Featured Course

Calculus

For a lot of students, calculus is like the broccoli of the curricular dinner plate. Some people love it — can’t get enough. And for others, well…it’s not their favorite but they take it anyway because they know it’s good for them. By the time they graduate, well over half of CSW students will have taken calculus — a statistic indicative of the importance of, and interest in, this sometimes overshadowed course.

The CSW “Calculus AB” program is taught over the course of three consecutive six-week mods. The first series of the sequence covers differential calculus and includes the study of limits, continuity, and derivatives of algebraic, transcendental, and trigonometric functions. The second section, Integration, covers definite integrals and areas, the fundamental theorems of calculus, techniques of integration, computation of volumes, arc length, average of a function, separable differential equations and slope fields and applications to physics, chemistry, and engineering. After “Calculus AB,” students have the option of pursuing “Calculus C” — a study of sequences, series, power series, Taylor and Maclaurin series, parametric equations, and polar coordinates — or even “Multivariable Calculus,” a rarity at the high-school level.

There’s no denying it — calculus is challenging. But according to CSW Math Department Chair Marvin Gutierrez, that’s kind of the point.

“We’re proud of the rigor and challenge our classes provide,” says Marvin. “When faced with a difficult math problem, too many people want to give up. But at CSW, we don’t let you do that. This teaches students important life skills like persistence, self-discipline, maturity, and character.” When students feel confused or frustrated, Math Department faculty employ a number of strategies to help navigate them through. First, it is crucial to convey to students that in the beginning, “not knowing” is okay. Research, contemplation, and exploration, whether it be through meetings with the teacher, YouTube videos, or an exercise break, are all natural parts of the process.

Visit math teacher Evelina Galper’s calculus course webpage and you’ll find a friendly reminder that when it comes to calculus, a growth mindset is a must. “Try to substitute ‘I don’t understand this’ with ‘I don’t understand this yet,’” she suggests, and “Try to substitute ‘this is too hard’ with ‘this might take a long time.’”

In addition, faculty make a concerted effort to familiarize students with both the mechanical and conceptual aspects of mathematical work. In order to effectively tackle a mathematical problem, students must first develop a framework for processing the material they are covering and understanding its relationship to what they’ve already learned and known to be true.

Finally, CSW’s Math Department makes a point of acknowledging and celebrating the sheer beauty of mathematics. The work that goes into solving a calculus problem can be messy, but the solution, once achieved, is uniquely elegant, orderly, and precise.

“Math is so interesting because there’s an element of absolute correctness that doesn’t always exist in other disciplines,” shares multivariable calculus student David Yu ’20, “and there is something beautiful about that.”

While most coursework is done with a pencil and paper, budding calculus scholars Winter O'Brien '20 and Maire Claire DuBard '21 complete a matching activity with function and derivative graphs.

Math teacher Julia Cornue Gruenewald goes over homework with Lev Goldman '20 and Mia Canning '20.

at CSW are pushed to type out the answers to their problem sets, allowing them the chance to produce and admire clear, polished, aesthetically pleasing work. What’s more, each class regularly contributes mathematical artwork to the school’s End-of-Mod Show, a modly celebration of student creativity at CSW.

“When people think of CSW, they don’t

generally think of math,” Marvin explains, “but I can confidently say that we have one of the strongest math programs in the country, and it’s time people knew that.”