Doing Hard Things: Math and Science Students Forge Ahead

Lattice-based cryptography is a promising area of post-quantum research that uses complex mathematical structures to create ultra-secure cryptographic schemes. It is close to impossible to describe it in any more detail to anyone who hasn’t studied college-level linear algebra. But for Colorado Academy Senior Loghan Meisner, who has, this tremendously difficult subject area has a clear appeal: How are cryptographic systems based on the theoretical math of lattices actually implemented in code?

Good news for Meisner: She was able to investigate this area of interest in depth during her Senior year at CA, in the cross-departmental Advanced Studies & Research (ASR) course Cryptography in History & Mathematics.

 

For her final project in the yearlong course, Meisner downloaded publicly-accessible code repositories for creating lattice-based cryptographic schemes from GitHub—a well-known software developer platform—and tested various models on her own to see how they could be resistant to the unimaginable power of quantum computers, which can theoretically solve most existing cryptographic algorithms with ease. Throughout the project, she could compare notes with fellow students in the course, who were digging into the multidimensional math behind the schemes or looking more closely at the historical evolution of cryptographic methods.

“There’s not just one track you can take in math at CA,” she says of the experience, which was a culmination of her four years of advanced work in the Upper School Mathematics and Science Departments. “Cryptography is the epitome of that: You’re never just pigeonholed as a math or science person here. You can reach across subject areas or increase the level of rigor as much as you want.”

Being able to pursue everything from AP Statistics and Post-AP Linear Algebra to Economics (ASR) and AP Physics C, while exploring other passions through electives like Philosophy & Literature (ASR) and Photography, Meisner explains, “That’s something that I’m so proud to have done, because it taught me a lot of things I would never have experienced if I was locked into a narrow STEM track all day long.”

Meisner, who completed CA’s Linear Algebra course through a partnership with the University of Colorado Denver, puts CA’s advanced math and science offerings up against those of any other high school in the state. “A lot of students and families are concerned about the rigor of the curriculum in terms of the college process,”she acknowledges. But like a baker’s dozen of her classmates, Meisner will find herself entering a top engineering program next fall with college credit—Duke Biomedical Engineering—and attests, “CA gives you the tools to compete against the best and be successful.”

 

What it is that accounts for CA’s year-after-year success in sending graduates to the most selective engineering, math, and science programs in the country, according to Upper School Math Instructor and Math Department Chair Dr. Michael Huntington, is that “Our goal is to get our students to the point where they can reason through a novel problem, something they haven’t seen before. Lots of kids can find success on AP tests,” he says, “but ultimately, that’s not what we’re preparing our most advanced students for. In the real world, we frankly don’t know what kinds of problems they’re going to encounter.”

‘THE HARDEST COURSE YOU’VE EVER TAKEN’

Huntington, who co-teaches Cryptography in History & Mathematics alongside Upper School Social Studies Senior Instructor and Social Studies Department Chair Liz Sarles, explains that CA’s ability to challenge even those high school students who enter Ninth Grade ready for precalculus starts with a math placement philosophy that meets each individual student where they are.

“We’re increasingly moving away from the black-and-white approach,” he says. “‘You haven’t seen this material at our school yet, so you have to take this required class.’ We’re looking at the level of critical thinking a student’s bringing with them, their ‘mathematical mind,’ and trying to place those kids who are ready for a bigger challenge appropriately.”

 

As Upper School Science Senior Instructor and Science Department Chair Amanda Zranchev puts it, “We rely a great deal on knowing the kids—having a deep enough relationship with them to be able to tell them, ‘Hey, this might be the hardest course you’ve ever taken, but here are the reasons why I think you’ll love it.’ All of us here in the Science and Math Departments believe a student should always have the chance to try a course, and that our job is to support them in that.”

Along the way, Huntington elaborates, built-in checkpoints allow teachers and students to reflect on the growth they’re seeing, and adjust accordingly from year to year. “If things are really clicking, we can move them up; they can take Calculus AB during the summer, for example, so they can be ready for BC a year early.” There are also spots that allow students to slow down, he notes. “If you’re not ready for an AP-caliber science or math course, what field are you thinking about? Pre-med, finance, engineering? We have options that are interest based.”

 

For Senior Gabe Miranda, who, like Meisner, is heading for a top college program—Mechanical and Aerospace Engineering at Case Western Reserve University—the individualized lens through which Upper School science and math teachers view their students proved transformative.

