AP Calculus BC is the capstone mathematics course at Ellis—the highest a student can climb within the math world before leaving the Upper School. The class represents a culmination of all the mathematical knowledge students have developed over the course of their academic career thus far, and it even reveals connections to disciplines outside of math, such as physics and biology. Just as important as the class’ subject matter, though, is the classroom environment in which it’s taught. As any senior taking it will tell you, it is a strictly judgment-free zone.
AP Calculus BC (BC) is considered a college-level course, offering students the opportunity to challenge themselves through advanced math learning. The class explores the ideas, methods, and applications of differential and integral calculus, including topics such as parametric, polar, and vector functions and series. Once the full curriculum has been covered, students then dedicate six weeks to preparing for the AP exam, completing booklets of practice problems and refreshing their memories on course material from both BC and AP Calculus AB (a course prerequisite) that they should expect to encounter on the final test.
But despite the course’s rigor, the BC classroom atmosphere is noticeably relaxed. There are no raised hands or lectures, but rather open discussions, and oftentimes even jokes, between the students, their classmates, and their instructor, Upper School Mathematics Teacher Nathan Young. As students tackle the complex subject matter, stretching their critical thinking and problem-solving skills, they ask questions freely. They are taught to dispel their fear of making mistakes, which results in the students speaking more honestly about what they need help with and being more emphatic when working together to understand class concepts.
“I think it’s extremely important to offer these more challenging courses at Ellis in large part because we do have such small classes,” says Mr. Young. “There’s a great sense of camaraderie in the BC course—we joke around, we talk, we discuss. It’s perhaps not what you would expect within a rigorous math course, but this type of atmosphere makes it possible for the class to delve into this challenging material more deeply than they would in a traditional lecture hall, and to do so in a very supportive environment where we’re all learning together.”
Mr. Young continues, “I try to model how to make mistakes for my students. I want them to remember that no one is flawless. I’ll work through problems on the board in class and afterward I’ll ask my students to review my work and see if they spot any errors—sometimes they do, and that’s okay. Fostering that kind of environment where mistakes are normalized is vital, because it’s going to happen; these are complicated problems. I strive to take away the fear that can sometimes come with making mistakes because then the students are more likely to ask questions and be willing to try. This has really resonated with the students and we have greater discussions now. They’re comfortable with opening up, with being vulnerable and asking whatever’s on their minds, and I think that’s such a boon to them as learners.”
The proof of the power of banishing judgment from the BC classroom can be found in the students’ performance on their final exams. Recent studies have shown that the number of high school girls who take AP math exams nationally is now just about even with the number of boys (96 girls for every 100 boys as of 20191); however, there’s still a considerable gender gap when it comes to achieving high scores, especially when it comes to top courses like AP Calculus BC, Calculus AB, and Statistics2. But at Ellis, the majority of the students who have taken the AP Calculus BC exam in the past five years have achieved a score of 4 or 5, and this year’s BC students are looking toward their upcoming test with confidence, which plays a considerable role in exam performance. This empowered attitude can in part be contributed to the support they’ve been shown by their teacher and peers in class. It has also been instilled in them throughout the BC course as they’ve been encouraged to identify connections between mathematical concepts they’re currently studying, what they already know, and what they will learn in the future. Provided with a mental roadmap of how much they’ve already accomplished and the steps they can take to further grow their skills, students can establish a sense of familiarity with the subject matter and feel more prepared when solving problems independently.
“I think that, for women in particular, this class solidifies that they can do anything they set their mind to,” shares Mr. Young. “Every once in a while my Algebra II students will come into my classroom and see notes on the board left over from the BC students, and they’ll be intimidated by them. But I explain that, even though it looks complicated, with the proper application of studying and experimenting and asking questions, it’s all achievable. The seniors who are in this class really get this material, and eventually you can too. It looks complicated, but it’s the same principles you’re learning now, just taken a few steps further.”
The fusion of this challenging mathematical material with a learning environment that promotes collaboration, curiosity, and self-confidence provides for an academic experience that inspires a love of learning and can lead to success in higher education and future careers. While the BC course promotes the independence and resilience necessary to pursue even greater challenges beyond Ellis, it also reminds them that they aren’t alone; they can ask questions and work together with their teachers and fellow classmates (and eventually managers and colleagues) to build a more thorough understanding of whatever complex topic they may be tackling.
In future studies of advanced math course participation and achievement, if students like Ellis’ BC seniors have anything to do with it, not only will the gender gap have improved—it simply will not exist.
1. Bahar, A. K. (2021). Will We Ever Close the Gender Gap Among Top Mathematics Achievers? Analysis of Recent Trends by Race in Advanced Placement (AP) Exams. Journal for the Education of the Gifted, 44(4), 331–365. https://doi.org/10.1177/01623532211044540.
2. Bahar, Kadir. “Girls Still Fall Behind Boys in Top Scores for AP Math Exams.” The Conversation, The Conversation US, Inc., 14 Apr. 2022, https://theconversation.com/girls-still-fall-behind-boys-in-top-scores-for-ap-math-exams-174192.