Abstract
It is often debated if mathematics is invented or discovered. If we are defining the laws of nature by the prowess of our reason or if we are uncovering hidden truths of our universe. Some of the greatest minds in the world have pondered this question for generations. However, in this paper, I will not answer that question. I would like in this document to discuss how my experience as a teacher, mentee and employee informed my methodology of helping students pursue the good, true, and beautiful through the lens of mathematics.
Teaching Experience
During my time as an undergraduate I worked as a teachers assistant for 2.5 years for a class called Quantitative Reasoning at Biola University. I spent many hours grading students assignments and corrected homework. My last semester I was a TA for about 80 students and had 5 sections to keep track of. I also held my own office hours for 4 hours a week where I would respond to students questions and work problems out on the board for them to see. Quantitative Reasoning was a non-math major course so many students had a strong aversion to mathematics. This cause a lot of students to have lack of motivation, so much of my project was trying to get students interested in the material they were studying. One way that I helped motivate students was choose data sets that correlated with their major to work with for their final project. It can be easy for students to feel like they get lost in the system and helping run a class where lots of students struggled with math, I saw firsthand what it looked like for some students grades to plummet. If no one came into my office hours on a particular day I would look over all my sections and see if any students were consistently not submitting assignments and email them directly to ask and see if they needed help. Sometimes the student had just forgotten to drop the class, but occasionally they had some emergency that they had not communicated to the professor. I worked to helped put them in contact with the Professor and offer any assistance if they needed it. This is a practice that I learned as a TA and want to continue as I teach my own sections. I also worked as a private tutor and drove to high school students houses and help them with homework. Having a personal connection with one on one meetings showed me that a part of teaching includes a personal component and each teacher has their own unique twist on how they like to try to get students to remember things. I have a deep interest in the history of mathematics and on numerous occasions I have told my students stories about the secrets behind the mathematicians who discover these mathematical truths. Some of my favorites include how Pythagoras not only invented the Pythagorean theorem, but he also religiously worshiped triangles believing it to be the perfect shape. How Descartes who invented the Cartesian coordinate system is known as the Father of modern philosophy because of his complete deconstruction of Aristotle’s Physics. Or my personal favorite how Pedro Pascal who discovered Pascal’s triangle often did mathematics intoxicated claiming, “Too much and too little wine. Give him none, he cannot find truth; give him too much, the same.” All of these things are in effort for them to have a clearer picture of the person behind these theorems than can appear so dry at times. It has been said that expertise in a subject is only achieved by being able to communicate thoughts to distinguished masters, as well to the most curious of first graders. In other words, that teaching should not only about explaining reasoning to people who are already proficient, but also being able to break that same idea into small enough pieces that the concept can be learned by someone who is entirely new to the subject. However, I am not someone who just believes in these things, but also acts on them. This summer, I decided to challenge myself by working at a tutoring company primarily for children ages 8 – 13. As I worked through countless workbooks with my students in groups of 2-5, I realized how much of the work book revolved around teaching methodology, but left the mathematical concepts behind the scenes. In teaching, it is essential that students understand not just how to get the right answer, but to use critical thinking skills to grasp mathematical logic. An example of this is when I tried to do this was when one of the chapters was about prime numbers. Instead of just simply listing out the first prime numbers, which would have been sufficient to solve the problem, I took part of the lesson to explain factor trees as well as go over the formal definition of prime. After this, I explained that one of the current mathematical unknowns is that there is no formal way to predict prime numbers. As the students were given background knowledge on what they were learning as well as a glimpse into the modern application of the field of mathematics, students will better be able to understand mathematical logic.
Teaching Goals
My fields of interest are curriculum design, history of mathematics, philosophy of education and low dimensional topology. I am currently working on my masters in mathematics at University of California Riverside and I plan to TA for the summer courses in 2022. Teaching at a University is my current goal because I want to give back everything that the educational community gave to me.
