Course reflection

This course has been the one that pushed me to think outside of my comfort zone more than any other. We were introduced to various ancient methods and strategies for doing mathematics, many of which I had never encountered before and had no prior knowledge of. It was both challenging and incredibly eye-opening to explore these unfamiliar approaches like different bases. Beyond the technical aspects, the course also highlighted the beauty of mathematics, showing how many mathematical pursuits originally emerged as ways to explore art, self-expression, and the deeper truths of the world. This perspective gave the subject a richness and depth I hadn’t fully appreciated before. While I had some awareness that there were disputes over discoveries and the credit given for them, I didn’t realize how widespread and frequent these issues were until this course. The history behind mathematical concepts and discoveries added a unique character and narrative to the subject, making it far more humanistic and interesting. This historical context is something that feels missing in typical high school classrooms, where the focus is often on the "how" of mathematics without delving into the "why" or the stories of those who contributed to its development.

Assignment 3 reflection

For our Math History Assignment 3, I believe our presentation went well overall. Raymond and I chose to explore the life of Émilie du Châtelet because we wanted to highlight some of the astonishing contributions women have made to the fields of mathematics and physics. It was fascinating to learn about Émilie's multifaceted life. Through our research, it became clear that she was a woman with an intense passion for knowledge, especially in mathematics, and a deep care for the people around her. We aimed to reflect this in the accompanying art piece. Beyond our own presentation, it was also wonderful to see other presentations showcasing women in STEM, such as Hypatia and Agnesi. I had never encountered these figures before this course, and I believe introducing their histories in a classroom setting could serve as an inspiration to other women

Assignment 3 Document

The link below leads our assignment 3 math history art project

Assignment 3

Assignment 3 topic and references

My partner Raymond and I will be working on the life of Émilie du Châtelet. Our art piece will be in the form of a sculpture.

Here is a draft list of references we found for our research.
Zinsser, J. P. (2007). Emilie du Chatelet: Daring Genius of the Enlightenment. Penguin.

Tamboukou, M. (2023). Exceptional women in science education? Émilie Du Châtelet and Maria Gaetana Agnesi. Paedagogica Historica, 1–21. https://doi.org/10.1080/00309230.2023.2238621

Shaw, W. (n.d.). Du Châtelet (1706-1749). Project Vox. https://projectvox.org/du-chatelet-1706-1749/

Pursuit of Knowledge. (2024, May 4). Émilie du Châtelet: Forgotten Physicist [Video]. YouTube. https://www.youtube.com/watch?v=MnaW7r6wMd4 

Assignment 2 reflection

The unit on quadratics was one of my favourite topics in high school, so I was amazed to learn that it has such a rich history spanning centuries and continents. I was fortunate to explore the topic geometrically, using algebra tiles, which mirrored the methods described by Al-Khwarizmi in his book Al-Jabr. This hands-on approach made the process ofcompleting the square much more tangible, and I was excited to share this activity with others. I feel that textbooks often overlook this intuitive way of visualizing completing the square, and focus strictly on the algebra, which is why many students struggle. Like several other topics we have discussed in class, there is controversy over who should be credited with the quadratic formula. However, unlike a theorem like the Pythagorean theorem, I am pleased the formula in the West is named for its application rather than after a person. This, however, is not the case in other parts of the world. We saw with countries like India and Brazil, the formula is named after specific mathematicians.

Watching the other presentations, I noticed that the issue of giving proper credit and the controversies surrounding it was a recurring theme across many of the topics. However, I think Caris summed it up beautifully by suggesting that, rather than getting caught up in the debate over who should be acknowledged, we should focus on celebrating the discoveries and advancements these concepts bring to society as a whole. I was also struck by the variety of roles that mathematicians used to occupy. Many of the individuals highlighted were not just mathematicians, but also scholars, philosophers, and artists, among other things. However, I find that I have compartmentalized mathematics into its separate category, distinct from other disciplines. Thus, I wonder how I might challenge my stereotype and celebrate mathematicians as multifaceted individuals with a range of identities.

Nov 13: Dancing Euclidean Proofs

This was my first exposure to seeing dance as a medium to represent and explain mathematical concepts. It was refreshing and eye-opening to see how effective movement and the environment could be in conveying ideas typically confined to paper. I believe this approach helps reduce the complexity and rigour often associated with mathematical proofs, which, in my opinion, may make mathematics feel less accessible and more intimidating. 

