They huddle together during SMART Lunch with their thick blue books cracked open, whispering about mysterious topics such as integrals and Riemann sums. Each night, they spend hours alone in their rooms, poring over pages upon pages of Taylor polynomials and power series. Yes, these devoted students are the brave souls who have dared to venture into the study of calculus.
AP Calculus: the most infamous math class at Leesville. Also, according to the Oxford Dictionary: “the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences.” In short, calculus is an enigmatic, complicated subject that only a small group of Leesville students learn each year.
After completing Math 3 Honors, Leesville students either progress to Advanced Functions and Modeling (AFM) or Pre-Calculus Honors. Those who choose the latter have the opportunity to, after passing Pre-Calculus, advance to AP Calculus. Between 60 and 90 students at Leesville take AP Calculus every year. Some of those students take only AP Calculus AB, equivalent to Calculus 1 at the college level, but the majority take both AP Calculus AB and AP Calculus BC, corresponding with the college-level course Calculus 2, all in one year.
That means that in any given school year, about three percent of Leesville students take AP Calculus, only amplifying the obscure nature of the course.
Sophie Cho, Leesville senior, and Arijit Jatkar, a junior at Leesville, completed both AP Calculus AB and AP Calculus BC during the 2017–2018 school year. For them, enrolling in AP Calculus seemed to happen on its own; they each had expected to take the course in high school.
“I just knew…going into high school that I was going to take [math courses] up to calculus.…I pushed myself to do it,” said Cho.
However, Cho and Jatkar gained much more from AP Calculus than the knowledge of how to solve related rates questions. As is the case with many calculus students, the course became more of a journey for them, and along the way, they learned not only the proper method of utilizing L’Hôpital’s Rule but also about themselves.
Prior to AP Calculus, both Cho and Jatkar found math classes to be simple courses that required little-to-no studying.
“Before I took calculus, math was always something that…was always…very easy and not challenging at all,” Jatkar said.
But AP Calculus differs from those previous math courses. Students find the complicated concepts more difficult to grasp; thus, Cho and Jatkar were in for a shock when it came to the amount of studying that AP Calculus requires. At first, Jatkar struggled in AP Calculus—the first math class that had ever challenged him. He only needed to listen to his teachers’ lectures in math classes before calculus to score well on assessments, but he found that to succeed in AP Calculus, he needed to actively review the material.
“Once you get to calc., you have to study, and you have to be sure that you do understand concepts that maybe aren’t naturally in your head,” said Jatkar. “Once [AP Calculus] AB came along, and I found out I did have to study,…it was a change of perspective for math overall.”
Keysha Mayfield, Leesville’s sole AP Calculus BC teacher, has taught struggling calculus students, including those who are floundering in a math course for the first time. She says that a lack of understanding of the material and the need for an increase in studying test those students and that they all respond differently to adversities.
“You have kids who try to just throw in the towel and give up. Some of those kids will just drop the class or accept grades that are below what they are capable of,” Mayfield said. “On the other end of the spectrum, I’ve seen kids who have really risen to the challenge [of calculus].”
Initially, during AP Calculus AB, Cho did not embrace the rigors of calculus by not devoting the necessary time to the course. She instead allocated more time to her other classes and used a popular online resource, Slader.com, to help her quickly complete her AP Calculus homework.
“I just kind of went through [AP Calculus AB], like, I didn’t really think about it that much.…I wasn’t actively, you know, trying to learn anything,” said Cho. “I did struggle in calculus, and I think it was partially…my fault, basically, because…I didn’t give it enough attention.”
After a disappointing grade in her first semester of AP Calculus, Cho turned her work ethic around for AP Calculus BC. Thanks to the challenge of calculus, she learned how to work hard despite previous frustrations, and that extra effort paid off at the end of the course.
“Second semester is definitely when I, like, started to study every night for calculus.…[I learned] to just chug through it.…With effort, like, you can really accomplish anything,” Cho said. “[Calculus] taught me how to study. It taught me how to accept and deal with failure and ultimately just overcome it and to learn.”
