I have never had to write an essay like this before and I have struggled with it since I first looked at the prompt. I've really felt like I have had no clue where to start or what this essay is supposed to ultimately look like.
Please offer any insight you might have.
My essay:
I am applying to the College of Natural Sciences Mathematics Department because I ultimately want to teach all levels of secondary school mathematics. I entered high school with the self-fulfilling mentality that I was not good at math. My self imposed mathematical handicap set the tone for all of my high school academics. As a result, I barely made it to graduation. Following graduation and 2 directionless semesters at Houston Community College I resigned myself to an unexceptional blue-collar life. I spent five years working in land survey and design. It was during that time that I found cycling.
Spending most of my childhood and adolescence in a relatively sedentary lifestyle, cycling became an exciting and fulfilling activity. It was hard, and I wasn't very good at it, but I knew that with time and dedication I could get better. And I did. After a few months I started to race, and my fitness and ability improved by leaps and bounds. For the first time in my life I was motivated to really succeed. I set goals for myself and achieved them one by one. As I achieved my goals I set new ones and I knew I could meet these as well. I developed a self-confidence that I had never before had. This was a turning point in my life. I was no longer willing to accept inadequacy. I developed a powerful motivation to improve myself.
As I gained seniority at my job I became ever more aware that without an education I would inevitably hit a glass ceiling in my field. I wanted more. I wanted to be the boss, but I knew that all the degrees related to surveying and engineering would require extensive coursework in math. I knew it would be hard, but I told myself that if I worked hard enough I just might be able to get through it. I enrolled at Austin Community College, full time with the intention of transferring into an engineering program and ultimately earning a professional surveyor's license.
I registered for trigonometry with some anxiety. On the first day of class I went to my professor's office and explained to him my history. That I've never been good at math and that I might not succeed in his class. He candidly explained to me that no one is bad at math, but that many educators are bad at teaching it. He told me that with hard work and dedication anyone can get good at math. I will never forget that conversation, because I whole-heartedly agree with his assertion. His class was hard, but I did well, and I actually enjoyed the coursework. I have always enjoyed puzzles and problem solving so shouldn't have been surprised by my fascination with math. I went on to pre-calculus and calculus and excelled in both.
My entire academic life I had viewed calculus as the highest form of math, an unreachable level of academia. I spent hours at coffee shops studying formulas, theorems and their proofs. Outside of class I often found myself helping classmates with their studies. I really liked being able to help and explain the coursework in a way that let them better understand it. What was even more satisfying to me was being told by more than one of my classmates that I explained things in a way that made it easy to understand. By the end of the semester I knew that teaching was my calling.
Looking back to high school I consider myself to be quite lucky. Had I not found something like cycling that allowed me to develop a strong sense of self-confidence I might have never considered pursuing my education. Choosing not to go to college does not mean a person will lead an unfulfilling life. A high school student choosing not to go to college because they believe they "can't do it" is unacceptable. All students should graduate from high school with a sense of the endless possibility the world has to offer. I believe that too many high school students graduate seeing more closed doors than open ones. I know that with the resources made available to me from the University of Texas and the UTeach institute that I can not only become a great math teacher, but also help my students see the endless possibilities that are out there.
The essay is solid, because it has the advantage of sounding sincere. You are speaking candidly and well about your experiences, illustrating your points with specific details and examples. I wouldn't change much here, because you don't want to lose that tone. I would, however, get rid of the quotes and and a transition word to the following sentence:
"A high school student choosing not to go to college because they believe they can't do it is unacceptable, though "