As I watched and read the article, two parts stood out: the sequencing of movements and the role of imperfection in dance. The article highlighted how the choreography "required a careful sequence of logical steps" to effectively portray Euclid’s elements. This observation made me stop and reflect on how the progression of dance, with the added dimension of time, allows the audience to grasp the proof more intuitively. One may see how each movement builds upon the last, leading to a final product. This contrasts with the fixed, polished diagrams in Euclid's original elements. As a result, I wonder how crucial the path of the steps is if the result remains unchanged. Would the audience still be able to make the same conclusions if the sequence of the dance changes? My second stop was on the role of metaphors and imperfection. The authors mentioned that the dance involves “metaphors sustained by the agreement between imperfect embodied experience and the imagination of abstract representation." I found it fascinating how the human mind can grasp the underlying message of Euclidean proofs, even when the dancers' measurements and diagrams are not to scale. It seems that this use of imagination, which fills in the gaps of imperfection, may be uniquely enabled by movement. I find that static representations like images or diagrams often require precise accuracy to convey the same message effectively. 

**EDIT**

This proof can be a helpful tool for learning and understanding math history because it offers an accessible entry point into Euclid's postulates without requiring advanced knowledge of mathematical terminology or notation. High school students often struggle with the complexity of math symbols, new vocabulary, and the use of variables. By incorporating dance and movement, this approach provides an intuitive way for students to engage with Euclid’s Elements and make sense of abstract concepts. However, while the dance activity offers a more intuitive understanding of the proof, it might not be formal enough for students to fully grasp the rigor of mathematical reasoning. As a result, I suggest using the dance as an introductory or supplemental activity, followed by the formal proof. This allows students to experience the concepts in a more embodied, exploratory way before reinforcing their understanding through the language and structure of formal proofs. Additionally, this approach fosters collaboration. Since the dance involves partners, students must work together to analyze and decode the movement and how it relates to the proof. Thus, it encourages teamwork and communication. However, there are also potential logistical challenges. For instance, my practicum school has small, densely packed classrooms. In that case, there may not be enough space for students to participate comfortably in a dance activity. Furthermore, some students may have physical limitations or disabilities that could restrict their ability to fully engage in the movement. These possible constraints need to be considered when planning the activity to ensure that all students may participate meaningfully.

Nov 6: Was Pythagoras Chinese?

Throughout our discussions, it has become increasingly apparent that math has been deeply shaped by colonialism. One example is the underrepresentation of non-European mathematicians and their contributions to the field. While many significant discoveries and theorems were made by scholars outside of Europe, the naming of mathematical concepts is overwhelmingly dominated by European individuals. I believe this has a substantial impact on student learning and understanding. Acknowledging the contributions of non-European mathematicians is a crucial step toward debunking the stereotype that non-European civilizations were intellectually inferior to their European counterparts. When students learn about the diverse cultures that have shaped mathematics, they are exposed to different methods, perspectives, and problem-solving strategies. As stated in the article, the Chinese were more interested in "rote memorization" and wanted to guide readers to "master methods for themselves". On the other hand, the Greeks were more open to "oral group discussions." Having access to both these strategies allows students to approach mathematical problems with a wider set of tools. This may enhance their ability to think critically and solve problems. 

I have never felt particularly attached to the names or theorems of mathematical concepts. However, I believe the tradition of naming theorems after individuals may be more problematic than helpful. In some cases, it overshadows the collaborative, cumulative nature of mathematical discovery, where ideas are often built upon by multiple scholars across different cultures and eras. Consequently, I propose that we reconsider the use of specific names for mathematical concepts altogether. It might be more effective to adopt labels based on the concept's application or use. For instance, the "Pythagorean Theorem" has been shown to have roots in ancient Chinese and Babylonian mathematics, yet the European association with the name has overshadowed these earlier contributions. Rather than crediting one culture and diminishing others, we could refer to it more neutrally as the "right triangle relationship theorem." This more accurately describes its function and application. Moreover, this approach would shift the focus from the person to the idea, ensuring that the contributions of all cultures are recognized equally.