Final course reflection

Learning history is important for everyone. This semester, I gained profound insights into topics I thought I already understood. Exploring historical contexts and engaging in problem-solving puzzles allowed me to approach math with persistence and creativity, much like ancient scholars did. This mindset is invaluable—not only in mathematics but in life. Even when faced with limited solutions or resources, we can still find innovative ways to tackle challenges.

I also thoroughly enjoyed working on projects with my classmates. Collaborating in a creative environment allowed us to approach traditional topics in unconventional ways, using our artistic freedom to make the learning process more engaging and dynamic. This approach not only deepened my understanding but also fostered a sense of teamwork among us.

Overall, this semester taught me the importance of combining curiosity, resilience, and creativity in both learning and problem-solving. These are skills I hope to continue to develop in my future teaching practices.

Assignment 1 reflection (Solving ancient puzzle)

This project made me reflect on how Ancient Egyptian geometry emerged from their need to measure, especially in managing land after the Nile’s floods. I thought about how math continues to play a key role in land and food systems today. In modern times, math is deeply involved in agriculture, from predicting crop yields and optimizing irrigation systems to more complicated problems, such as managing resources like water and soil. Advanced geometry and data analysis help farmers design planting patterns. This reminded me of what I saw in rural France when I went on a trip many years ago. In the highly industrialized agricultural areas, French farmers used GPS systems for farming. Similarly, in land management, math helps calculate areas for conservation, and engineers can plan urban expansion accordingly. 

Also, I believe the relationship between math and food will have a big implication in the future. Algorithmic calculations are used to minimize food waste; geometric principles are applied to packaging to reduce material waste. This is similar to the Egyptians’ application of geometry, who used math to address their own needs.

My teammates, Sahl and Brandon, worked on solving the truncated pyramid problem. My first thought was to break it into small, simple parts, but they introduced much quicker and easier methods. Brandon found a video that explained everything so clearly yet so captive. Seeing their different approaches reminded me of how math encourages different ways of thinking and the power of combining ideas. 

Euclid and Beauty Response (Nov. 4 Reading)

I remember learning knot theory during my undergraduate, and oftentimes I marvelled at how deeply interconnected geometry is with calculus. Geometry is useful and applicable because it provides the foundation for solving complex mathematical problems. For experts in the fields such as engineering, science, and even art, it offers a way to interpret abstract concepts tangibly. 

Similarly, Euclid simplifies complex geometric ideas into understandable patterns, such as  Elements. For instance, Euclid’s fifth postulate, the "parallel postulate," very much laid the foundation for understanding spatial relationships. The beauty of these postulates lies in their simplicity and showcases the elegance of math. This attracts experts and their interest in the development of geometries. Euclid’s work on geometry is also a shared mathematical language, as it removes cultural and linguistic barriers. Different math experts all over the world are able to unite their shared passion for math. 

For high school students, learning Euclid’s principles is extremely useful for learning trigonometry, because it helps students develop the reasoning skills needed to understand relationships between angles and sides. I can use this in the unit circle or the sine and cosine functions. Studying Euclid can enrich their understanding of mathematics, but also foster critical thinking. Specifically, one of Euclid’s common notions, "things that are equal to the same thing are equal to each other," is in my opinion a very useful teaching tool in high school geometry, where students learn to apply it in, for instance, solving equations.

Dancing Euclidean Proof Reflection

I found myself reflecting on the powerful role the mind-body connection plays in cognitive learning, especially in mathematics. Movement can enhance cognitive engagement, and that I believe is a compelling force existing within everyone. Where physical actions represent abstract mathematical ideas, students' understanding of math concepts can be deepened. This connection between body and mind highlights how movement can serve as a bridge, making seemingly difficult concepts more accessible and memorable. 

Moreover, I think the reading resonates with my long-time belief that learning math is a process that requires engaging multiple senses. Using sight, touch, and sometimes sound to create a unique sensory experience. By turning mathematical steps into physical movements, students activate kinesthetic learning. I believe it is important for students to "feel" the math as they perform it. As taught by my pilates instructor, one only comes to a deep understanding of an art when being physically present in it. 

Given the growing popularity of choreography and dance among teens, particularly influenced by K-pop culture, I think incorporating dance into high school math lessons could be a good opportunity for future educators to build relevance with the student body. Many students are already familiar with choreography through social media and music videos. It is thus easier for us to seek ways to create connections between their interests and mat. I could collaborate with students to create routines that represent various math concepts, like function transformations. This would make math learning a lot more interactive. 

