class as well as the Bridges Math & Art article.

One idea that stood out to me was how the temporality of dance contrasts with the "all-in-one-ness" of the images or proofs we often read in math textbooks. The choreography adds an element of time where you can see each step of the proof sequentially build on each other. Scanning through a proof by reading it simply doesn't offer the same allure. Breaking proofs down into their individual components allows a greater appreciation for the methods and ideas behind the proof that are often lost. Too often we see these proofs as just one overarching idea, without recognizing the great amount of thought that went into building each step. This also more closely aligns with my experience with solving proofs. Rarely would I simply zoom through creating my own proof from start to finish. Instead, I would proceed methodically and carefully considering potential next steps in my argument. I also appreciate that the performance was done on the beach. Using nature as the backdrop for a math proof helped the audience connect with the inherent beauty of the argument. It starkly contrasted the typical institutional setting in which math is carried out. This would be an interesting addition to a high school math class as a final project perhaps in a geometry unit. I wonder if there could be other ways to modify the project for other math topics such as graphing or algebra. I would also consider altering the dance to other non-proof examples. There would likely need to be a certain level of maturity for this project to be carried out effectively and I wonder if some of the students may not want to buy in due to its performative aspects. Dancing can be a vulnerable act, especially for a teenager, and I wonder how we could potentially modify the activity to make it more accessible for all students.

Thanks for reading,

Josh

Was Pythagoras Chinese?

Hello twins.

The following is a response to an article which examined the Chinese & Greek contributions to Math history.

I recently observed a Math 8 class where they were learning how to use the Pythagorean theorem and apply it to word problems. Now the teacher did not discuss any of the history related to its origins by exploring who Pythagoras was or the contributions of other civilizations. Although the students were completely unaware of the history behind it, this did not impact their ability to practice using the theorem when solving their world problems. However, it did miss out on an opportunity to provide historical context on how the theorem came to be. Acknowledging how other civilizations have contributed could open the minds of some students by making the topic more inclusive and perhaps relevant. For example, students with Chinese heritage could feel more connected to the content and thus become more engaged in class. It also encourages appreciating diverse perspectives on a topic. For example, how Indian & Chinese mathematics have shaped our contemporary understanding of the subject.

On a similar note, the prevalence of Western names in Math textbooks overshadows the contributions from a diverse array of cultures. While it may be too late to rename them, providing students with alternative considerations can help globalize our approach to teaching math, which is especially important in today's world. This aligns with approaches to decolonization that may be more prominent in other subjects such as social studies. Students in math classes come from a variety of different cultural backgrounds, and finding ways to foster a sense of belonging and pride in their cultural heritage is important. By highlighting the contributions of diverse cultures to mathematics, the subject becomes more accessible and engaging for all students.

Thanks for reading, 

Josh