Functions and Trigonometry: Considering All the Angles

Functions and Trigonometry: Considering All the Angles

On a recent spring day, in the shade of trees in the outdoor classroom bordered by the track and the Richard B. Fisher Middle School, a small group of students assembled a geodesic dome in the grass. It wasn’t their first geodome—in fact it was their fourth, each of varying sizes and materials—and by now they moved along with confidence, building it within a 70-minute class block. (At least until they decided to make the doorway larger.) 

A geodesic dome, enclosing the largest volume of interior space with the least amount of surface area, is a sphere composed of triangular facets. The geodome on PC’s campus was one of three projects that students in teacher Charlie Brown’s math class would accomplish in this academic year, and each one was built with the needs of different communities in mind. 

Outdoor Garden Furniture 

Macie Bergmann described one of her group’s objectives in her application for a Lehr grant: “Design a project which requires community research, planning, attempts, failure, and connections to our math curriculum. This connects to the skills that the Center for Public Purpose focuses on with students: creative problem-solving, lifelong learning, constructive listening.” 

Functions and Trigonometry, an Upper School math course, is designed to reinforce and build upon topics learned in algebra and geometry, with an emphasis on problem solving, multiple representations of functions, and written and verbal communication skills. When Charlie Brown Hon. 1689, who moved to the Upper School this year after teaching in Middle School for 36 years, decided he wanted his class to engage in project-based learning, he teamed up with Aly Goodner OPC ’96, director of the Center for Public Purpose. Using both PC relationships and outside community connections, Goodner and Brown helped match students with on-campus and off-campus needs. 

“In the beginning of the year,” junior Macie Bergmann said, “Mr. Brown asked what we wanted to do: a project inside PC or outside to benefit the 

wider community. My dad is super into building stuff, and I wanted to learn how to help with his next project.” 

So Macie’s group chose a project that would help Thrive Village, a neighborhood development effort in West Philadelphia’s Parkside, founded by Leon Caldwell OPC ’87. Thrive needed seating for an outdoor garden and community space for its planned healthy-food retail court. In what Brown calls “Saturday morning happenstance,” he spoke with Caldwell at PC’s annual Run for Peace in September and learned about this opportunity at Thrive Village that his students could turn into project-based learning. 

“I thought Leon's mission for Thrive to support West Philadelphia families with nutritious foods was cool and unique,” Macie said. Caldwell connected the students with Tiny WPA, a Philadelphia nonprofit that supports citizen-led design improvements in community spaces. The organization came to PC’s IdeaLab and taught them how to make a picnic table and benches using a power drill, driver and chop saw. 

Students in Functions and Trigonometry each specialized in one project but collaborated on all three projects, such as the construction of a picnic table and multiple benches for an outdoor community space. 

To pay for the materials and for the staff support and supervision of Tiny WPA, Goodner suggested Macie apply for a grant from PC’s Lehr Fund. The Lehr Fund for Public Purpose Programming, established in 2019 by Seth and Ellyn Lehr, OPC parents, enables students and teachers to design learning experiences that prepare graduates with skills and competencies to lead lives that make a difference. 

The grant application process itself is a learning experience that requires critical thinking, problem solving and writing skills. Students must estimate a budget for the project, align it with the Center for Public Purpose and determine measures of success. 

In addition to the application of our math we are learning in class,” Macie wrote in the proposal on behalf of her group, “we are also learning communication, budgeting and partnership skills that will serve us in our lives.” 

The grant proposal was successful, and the students applied trigonometry to craft a picnic table and benches, painted a vibrant purple, helping to furnish the outdoor community space at Thrive Village in West Philadelphia. 

"I was excited to engage Penn Charter students in Thrive for them to learn about this community initiative and to contribute to a neighborhood that is important to me,” Caldwell said. “My education at Penn Charter was enhanced by self-directed project-based learning. The students’ willingness to engage, learn, reflect and get to work has been inspiring and continues the PC tradition of learning while serving." 

Stained-Glass Window 

Meanwhile, the Writing Center, which had moved this year from the Upper School basement to a renovated space on the second floor, had realized a new problem: The sun shone too directly through the window each afternoon. When Head of School Darryl J. Ford Hon. 1689 learned that Brown’s math class was considering a stained-glass window project, he suggested they install it in the Writing Center to help diffuse the sunlight. 