When he arrived at CA as a Fifth Grader, he recounts, “I won’t lie: I didn’t like math. I wasn’t good at it.” That held mostly true through Middle School, too, he acknowledges, but once he reached Ninth Grade, everything changed.

Taking Math 1 with Dr. Camille James, Upper School Math Instructor and Grade 9 Dean, Miranda explains, “It all just clicked. Dr. James loves math so much; she helped me make sense of it.” James never took a one-size-fits-all approach to teaching, he observes. “She taught math in so many different ways, giving multiple explanations for a single problem and working with each and every one of us to find out how we could understand it best. From that moment, I’ve loved math.”

And not only math, Miranda adds. “When I took AP Physics I, I found the science I loved, too. I’ve always wanted to understand how things work, and since Physics is basically how the world works, I loved it. I loved the feeling of being challenged by something that was math related.”

The classroom approach of his Physics teacher, Michael McLaughlin, underscores what makes CA’s Upper School Math and Science Departments so special, he says. “The teachers love what they do, and their passion rubs off on you. It makes you want to understand a problem that might make zero sense on the board; it makes you want to find out what’s coming next.”

A RIGOROUS PATH

When they do find out what’s next—the rigors of a college path such as science, engineering, or pre-med, in this case—CA’s math and science students have “a leg up” on many of their peers, according to Zranchev.

“Lots of our graduates come back and share with us that the experience they had doing and writing labs at CA sets them apart from a lot of their first-year peers,” says Zranchev. “We’ve heard that they’re teaching their fellow students how to write a lab report, even how to safely handle chemicals.”

CA’s ever-expanding course offerings are another way that CA graduates seem to have an advantage in some of the most competitive programs in the country.

“Any student who wants to go on to study engineering of some kind in college is probably going to take AP Physics C,” Zranchev explains. “But not many schools do what CA does: We decided to combine Physics C - Mechanics and Physics C - Electricity & Magnetism (E&M) in the same school year. In many high schools, E&M requires another entire year, or it’s not offered at all.”

The AP Physics C route is so popular at CA that the Science Department has added a second section of the class and hired additional faculty members to meet increased demand. And in the 2025-2026 school year, CA will debut an entirely new astronomy offering as an ASR course, on top of recently-added Advanced Topics Biology courses in genetics and zoology/taxonomy.

CA’s longstanding and highly-regarded two-trimester Tiny Earth course sequence is yet another differentiator. Headquartered at the University of Wisconsin-Madison, the Tiny Earth initiative arose just over a decade ago to crowdsource solutions to one of the most pressing global health challenges of the century: the diminishing supply of effective human antibiotics. Most students and teachers who are part of the Tiny Earth network are working in labs on college and university campuses; CA is one of the only high schools anywhere in the world to take part.

 

Senior Noah Keil, who pursued an independent-study followup after taking the course as a Junior, says of the realworld scientific experience, “What is so exciting about Tiny Earth is the possibility for genuine scientific discovery in school. I feel like in so many classes, you’re learning and maybe preparing to go change the world, but in Tiny Earth, it’s different. You’re actually doing hands-on science and possibly making a discovery that no one else has.”

Keil’s independent-study project, looking at the potential for CRISPR gene-editing technology to target and deactivate genes that cause antibiotic resistance, took him to the next frontier of antibiotic research and development, and next year, he’ll continue what he started on a pre-med track at Amherst College. Argues Zranchev, “More than any other school I’ve seen, CA does an excellent job of letting a student develop a hypothesis of their own, and then design an experiment to test it. The result is that they learn the theory or concept through data, rather than a teacher pointing to a slide deck.”

Huntington says something similar about math at CA. Starting in the Lower School and going right through to graduation, he explains, the focus is squarely on problem-solving and critical thinking; rote memorization comes second. “What happens when you take that approach is that your enthusiasm for math, your ability to think about and even formulate a problem, becomes a fully developed asset. In so many schools, that skill remains underdeveloped.”

Recounting his work with a pair of Fifth Graders who came to him for help researching one of math’s unsolved problems, Huntington says, “America’s math curriculum is ‘anti-creative.’ Everything’s already been figured out: Do these steps, follow this algorithm. Shifting away from that is very difficult, but I believe it’s valuable.”

The age-old question learners ask about math—“When am I ever going to use this?”—has a simple answer that’s true for many, he jokes: “Probably never.” But there’s a more complex answer that’s even more true for most students, says Huntington: “What kind of thinking did you develop around this math problem? That’s what will last a lifetime.”