Reflection on the Assignment 2

Reflection on the 2nd Assignment

First of all, I want to express my amazement at how creative and engaging my classmates’ assignments are. Some use comics or videos to explain their topics, while others connect mathematics with their interests, such as the fashion industry. They present concepts that I’ve seen as ordinary for years in such intriguing ways. This is an experience I haven’t had in other classes—it’s both enriching and an aesthetic pleasure to appreciate their work. Reflecting on my own educational journey, I realized that "aesthetic appreciation" was not emphasized in my learning process, which was often monotonous and dull. Although I hesitate to admit it, my approach to learning has also become dull and one-dimensional.

When planning my assignment, my focus was primarily on the knowledge itself, such as, "How can I present this concept in a way that makes it understandable?" I didn’t pay much attention to making it engaging. Another thing I noticed was how confident and clear my classmates were during their presentations. They expressed their ideas with such composure, while I sometimes get nervous. I often realize after my presentation that I’ve made errors in my explanation (oops).

Secondly, as I explored the origin of radicals in my topic, I initially assumed that the square root symbol inherently carried the meaning of taking a root from its inception. It wasn’t until I learned about the story of "doubling the cube" that I realized how concepts are defined and constructed. It felt like an obvious point, but it struck me profoundly in that moment of realization. I’ve used the square root symbol for so long and taught students how to calculate with radicals, but I had never thought about the process of its development. It’s difficult to describe the feeling—it’s like realizing that something we’ve taken for granted wasn’t always the way it is now.

When exploring how Greek mathematicians represented cube roots of 2 using geometric methods, it struck me how complex their approaches were without the square root notation or tools we now take for granted. Since the advent of calculators, I’ve been able to compute the exact value of a root in seconds. But in their era, without such tools, how did they determine the value of the cube root of 2? It left me in awe of their ingenuity and dedication.

Finally, this exploration brought me back to my childhood. As a child, I couldn’t understand why the result of the square root of 2​ was an infinite non-repeating decimal or why it couldn’t have an integer root. Looking back, I think I didn’t truly grasp the concept of square roots. Similarly, my students often face the same confusion when they first learn about radicals. They frequently struggle with understanding why the result of a square root can’t be calculated directly by hand, why we need a square root symbol to represent a specific value, or why a symbol can stand in for an actual number. Through this inquiry, I’ve found answers to these questions and realized that I could encourage my students to try exploring how to calculate/demonstrate the square root of themselves. This could help them understand its meaning more deeply.