The Acceleration Equation

For most Stuyvesant students, their math coursework progresses alongside their grade level. However, some students enter Stuyvesant having already completed several years of the high school math curriculum. For these students, courses such as Multivariable Calculus and Linear Algebra, which can include students from all four grades, can become part of their freshman schedules. Their experiences reveal how students become so far ahead in mathematics, why the subject lends itself to acceleration, and what being ahead means once it becomes routine. 

Freshman Landon Faigle took Algebra I in fourth grade, eventually reaching AP Calculus BC in eighth grade. Freshman Daniel Marakov also reached AP Calculus BC before entering Stuyvesant, while junior Michael Shakhnovich, now in Differential Equations, took Multivariable Calculus as a freshman. Their paths to advanced mathematics, however, were far from identical. 

Faigle’s mathematical acceleration was largely shaped by his schooling. He does not view his progression as an intentional attempt to move through the curriculum as quickly as possible. After finding his elementary school in Boston too easy, his parents transferred him to Speyer Legacy School in New York City, where he encountered a much more advanced level of math instruction. “They propelled me not at a faster pace but with deep coursework,” Faigle said. His progression was less a race through the curriculum than a response to increasingly challenging material. 

Marakov’s path involved more independent exploration. During the COVID-19 pandemic, he began self-studying through resources like Beast Academy and Art of Problem Solving, later attending Math-M-Addicts and spending three summers at MathPath. These are just some of the many prestigious, elite mathematics education programs that focus on honing problem solving skills. At Speyer, he eventually took AP Calculus BC with five other eighth graders. Marakov enjoyed difficult problems and wanted classmates who were equally interested in math. “I really wanted to attend Stuyvesant because I would have the opportunity to continue taking advanced math courses and to have peers just as excited about math as I am,” Marakov said. 

Shakhnovich followed a different path. He took Algebra I in fourth grade at BASIS Independent Brooklyn and eventually took Multivariable Calculus as a freshman at Stuyvesant after completing AP Calculus BC. His former school generally discouraged students from accelerating too far. Although Shakhnovich wanted to take AP Calculus BC and Multivariable Calculus earlier, the school did not allow him to progress at that pace.

These three different paths reflect a larger feature of mathematics: its relatively defined sequence. Faigle sees each level as building naturally on the one before it. “No matter your age, if you master each layer, you can usually master the next,” he explained. Unlike subjects such as history or English, where studying one period does not necessarily prepare a student for another, mathematics has clearer prerequisites that can make readiness easier to demonstrate. 

Shakhnovich points to another reason: mastery in mathematics can be demonstrated relatively clearly. In order to advance, students need some way to show that they have already learned the material and are prepared to move forward. “To get far ahead in a subject, you need some way to demonstrate that you already know the material and are ready for more advanced work,” Shakhnovich said. 

The structure of the math curriculum also creates an unusual classroom dynamic. Because courses such as Multivariable Calculus and Linear Algebra can include students from all four grades, students may find themselves learning alongside classmates several years older or younger than them.

For Faigle, the age difference is noticeable. Although he had generally studied mathematics with students around his own age or slightly older, entering a class with seniors was a new experience. “It’s really unbelievable to be with seniors, but I love it,” Faigle said. While the age difference initially felt unusual, Faigle said that he enjoyed learning alongside older students. In particular, seeing seniors remain relatively relaxed despite the pressures of college applications gave him a different perspective on the challenges of high school.

Shakhnovich, meanwhile, had already become accustomed to this type of classroom before entering Stuyvesant. He took mathematics classes with high school seniors while he was still in middle school, making the age differences at Stuyvesant less unusual to him. “I got used to being ahead in math in elementary school, so it didn’t feel unusual at all,” Shakhnovich said.

Similarly, the age difference does not make the classroom unusual for Marakov. Having already participated in math programs with students of different ages, he believes that age does not necessarily need to determine who learns together. “Math classes should be grouped around what people are trying to learn rather than their age,” Marakov said. 

The same emphasis on learning rather than age shapes Marakov’s view of acceleration. “It seems plausible that someone could assume moving ahead means rushing through material and sacrificing depth. This, however, has not been my experience,” he said. In fact, he finds that advanced mathematics can deepen his understanding of earlier concepts. A proof that initially seems to rely on an unexplained “trick,” he explained, can become more intuitive once he learns the mathematics behind it and sees how the idea can be generalized. 

Faigle’s experience also complicates the idea that acceleration is necessarily driven by competition. Although some students may feel pressure from parents or schools, he described his own progression as largely a product of his interest in mathematics. “I went with the flow, and somehow ended up here,” Faigle said. He described solving mathematical problems as a way to relax, making his path through the curriculum feel more like a continuation of something he genuinely enjoys than a race.

Shakhnovich’s experience, however, provides a different perspective on the relationship between acceleration and preparation. Although he believes students should be able to advance when they are prepared, he has also found that being ahead does not always mean having stronger mathematical foundations. “I learned that being ahead is not always a good thing because foundations are just as important as advanced work,” he said. Although he had already completed calculus before arriving at Stuyvesant, he later found the school’s prerequisite courses more rigorous and believed taking them would have given him a stronger foundation. 

For students who reach advanced mathematics, moving through the sequence can also change how they understand the subject and where they see it applying beyond the classroom. After learning about the roles of multivariable calculus and linear algebra in artificial intelligence, Faigle began applying the mathematics he had learned to his own coding projects. “Everyone should have the opportunity to see how math isn’t just a random game of numbers that dance around equals signs,” Faigle said.

For Shakhnovich, the effects of acceleration have become less obvious with time. He is currently taking Differential Equations as a junior and plans to take AP Statistics as a senior, but he remains uncertain about pursuing mathematics professionally. As a freshman, he remembers classmates approaching him to ask whether he was really taking Multivariable Calculus. Now, he said, being ahead has had little effect on his overall experience at Stuyvesant. What once made him stand out has become part of his academic routine. 

Importantly, Stuyvesant’s Math Team offers another form of acceleration outside the standard course sequence. Meeting daily during the first period and after school, the students that make up the highly successful Stuyvesant Math Team focus on developing problem-solving skills rather than progressing through a prescribed curriculum. Junior Shanya Tissera, who’s been part of the team since her freshman year, explained, “[Even though] the complexity of the raw computation involved is usually simple, the problems make you think a lot and reason far more than you’d have to in a normal, even advanced, math class.” She also described how Math Team has simply a different kind of dynamic than in a standard class. “Math Team teaches you to think logically and creatively [...] There’s also the “team” aspect that you don’t get in normal math classes. The people I met in Math Team are some of my best friends,” she said.  

These students reached advanced mathematics in very different ways, and none see being ahead in quite the same way. Faigle describes it as a natural extension of his interest in mathematics, while Marakov sees advancement as a way to keep learning alongside students who share his enthusiasm. Shakhnovich’s experience, meanwhile, shows that moving quickly is not always the same as moving well; the foundation built along the way can shape how useful that acceleration ultimately becomes. 

For Marakov, advancing through mathematics has not made the subject feel smaller or more finite. Instead, each new layer has revealed more beyond it. “The more math you learn, the more you realize there is a lot more,” he said. 

At Stuyvesant, where freshmen can enter classrooms with seniors and post-Calculus courses can span all four grades, being ahead is not simply about finishing the curriculum faster. It means reaching the next layer while there is still more to discover—and having the opportunity to decide where that distance takes you.