One potential setback would be that students with physical disabilities might feel left out because they cannot participate in these dancing activities. While trying to be creative in our classrooms, we should also remember to be inclusive and understanding of every individual around us. 

Assigment 2 reflection

My presentation on the Newton-Leibniz controversy was inspired by the current buzz around the Mike Tyson vs. Jake Paul debate. Hearing that the two collaborated behind the scenes to fool the internet and monetize their rivalry got me thinking about parallels in other fields. I wondered if mathematics had a similar story, and that led me to the debate between Newton and Leibniz over the invention of calculus. The historical rivalry between these two great minds revealed how conflict, whether genuine or manufactured, can sometimes serve as a driving force for innovation. I concluded my presentation with a positive takeaway: while rivalry can be contentious, it can also push the boundaries of what’s possible and lead to remarkable achievements.

This exploration of rivalry left me reflecting on its potential role in teaching. I’m curious about how this might play out in Vancouver high schools, where I’ll be teaching. My theory is that rivalry between teachers isn’t likely because every educator has their own unique strengths, and these differences cater to a variety of learners. For example, one teacher might excel at fostering curiosity through project-based learning, while another might shine in building confidence through structured skill-building. This diversity creates a collaborative, rather than competitive, environment. During my practicum visits, I have been noticing contrasting teaching styles of different instructors. Before then, I believed there was a golden standard of what an idea teacher should be following. But observing a wide variety of real life teachers in real time, I have new understanding of this subject matter.

An intriguing question from my classmate Jacob further inspired me: was there any money involved in the Newton-Leibniz controversy? While there’s no evidence of financial stakes, the question reminded me of how external motivations, like recognition or resources, might influence rivalries. 

Nov.6 reading responsee

One thing that struck me was how Eurocentrism in the history of mathematics continues to be reinforced even today. This brought to mind my middle school math teacher, who lamented the fact that the globally accepted origin of the Pythagorean theorem was primarily attributed to the West, while he believed it originated in China. Ancient Chinese texts refer to it as the *gou-gu* theorem, discovered by a teacher named Chen Zi and his student Rong Fang, although they were not widely acknowledged historically. Because non-European contributions have often been marginalized in the history of mathematics, potentially due to lost records or the failure to credit early math innovators, it is more important to educate students on the importance of math contributions from other cultures. Another aspect that surprised me was how non-European mathematical contributions continue to be overlooked in modern education systems. This remains true in current school curricula. For example, when I learned about Pascal’s triangle in high school, it was taught as a European discovery. Yet, mathematicians like the Chinese scholar Yang Hui made significant earlier contributions to this concept. Despite this, we never explored the diverse historical background of the triangle, leaving us with the impression that it had a singular European origin.

The Dishes Puzzle problem

The way I approached the problem was by finding a lower limit and upper limit for the number of guests. Given that we have 65 dishes, the situation where there are least amount of guests will have be that everyone is eating rice only, so 65*2 = 130 guests. And the max number of guest will be that everyone is eating meat, so 65*4 = 260 guests. With a range, we can test out each number. And see if when being divided by 2,3,4, the sum of the dividends will add up to 65. 

Offering students a historical background in mathematics not only supplements their learning but also deepens their appreciation for the subject's vast diversity. By understanding the origins of mathematical concepts, students can see how different cultures across the world contributed to its development, from ancient Egypt and Mesopotamia to China, India, and the Islamic Golden Age. This awareness helps them recognize that math is not a static or isolated subject but a universal language shaped by human experience across time and geography. It opens up perspectives, allowing students to embrace other cultures and recognize the global impact of mathematical discovery.

Additionally, incorporating puzzles and imagery into word problems makes the scenarios feel more grounded and authentic. This approach reminds students that mathematics is not just an abstract concept confined to the classroom but something rooted in everyday life. When students are searching for solutions, it helps to see math as a reflection of real-world situations and challenges. By grounding problems in reality, we emphasize that mathematical thinking stems from the natural world and human experiences. This connection not only enhances problem-solving skills but also adds meaning to the task, making it more engaging and relevant. Ultimately, this approach brings math to life and fosters a deeper understanding of its practical applications.