Dolphins and the Intermediate Value Theorem

“A dolphin that wants

To leap out and breathe fresh air

Must touch surface first.”

This is a poem that I recently wrote for AP Calculus. When I read the description of the assignment, I couldn’t help but smile. I had to “write two (2) original math-themed haiku” based on “mathematical ideas from our course.” I eventually settled on the Intermediate Value Theorem, a powerful theorem that can be applied to continuous functions, as my subject.

So far, my teacher this year has encouraged more creative assignments, such as writing about a mathematical observation, taking a photo that reveals continuity or differentiability in the real world, and composing poems. However, in previous math classes at Stuyvesant, the homework placed a huge emphasis on reviewing material and solving problems. This created the impression that math was exclusively serious, with no time for freedom and experimentation.

It is easy to feel disconnected from our math classes because the focus is often placed primarily on problem-solving and mathematical rigor. As a result, we often lose sight of the truly beautiful aspects of math, and we forget to seek math in our surroundings. I’m not just referring to real-world problems that involve calculating the amount of money gained from an investment. A few weeks ago, I noticed that the sky’s color changes continuously when the sun sets. My classmate pointed out that the top of their shower curtains resembles a sinusoid. Similarly, my class this year had a serious 20-minute conversation about the validity of the phrase “instantaneous rate.” Creative assignments help people see math in a genuinely inspiring, culturally relevant way, and they make us want to learn more. Noticing cusps in the pattern created by melting snow gives new meaning to a subject that can, at times, feel rote and empty.

My first experience with a math class that allowed me to freely explore new concepts came freshman year. Math Team, a class that I initially regarded with apprehension, became my favorite period of the day. We were always learning something new, and whether the lesson involved encoding information in arrangements of coins or working through the basics of graph theory, it challenged me to constantly adapt the way I thought about math. Most of the class was devoted to experimentation, and there were no consequences for wrong answers. It became much easier to learn because the mindset of the class was drastically different. At the end of the day, the goal was not to check a series of boxes and learn a set of procedures; we were there to expand our conceptual understanding and see math in a new light.

In order to truly engage their students, math teachers need to change the message that their classes send by encouraging exploration. More often than not, success in a math class is measured solely by test scores and problems solved. This discourages students who are not natural test takers and prevents them from enjoying math. That’s not to say that tests aren’t important: at the end of the day, students need to be able to use the mathematical tools that they’ve learned. However, focusing equally on the creative aspects of math can inspire students in a way that tests never achieve on their own. In fact, research has shown that using creative teaching methods not only reduces mathematical anxiety but also facilitates up to a 57 percent improvement in test scores. Creative and traditional teaching methods can be used in conjunction to teach math effectively. 

In essence, I love creative assignments because they foster a healthy mindset. They allow students to approach math in their own way, which ultimately leads to deeper understanding and enjoyment. Teachers should increase the flexibility of math classes because it ultimately makes them better for everyone. This doesn’t require redesigning the entire curriculum: every teacher can make a difference through small adjustments in the way they present the material. They can encourage students to work in groups and derive formulas on their own, prioritizing the thinking process over memorization. They can entertain students’ incorrect ideas and have genuine, thoughtful discussions about suggestions that might seem silly. Most importantly, teachers can encourage their students to discover math in the world around them. After all, I don’t know if I’ll remember Brahmagupta’s formula in thirty years, but I am confident that I will think about calculus every time I see a sunset.