Assignment 1 Reflection

This project has shed some insight towards the need to understand why certain math concepts were looked at in the first place. My presentation topic was the Egyptian method of chords. In all honesty, I was always taught the math behind finding the length of a chord but was never taught how and why it is used in the real world. I always saw chords as irrelevant because most of the time, we have the radius, which has been generally taught as more versatile mathematically. Hence, it was interesting to learnthe importance of chords both in the context of ancient Egyptian civilization and modern day times. I also thought the the activity we used to illustrate why chords are sometimes used over radii would be a good tool to use in the classroom, as it allows the students to move around, giving them a stretch break and a good laugh in the classroom as well. Oftentimes, the most memorable moments in school are the ones that were the most entertaining. Overall, I felt that using the method we used today could be a good way of teaching high school students real life applications of circular geometry.

For the extension, I struggled with it for weeks. I tried out different ideas and proofs for various theorems and found them irrelevant or out of the scope for the project. I then looked at the whole idea chords being used for road making, and then it dawned on me. I was thinking of how city planners estimated how much material is needed to make a road turn and the whole idea of arclength came up. Thus, I looked into the relationship between arclength and chord length. Initially, I was stuck because nowadays, people use trigonometry and angles to find the arclength. However, I thought to myself, "are angles always accessible? How did the ancient Egyptians provide estimates for arclength in the past?" Looking into mathematics I've learned in my undergrad, we learned about many estimates and approximation techniques without learning about why they are important, especially since now we can obtain exact answers for most things. But can we obtain exact answers for all things? Not quite. With that thought, I looked into how the pythagorean theorem can be used to create a lower and upper bound for arclength and how doing so provides a good estimate of how much material to gather for a project. I was pretty happy with my results, because such an extension is applicable and uses simple concepts that grade 8s and 9s can understand. Hence, it is practical and can be easily used in the classroom setting to teach 8th and 9th graders how to critically think as well. It also ties in to the pythagorean theorem unit and teaches its applications. Overall, this project allowed me as a prospective teacher to stretch my creativity as well as shed insight on a topic that most high school teachers do not go deeply into.