From self-taught teenager to peer tutor
How many high schoolers can skip calculus and linear algebra because they’re already studying college-level math? Graham Bertele is one of them thanks to his own deep dive into MIT Open Learning’s online educational resources. Now the 17-year-old is helping his classmates see that they can stretch their potential, too.
“Two summers ago, I found Gilbert Strang’s 18.06 (Linear Algebra) playlist and loved it,” Bertele says. “Since then, I haven’t stopped learning.”
Linear Algebra is just one of thousands of free online courses and resources offered by MIT OpenCourseWare, part of Open Learning.
“The open access to the course materials and video lectures is invaluable,” Bertele says.
His independent learning didn’t just help him test out of his school’s highest-level math requirements; it also inspired him to launch an after-school program with his sister to tutor his classmates.
“In math, I’m under the very strong belief that anyone can learn or understand anything if it’s explained well enough,” Bertele says. “If you are someone who is struggling with understanding something, then it’s not a sign that you won’t ever be able to do it. Try going online and seeing if you can find different explanations for it.”
Linear algebra, he says, has an intimidating reputation at Bertele’s school since it’s the highest-level math course on the books. Determined to change that, Bertele breaks the subject down with clear language in his after school program that he runs with his sister, swapping intimidating terminology for explanations that invite students of all grade levels to engage with concepts usually reserved for college classrooms.
“That’s probably one of my favorite memories,” Bertele says.
Diving into advanced math
Bertele’s inspiration to pursue higher-level math came in eighth grade when another student got on an advanced track in calculus.
“Before that, I only knew calculus existed because of TV shows,” Bertele says. “I wanted to see if I could learn it myself, too.”
Early on, Bertele found a website about integrals and completed problems through the guess and check method before exploring math content on YouTube. The summer before his junior year, he connected with a local professor who recommended textbooks and other educational resources including MIT OpenCourseWare.
OpenCourseWare offers free online educational resources from more than 2,500 MIT courses, available to anyone in the world.
“It was so helpful because I hadn’t really had that kind of structured learning before,” he says, comparing the comprehensive 18.06 (Linear Algebra) curriculum to his prior ad hoc approach depending on what he found interesting in the moment.
The teaching style behind Strang’s course — alongside that of 18.01 (Calculus I: Single Variable Calculus), 18.02 (Multivariable Calculus), 18.100A (Real Analysis), and 18.102 (Introduction to Functional Analysis) — resonated for Bertele in a way that textbooks alone couldn’t.
Since Bertele was studying alone without classmates, he says the “lectures are very helpful for me because they show all those intermediary steps and focus on what’s really important.”
Bertele appreciates how Strang and other MIT instructors, like Casey Rodriguez, start with an overview to show where the lesson is going before drilling down into a rigorous new proof or major idea. Their lectures helped him build strong conceptual intuition, which would support him as he started learning more advanced topics.
Learning how to learn
With guidance from his local professor, Bertele went on to explore real analysis, measure theory, and functional analysis — subjects rarely encountered before college.
As Bertele moved through 18.102 (Introduction to Functional Analysis), he noticed a familiar pattern: Conceptualizing new ideas became easier because it felt similar to how he learned linear algebra and geometry. This realization, he says, helped him gain confidence in his ability to tackle difficult topics.
MIT OpenCourseWare didn’t just sate Bertele’s natural curiosity; it enabled him to create his own accelerated track at school. 18.100A (Real Analysis) equipped him to bypass the typical junior year calculus AB class, skipping straight to calculus BC with the seniors. Now a senior, he also tested out of the school’s linear algebra class, so he’s filling his free math period with an independent study in advanced linear algebra.
As he prepares for college, Bertele is eager to keep exploring functional analysis. He has built a solid foundation in the subject but he says there’s plenty more to learn.
“I hope to do meaningful math research in the future,” Bertele says, adding that he wants to attend graduate school and ultimately become a professor.
Bertele, who already gained a taste for teaching through his after school program, says “If you’re worried about not being able to understand it, definitely don’t let that stop you.”
He adds, “It takes a lot of time to build up that momentum, but once you do, it’s very hard to stop.”
From self-taught teenager to peer tutor was originally published in MIT Open Learning on Medium, where people are continuing the conversation by highlighting and responding to this story.