4 Lessons I Learned From My Senior Math Project
A valuable experience
Over the last few months, I have been exposed to an introduction in linear algebra, teaching myself the basics. It was for a project for my math class at school, which culminated in me giving my classmates an in-person lecture. Since linear algebra was a completely new topic to me, I did struggle from time to time with the mechanics and the reasoning behind the math, but in the end, I felt like I had a good grasp of all the topics I taught. Today, I want to reflect on a few lessons that I learned about math and myself as a result of this experience.
Linear algebra isn’t exactly easy. Even though I just covered the beginning parts of the topic, I needed to think a lot about what was really going on with the math, especially when I got to eigenvectors. I was expecting it to be hard. So, when it came down to it, I just had to read over the text more or consult extra online videos for help. In the end, this endurance proved to be key; as I mentioned before, certain topics within linear algebra took longer to understand. I needed to stay focused on understanding the math behind the mechanics, and if that meant looking over the work multiple times, I was ready to do so. As a result, I felt like the experience taught me both math and life skills. As I make the transition into college, I know the math will get harder, so I will make sure to keep hammering away at different concepts and problems that give me issues.
2. Math is Visual
As somebody who has been involved with numbers inside and outside of school for as long as I can remember, I have to say that I didn’t always think very visually of math. In lower school and middle school, I mainly just thought about my arithmetic, my equations, and my algebraic skills (there were a few times where I used graphs). That was enough for me to survive up until high school. In 9th grade, I learned about geometry, and that opened me up to a bit of what it meant to think visually. However, I think I really started thinking in a more visual manner throughout the second half of high school. When I learned about related rates in calculus, I would always draw about the shapes and rates that were involved. With optimization, whether it be the area of a region or the volume of box, I would also always draw about the shapes and label specific measurements. In my head, I would then think about how the regions/shapes would change over time.
Similarly, I found that linear algebra stimulated the visual part of my math brain. Even at the very basic level with vectors, I made sure to think about what they looked like in space. With vector scaling and addition, I also visualized how vectors added or subtracted from each other (the method is in a previous article), or how a vector’s length changed with varying scalars. One of my favorite concepts from my early involvement with linear algebra was span. How much “space” can a combination of vectors of any scaling cover? Well as long as the two vectors aren’t the same or on the same line, they can cover everything! I imagined all the different combinations of vectors in the air, swirling around and hitting all of the points in this imaginary “space.” I then imagined two vectors on the same line. Well, no matter how you scale or add them, they’ll always end up on the same, original line. If you think about it in your mind, this fact becomes clear.
3. Teaching is Fun!
Now I’m not sure if I’m actually going to go into teaching in the future, but I liked standing up in front of the class and sharing the knowledge I learned. I had prepared extensively before I gave my presentation, creating a big lesson plan and a big packet of exercise problems for the class to work on. I was a tiny bit nervous in the beginning, but as I settled into it, I became more and more relaxed. I think I liked my teaching experience because it allowed me to talk my way through what I was thinking and to see if my work was logical or coherent. When I got a question from a classmate, I tried my best to answer in the best way I could so that everybody would be able to understand. I also must say, standing in front of the class and operating on the whiteboard is immensely different from sitting in one of the seats. I got to see everybody from a different physical perspective. But, I pushed through the topics, and I loved my experience writing out the math and speaking my thoughts. It was very comfortable, and I think my classmates ended up learning as well.
4. Embrace Learning
As somebody who already enjoyed math and numbers, this came naturally to me. I knew that linear algebra had ties with computer science, another one of my interests, so I made sure to choose this topic when we had to select our presentation. I wanted to give myself a challenge while also learning about something that truly interested me. Linear algebra was the perfect choice. When I got down to work on my project, none of it felt like I was being forced to finish. Of course there was a deadline that I had to meet, but I was able to work on sections of my presentation without feeling stressed or bored. I felt that I truly appreciated doing independent work and digging deep into an unknown territory of math. Because I liked the work I was doing, I was able to embrace the learning process, even if it meant initial failure. As I move forward, I will keep this mindset with me. One of my favorite movies is 3 Idiots, a Bollywood film about education and passion. It heavily changed my view about learning, and I highly recommend the movie, as it contains real lessons. It emphasizes the power of passion when it comes to learning and how we should take in all the knowledge around us. I further learned to embrace all the difficulties of learning math at the conclusion of this project.
Overall, I think that this math project was one of my favorite school-related pieces of work. Not only was I able to gain a deeper understanding of linear algebra material, I was also able to dive deeper into teaching. As mentioned before, I will take not only the knowledge I learned from this experience, but also the lessons gained along the way as I make the transition into the next big part of my life. Thank you!