Assignment 1: Ancient Puzzles Project Reflection

        Prior to this project about Ahmes’ loaves, I had never utilized the method of “False Position” or regula falsi purposefully because algebra was always my first resort. Algebra was a concept that was constantly forced onto me throughout high school so I felt like I could always rely on it to solve my day-to-day problems. I did not realize that it overshadowed all the other ways of logical and creative problem-solving until we did this project.

        The first day Aakriti, Sijie and I sat down as a group to tried and solve the loaves problem in the ancient way, we were completely stumped by how Ahmes got the 5 ½. Through researching, we discovered regula falsi. It was fascinating how we had to attempt the problem first, and then ask ourselves why or how did Ahmes get certain numbers. This sort of reverse-engineering and finding creative ways to achieve what the Egyptians did was the highlight of this project. It also goes to show how much math has progressed since then. What used to be a composition of unit fractions and a sophisticated guess-and-check method can now be achieved by simple algebra. 

        After learning about how regula falsi can be applied, I would like to use it as a tool in the classroom. Instead of relying on algebra, I can ask students to find different ways of reaching the answer, and then justifying why it works. This would benefit students who struggle with algebra by presenting them with another method of solving for variables. In addition, I find that this method of dealing with arithmetic series and progression to be more contextualized than giving students a formula and instructing them to memorize what each variable represents and how to use it. 

        Math education has become so accustomed to instrumental learning focused on the use of equations and algebra that sometimes students do not understand its purpose. Math has always stemmed from problem-solving, and this assignment allowed me to take a huge step back to rethink how I view math, as well as how my students may view it in school.