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.