This blog was written by Antonio, a student at New Tech High School in Napa California, reflecting on his experience with project-based learning in a Math III course.
Implementing project-based learning (PBL) in mathematics can be challenging due to the subject’s emphasis on individualized practice. Math is often taught most efficiently through lectures and repetitive problem-solving, which can leave little room for large, overarching projects or student collaboration. However, that doesn’t mean math classes are devoid of these elements, nor that they aren’t effective ways to teach and learn math.
From my own experience, many of the math courses at the local community college place a strong emphasis on student collaboration and include assignments that resemble PBL. These are often the assignments that focus most on understanding mathematical theory and applying it to real-world situations. Unfortunately, projects like these are less common in high school-level math courses. That said, New Tech High in Napa does make a conscious effort to incorporate them where possible. One example that stands out comes from a Math III course I took recently.
PBL in Math III
Math III is one of the courses offered at New Tech High School, typically taken during a student’s sophomore or junior year. The class covers a range of topics—from foundational concepts in trigonometry, like Pythagorean identities and graphing waves, to logarithms and their real-world applications, such as calculating compound interest and percentage growth.
For our final project, we were asked to create a 5–7 minute video that synthesized two major topics we had learned during the course. Our grade was based on how clearly we communicated our ideas and how accurately we applied the mathematical concepts. I worked with my friend Isabella Bautista on this project, and together we chose to focus on the unit circle and normal distribution.
I’ve included timestamps below to match parts of the video with the sections I’m referencing.
The Unit Circle
Our decision to focus on the unit circle came early in the process. We felt it represented a culmination of several key ideas from the course, and since it was part of a more recent unit, the material was still fresh in our minds. Choosing a second topic proved to be more challenging. We wanted something clearly distinct from the unit circle—something that wasn’t directly derived from it. After some consideration, we landed on Gaussian (or normal) distribution, which provided a creative way to connect two seemingly unrelated concepts using the video format.
Our idea was to ask students and teachers to memorize the unit circle, then fill in a blank version from memory. We would then graph their results to see what kind of distribution emerged. Our goal was to determine whether their scores followed a normal distribution—a clever way to bridge trigonometry and statistics within a single project (see 1:44–2:22 in the video).
A central part of this process was reviewing past material and reflecting on how different concepts connected. In a way, we were stepping back to look at the semester’s work from a broader perspective, which helped us understand how the different topics built on one another. Because this was our final assignment of the year, it gave us a unique opportunity to appreciate the full scope of what we had learned—and to better prepare for future courses that would deepen that learning.
To me, this kind of reflection is a core strength of project-based learning. Projects encourage more than just repetition or narrow focus—they demand the use of multiple skills and invite deeper thinking. What made this assignment especially meaningful was that it stretched our thinking across the entire course, rather than limiting us to just one chapter or unit.
Accurately Applying Our Topics
While the foundation of our video was built around using the unit circle as a test, we realized that just showing it in action wasn’t enough. To help the audience fully appreciate its role—and to meet the expectations of the project—we added a segment that explained what the unit circle actually is and why it matters. This gave important context and made the content more accessible and informative.
Explaining Gaussian distribution was a bit more straightforward. We focused on clearly defining what it is and what characteristics we’d be looking for in our data that would indicate a normal distribution. Our goal wasn’t to ensure a specific result, but rather to communicate the concept accurately and tie it meaningfully to our project. In the end, the shape of the graph mattered less than the story we were telling and how well we used the data to support that narrative.
This experience highlighted one of the key strengths of project-based learning: it requires students to truly understand the content they’re working with. You can’t complete a project like this by simply memorizing steps or formulas—you have to internalize the underlying concepts well enough to explain them clearly. That kind of thinking leads to deeper learning and stronger retention. This project challenged us to revisit and articulate the core ideas behind each topic, which ultimately led to a stronger grasp of the material.
Making Math Meaningful Through Engaging Communication
A big part of creating an effective presentation was making sure our video was both informative and engaging. We didn’t want to just demonstrate our understanding of the topics—we also wanted to keep the viewer’s attention. To do that, we incorporated music, transition cards, and creatively edited video clips to make the final product more dynamic and enjoyable to watch.
One of the most important lessons we learned was that communication has to be tailored to the audience. You can create a technically perfect and detailed presentation, but if it puts your audience to sleep, it’s not successful. Effective communication goes beyond just explaining the content—it’s about helping the audience retain and understand the message.
In projects like this, especially in formats like videos or presentations, students need to clearly connect their work to the larger unit or concept. Over time, this kind of practice helps students improve their ability to relate to an audience and make meaningful connections between the project and the subject matter. In a subject like math, where communication can often be overlooked, learning how to present ideas in a relatable and clear way is especially valuable.
Conclusion
Looking back on this project, I’m really proud of the final product and the work we put into it. It was genuinely fun to create—especially going around campus and asking people to fill out the unit circle. More importantly, the process helped us deepen our conceptual understanding of the material and pushed us to think critically about the connections between topics we had studied throughout the year.
This project reinforced for me the value of project-based learning, especially in math. While traditional methods like lectures and practice problems are certainly effective at times, projects like this offer something different—they promote collaboration, creativity, and reflection. By requiring us to explain concepts clearly and connect ideas across units, this kind of work lays a stronger foundation for long-term learning in the subject.
