Lesson on Optimization: Using Critical Thinking Skills in the Real World by Shayna

Lesson on Optimization: Using Critical Thinking Skills in the Real World by Shayna - July 2026 Scholarship Essay

As I ventured into higher level mathematics, I used to look for immediate clarity—that sudden "aha!" moment where a complex concept became instantly clear. However, with calculus and especially its underling topic of optimization, my approach to learning changed. Optimization problems, like solving for the maximum volume of a box or the minimum length of wire needed to connect two poles, initially felt like random puzzles, satisfying to solve but of little importance. That all changed when I began to notice this concept showing up in the everyday life.

As part of my daily travels, I started looking at the tools and products we take for granted through a lens of calculus. I realized that the packaging of every product on a supermarket shelf represented a physical example to an optimization problem: minimizing cardboard material costs while maximizing volume. Utility poles located alongside the highway were not randomly placed, but rather were placed to ensure minimal use and minimum strain on the wires. Looking at things from a mathematical perspective made me understand the importance of developing critical thinking skills. After learning optimization, I noticed that my brain liked to use mathematical reasoning to make this simpler or easier—and naturally, even without the volume formulas, it did. My brain rounded 26 apples to 30 and estimated how long it would take for me to walk somewhere versus drive. When I thought math was the major complication, it was the solution. I saw that I could train myself to work on chaotic situations with multiple constraints and variables and use my critical thinking skills to think of the best pathway.

Solving optimization problems also required me to watch my classmates present their work on the board—and pushed me to share my own processes despite my nervousness. I learned that critical thinking isn't a solitary practice. The skill is sharpened when we challenge our own mental thinking by evaluating how others think through a problem.

Ultimately, this math lesson taught me that critical thinking is a skill that can be developed through practice and looking through a less narrow lens. There are no effortless shortcuts to mastering most concepts—unlike what math can do when a business uses it to cut costs or adjust prices in the most optimal way.

Overall the academic challenges I encountered challenged my confidence. When I once equated my self esteem to a correct answer, I now tie it to the work I did to get there. I must hold myself accountable, recognizing that thousands of students face the daunting challenge of finding the volume of a solid perpendicular to the y-axis, but the defining line between an "A" and an "F" is the willingness to take personal responsibility for one's own shortcomings.

This mental toughness and critical thinking skill have prepared me for the next chapter of my education. This upcoming school year, I will be tackling a rigorous schedule that includes biology, biology lab, and calculus. By discovering that any complex system can be mastered through critical analysis and sustained effort, I am starting school again not just as a student ready to pass a class, but as a future professional equipped to solve real-world problems.