Geometry Students Angle into Architecture Through Project Learning
When learning is based on projects, math becomes relevant as well as rigorous.
Editor's Note: Educational consultant Eeva Reeder passed away in August of 2010 at the age of 53. We are grateful for her many contributions to the field of project-based learning and to Edutopia, and she is greatly missed. Mountlake Terrace High School discontinued the Schools for the Year 2050 project when Eeva Reeder moved on from the school in 2002, but it remains a great example of a rigorous high school math project.
Seemingly countless details attend the construction of any building, especially one that, like a school, is designed to accommodate many people with diverse purposes and needs. A small sample of such questions includes the following:
- How many windows should it have?
- What should be done about parking?
- How are the buildings shaped?
- Can geodesic domes be considered?
- How will students get from floor to floor?
Designing a School for the Future
Every spring at Mountlake Terrace High School, near Seattle, students in Eeva Reeder's geometry classes work feverishly to complete an architectural challenge: Design a 2,000-student high school to meet learning needs in 2050, fitting it on a given site.
In a period of six weeks, students must develop a site plan, a scale model, floor plans, a perspective drawing, a cost estimate, and a written proposal. They must then make an oral presentation to local school architects who judge the projects and "award" the contract -- all making use of geometric and mathematical concepts. (Read this Edutopia.org outline of the project, which includes several Edutopia videos that profile student-architect teams.)
Students also maintain a design file, which contains their working drawings, notes, and group contracts, such as the Team Operating Agreement (adapted from a similar form at the Boeing Company), in which team members come to consensus on items such as expectations of themselves and each other, how decisions will be made, how misunderstandings will be prevented, and how conflicts will be resolved.
Last year's site plan consisted of a beautiful wooded area, a stream, a small hill, and a marshy area. It was designed by junior Chris Armstrong, who had participated in the project as a freshman. Armstrong also served as the computer-assisted-design (CAD) guru for Reeder's students.
Architect Mark Miller advises a student on his classroom model.
Curved Classrooms and Holographic Lecturers
Teams of two to four students constructed models, researched solar panels and other special features, and talked with visiting architects as they worked to make their dreams become realities. The team of Peter Gudmunson, Devin Lowe, and Amanda Reeves developed a design emphasizing curved spaces instead of the usual rectangular classrooms, more open space and light, underground parking, and energy-efficient features, such as self-darkening windows. Guest lecturers would be brought in via three-dimensional holograms. Although their design would be expensive to implement, it garnered second place.
Reeder is passionate about the importance of hands-on, real-life applications of abstract mathematical concepts, as well as the value of experience in working as a team to produce a product. "The ability to work collaboratively is a learned skill," she says. "Students need repeated opportunities to practice it within a complex, high-stakes context -- similar to what they'll encounter in the community and workplace as adults.
"It may be fairly easy for teachers to create work for groups of students, and it may also be fairly easy for one member of the group to do all the work," she adds. "That's why the teamwork rubric that students talk about, refine, and sign is key. They define what is expected of each member and what will happen if a team member is not participating."
It must be working. Only those who don't show up fail her class, and she consistently scores the highest retention rate in geometry classes in the math department.
A design group consults with teacher Eeva Reeder on the intricacies of their plan.
Multiple Forms of Assessment
Assessment of the design projects occurs in several ways. At the beginning of the project, students are given the scoring rubric by which their work will be measured. Each part of the project is evaluated based on quality and accuracy, clarity and presentation, and concept. Reeder also evaluates teamwork (participation, level of involvement, quality of work as a team member) during the course of the project and at the end.
Throughout, she offers feedback and suggestions and meets with the class and each team after the completion of the project. During this final session, the students reflect on their work and what they would do differently to improve. "The longer I teach, the more I understand the need for reflection," says Reeder. "We learn by doing and by thinking about what we've done. It's like learning twice when you reflect. It unquestionably deepens understanding, which is always the goal. I want them to keep their learning, after all!"
Sometimes a team will write their reflections, as with one group that never quite came together as a team and didn't score well -- an atypical situation for the individuals involved. Team members, however, honestly assessed their individual contributions and what they'd do next time. "The best part was the next day, when each team member approached me at different times," recalls Reeder. "They actually expressed gratitude to have had the chance to learn these things now, rather than later, when the stakes might be much higher."
Many forms of assessment determine the grade each student receives. However, Reeder extols the power behind using scoring rubrics as feedback and reflection tools rather than simply ways to assign a grade. "Students are more readily able to separate their personal worth from the quality of their work, and they're able to separate the particular aspects of their work that need improvement from those that don't," she explains. "It demystifies grades, and most importantly, helps students see that the whole object of schoolwork is attainment and refinement of problem-solving and life skills."
Students present their project to visiting architects as the final stage of their design work.
Professional Architects as Project Judges
At the culmination of the project, each group makes a short oral presentation to the panel of architects, who view the students' work and fill out a scoring sheet. The next day, they review their evaluations with the students during a visit at their downtown Seattle offices. They identify the projects' strengths based on concept, site planning, educational vision, technology use, environmental impact, and teamwork during the presentation. Students also have the opportunity to ask specific questions about their designs and presentation.
Architects Kirk Wise and Mark Miller enjoyed their part in the process. They visited the class several times during the work phase, offering suggestions and answering questions about issues such as the efficacy of solar panels in rainy Seattle and the use of particular building materials in conveying comfort in a learning space.
Wise and Miller donate their time because they recognize the value to students of their insights into a working architect's world. And they have incorporated student ideas into their own school designs. "One student helped us rethink the design of a cafeteria," recalls Wise. "She said we adults worried too much about it -- kids just wanted a place to hang out. So we incorporated a café into the space."
The students have their own stories: One girl went home on the first day of the assignment and couldn't sleep, out of excitement about her team's ideas. A boy found that peers valued his thinking and design skills valued in new ways. He became a team leader -- quite different from his experience in other classes. "This project has been my salvation," he told Reeder.
Another girl discovered that an early warning -- don't work with your best friends -- was a good one. "It got really hard to try to get work done," she says. "You couldn't tell them what to do without them snapping back at you." For everyone, learning to plan their time to get the tasks done was a challenge at many points.
One of the most thrilling parts of the project happened on the day of the students' visit to the architects' offices. "We heard comments from the architects telling the kids that their work was on par with first-year architecture students at the university. That means a lot to these kids, and it's not something I can say with the same amount of credibility," Reeder recounts. For herself, she says she felt the same sense of pride, similar to what parents must feel when they let their kids go "and they realize they can make it on their own out there in the real world."