Brown and a group of his students collaborated with English teachers in the Writing Center to create a stained-glass window that would honor Cheryl Irving Hon. 1689, a beloved English teacher, Writing Center mentor and tennis coach who died in 2014. After the Upper School students asked Joe Maguire’s second grade class to collaborate with them, teacher Sarah Moses shared with them things that were meaningful to Irving. The students decided the stained-glass window should represent things that Irving loved, such as tennis, her house and a journal, and they set about drawing images that reflected her life and legacy. 

Joey DiBenedetto and Bella Toomey learned the intricacies of making stained-glass windows from Joe Beyer at Beyer Studio. 

Artisans from Beyer Studio in Germantown, which creates and restores stained glass, designed and made the window using second grade’s drawings as inspiration. As part of the process, they visited campus to tour the Writing Center and consider the space, and with the student leaders they measured and determined the dimensions of the project. They also revealed that they wanted to donate their time and materials to make this project a reality for Penn Charter and the trigonometry students. 

Brown’s class visited the studio twice to see the operation, the artists at work. “It’s a pretty cool place—a huge room full of different stations of glass,” junior Joey DiBenedetto said. The process taught Joey self-advocacy—asking for what he needs—as well as how to communicate respect. “I wanted to make sure they know that we’re grateful,” he said. 

Senior Bella Toomey learned a lot about working with a business as well as how to team up with her classmates to meet goals and deadlines. “I also think I learned more about how to be a leader and make timely and important decisions and also to trust myself and trust my peers,” she said. 

Geodesic Dome 

The geodesic dome project, throughout its many iterations, also developed students’ collaborative skills. What purpose should the dome have? Who would use it? Where on campus does it belong? 

“We said if we are interested in this, who else on our campus would we need to talk to to understand the need, complications and other considerations we need to know?” Goodner said. 

So the math students consulted some experts: Director of Facilities Ansley Cox to discuss location, science teacher Corey Kilbane for IdeaLab help, Lisa Turner, who coordinates PC's learning gardens, to consider using it as a greenhouse. Perhaps the function of the geodome will evolve over time, but for now an outdoor meeting space—or even a space to gather and chill— seems to be where the geodome has landed. 

Left: Kariyah Hunt, Oliver Jackson, Carolyn Quinn, Davin Barnett and math teacher Charlie Brown Hon. 1689 assemble a smaller, earlier version of a geodesic dome. Right: Junior C.J. English was drawn to the engineering aspect of the geodome, including working with 3D modeling program Tinkercad, as well as the feedback and revision process. 

Calculating Outcomes 

One of the goals of Functions and Trigonometry is for students to develop knowledge and skills through the exploration of real-world challenges and problems. The project-based nature of the course, Goodner said, “requires them to engage partners through written communication, chart their progress, continuously reflect on new information and apply it to the project for the community. This particular group of students has been excited to engage in this process to listen and to learn with the hope of using their math skills to support and create new resources for our PC community and partner organizations in Philadelphia.” 

This math course that teaches skills and competencies beyond logarithms underscores elements of the Portrait of a Penn Charter Learner. As Courageous Learners, the students think critically, problem-solve and take ownership of their education. These Constructive Communicators actively listen to understand others’ perspectives, participate meaningfully in discourse, and actively evolve their ideas to best serve the community. And as Change Cultivators, they engage in their communities to shape and impact their world in powerful ways. 

Brown, after 36 years of teaching middle graders, applies the same blueprint in Upper School that he did in Middle School. 

“The most important thing in teaching is building interpersonal relationships,” he said, “and if you can get a person to recognize that you believe in, admire and care about them, they’ll work hard for you in math class. Working together toward a goal makes it feel like you're on their team. 

“I’m gonna remember my first time teaching Upper School every time I see that geodome... And I'm certainly going to go to visit Thrive Village some day and say, ‘I helped make that picnic table.’ I definitely hope my students will do that too. I hope Bella and Joey come back 10 years from now and say, ‘See that stained-glass window—that’s my project.’” 

– Rebecca Luzi