442 Reflection

Hello twins.

The following is a reflection on my experiences during EDCP 442.

This course really opened my eyes to two major themes. One is how fascinating it can be to explore the often-overlooked history of the major ideas present in modern mathematics. I had not explored this really at all during my time as a student or teacher. I can see the value in enriching one's understanding and providing a greater appreciation that it can provide. I would like to implement more history into my lessons by picking spots to integrate them into certain topics. I really enjoyed it when we explored ancient methods as well and got to practice solving problems using algorithms or techniques that they would have used around that time. It was fascinating to explore the ingenuity of ancient civilizations and to see authentic demonstrations of their calculations during that time. I believe students can definitely benefit from seeing these demos. The other major takeaway was how much math has been influenced by other cultures. Math textbooks and resources tend to mostly focus on Western contributions and white male figures. I enjoyed reading how these mathematical ideas were discovered at different times across the world and how cultures had their own unique ways of looking at a problem. During our class presentations, it was clear that this idea had been received by all the students in the class. We often focused on incorporating the contributions of multiple cultures on our math topic and recognizing how ideas stemmed from a variety of figures. 

Thanks for reading,

Josh

Art History Reflection

 Hello twins.

The following is a reflection on my art history project on Hypatia of Alexandria.

I was really glad with the topic I had chosen for this presentation. I wanted to cover a female mathematician and enjoyed researching Hypatia's colourful life. From the start, I knew the sort of project that would work best as artwork. The portrait using ellipses was a laborious endeavour just due to the sheer size of the file. Reaching 1800 equations in geogebra was very challenging for my computer and I had lots of setbacks with my project lagging and not saving properly. But I persevered to the finish line because I was convinced it'd be worth finishing. I was happy with how the finished project turned out and it received a positive reaction during my presentation. During my presentation, I gave a quick overview of the major events in Hypatia's life without emphasizing her infamous demise. I was glad to find out that she had been a teacher as well and some of the principles she instilled in her "classrooms". I would like to explore more about other women in ancient academia and their stories from different parts of the world.

Thanks for reading,

Josh

Art History Project

Hello twins.

Here is the link for my presentation on Hypatia of Alexandria.

https://docs.google.com/presentation/d/1vwS-G2nOsEP0SHdNQWbT-GbLkIUvUC3eofVKYcpwpuc/edit?usp=sharing

Thanks for reading,

Josh

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

Euclid & Beauty

 Hello twins.

The following is a response to a biographical evaluation of Euclid's work from St. Andrew's University.

Euclid's Elements provided a synthesis of mathematical thought at that point in history. It compiled centuries of Babylonian, Egyptian and Greek mathematics into a single text. The book was crafted in a logical manner which provided the framework of mathematical thinking for centuries. He outlined the fundamentals which could serve as a friendly starting point for beginners interested in the field. He then builds upon those basics to explore more advanced topics relevant to more advanced practitioners It also introduced key ideas for points, lines, angles, and shapes which likely had applications to other disciplines. There was likely an aspect of convenience as one could refer to a single book instead of tracking down many independent works. There is an inherent satisfaction in an all-encompassing text for a subject and these summaries are highly valued in modern contexts.

As a math student, I have often heard instructors refer to an aspect of beauty or elegance in certain mathematical ideas. A skeptical outsider's perspective may be quick to dismiss this claim by questioning how a subject like math could ever contain an element of beauty. However, as I began to take more abstract math classes which dived deeper into the theory I discovered what they had described. There is beauty in the contrast between using a simple argument in an explanation for more advanced and complex ideas. There is also a deep satisfaction that can occur when math problems conclude cleanly and concisely. For our recent math history project, we had a puzzle that we presented to the class involving arc geometry. After solving the puzzle on my own, I messaged a group member saying that the puzzle was a beauty. I was referring to the extremely satisfying way in which the problem worked out when solving it. There was a variety of cancellations in the algebra which led to a very concise formula. Thus I suppose one must get their "hands dirty" by working with math to see the beauty that others describe.

Thanks for reading,

Josh