Furthermore, through AP Calculus, students strengthen certain abilities in ways that they themselves do not always recognize. For example, Mayfield believes that students hone their problem-solving abilities while studying calculus because the class forces students to apply their knowledge to scenarios that they have not previously encountered.
“There’s a lot of higher-level thinking skills involved [in AP Calculus], and not just in terms of understanding the mathematics, but understanding how to approach a difficult situation, so I think problem-solving is one of the biggest things that students can take away from this course,” said Mayfield.
Besides mastering practical problem-solving skills, students in AP Calculus likewise discover more about themselves. Because of calculus, Jatkar realized that he could increase his effort when it came to math.
“I learned that my work ethic wasn’t very good, and, again, honestly, it didn’t need to be in previous math classes, but once calculus came along, I learned that I have to learn to work in math and to learn to practice math prior to a test,” said Jatkar.
Like it did for Jatkar, Calculus taught Cho that she has the potential to apply herself. Additionally, though AP Calculus reinforces some students’ love for math, it prompted Cho to realize that she does not want to continue to study math beyond high school.
“I learned that math is not one of my interests through calculus and that I don’t want to pursue math in the future.…[and] that also I can work hard and that, like, there is a part of that in me,” Cho said.
As a calculus teacher, Mayfield witnesses firsthand the changes that her students undergo throughout the course. Since AP Calculus is often a class that challenges students for the first time in math, these students must adapt to and rebound from any setbacks.
“Students learn that they are capable of much more than they thought [in calculus],” said Mayfield. “They get to learn more about who they are as a person, how they react when things are challenging.”
At the close of AP Calculus BC, Mayfield asks her students a seemingly simple question: what is calculus? In response to this inquiry, she does not want them to define calculus, but she wants them to elaborate on their journey through calculus and what calculus means to them. Through the “What is Calculus?” assignment, students discover that they do not just learn math during AP Calculus. After all, teaching as a whole is not singularly about teaching the material of the class—teachers want their students to grow as people, too.
“I see a lot of kids have lightbulb moments [while completing the ‘What is Calculus?’ assignment]. The lightbulb goes off. They suddenly realize a little bit more about what they learned [in AP Calculus], not just mathematically, but what they learned as a person, what they learned about themselves, what they learned about their capabilities.…[They realize] what their journey was, what their experience was, because it’s different for everyone,” Mayfield said. “I do this assignment really to help kids kind of come a little more full-circle with the course and to help them realize that it’s about more than just the mathematics.”
Mayfield’s students enjoy reflecting on their calculus journeys just as much as she enjoys reading their responses to her question. Cho liked the assignment, and, true to its purpose, it opened her eyes to how AP Calculus shaped her.
“I reflected on my whole math career, and…it just helped me to realize what I took away from calculus and how…transformative of a class it was,” said Cho.
Through his “What is Calculus?” assignment, Jatkar drew a connection between what calculus literally means and what calculus means to him. Parallel to how the study of calculus involves the exploration of changes, AP Calculus bettered Jatkar.
“For me, the ‘What is Calculus?’ assignment was a definition of change, and while that’s the official definition of calculus in terms of its math aspect, it was a definition of change for me in which I changed and my work ethic changed,” Jatkar said.
Despite the rigorous nature of AP Calculus, both Jatkar and Cho have decided that calculus was worth it due to the transformations that they underwent and what they gained, both thinking skills and self-understanding. They recommend AP Calculus to any student who believes that he or she can rise to the challenge of the higher-level concepts and the grueling workload. Mayfield agrees that calculus ultimately benefits its students.
“[AP Calculus] is a tough course. It requires a lot of work and requires you to kind of reevaluate how you’ve done math in the past, but in the end, I think it’s a very rewarding course,” said Mayfield.
Students who complete both AP Calculus AB and AP Calculus BC learn much more than they expect. Besides just mastering mathematical concepts, they grow in their problem-solving skills while adjusting to the adversities present in calculus. So, for those courageous individuals who have delved into the study of calculus, it’s not just about the shell method and Lagrange error bounds; it’s about the journey.