Katherine Weeden's Trail Running Is About More Than Exercise
A math teacher and coach at The Hill School in Middleburg since 1996, she majored in mathematics at Smith College, has a Masters in numerical science from Johns Hopkins, and worked in government and the private sector as a mathematician before deciding on teaching as her life's work. So it's probably fair to say that numbers are often on her mind.
"When I'm running, it centers me," she said. "I guess that allowed me to start noticing numbers in nature, the number of petals on a flower, the number of leaves on a tree. I thought it would be fun to somehow put nature on a number line - one that the children could create."
Weeden spoke about her project idea to Linda Conti, the long-time head of the school's art department. Conti also was enthusiastic, offered a few ideas of her own and told her colleague she would support the effort in her own classes, as well.
"At the beginning of the year, we challenged the students to go outside and find numbers anywhere they could and then we would put them on a giant number line," Weeden said. "Sometimes they have a hard time transferring math from the classroom to the outside world. But this was a fun way to do it, and it became a project for the whole school. The number line started with a zero a student saw in the knot of a tree."
The success of the number line prompted Weeden to look for other ways to bring the campus into her curriculum. One of the seventh-grade math topics involves what she described as "proportional reasoning, stretching and shrinking things. If you reduce something in one of its dimensions, you must reduce its other dimensions by the same ratio, while keeping any angles the same."
She challenged students to draw an accurate and proportional circle of trees similar to Hill's tree circle. They went outside, identified the trees and used tape measures and dowels to create similar triangles to estimate their heights and spreads.
In the classroom, they used the tree measurements to draw trees scaled down, so one foot in the field correlated to a quarter-inch on paper. They positioned the resulting, proportional trees on a circular number line, around the points of the compass corresponding to those on the tree circle.
"It was just a cool way to bring nature into the classroom," Weeden said. "They bought into it, and they ran the show."
Another seventh-grade project involved three-dimensional scaling, where the students made a scaled model of the courtyard outside their math classroom. At the end of the school year, they were making another model of the school's new Solar Field.
Other numbers came into play. They did a cost analysis by comparing the amount of power generated from the Solar Field versus fossil fuels and how much money was saved on the electric bills.
"It's something that's very real," Weeden said. "And the group loves it. It gives them a sense of what numbers mean—how much power it will take to run the gym, and how much will be saved using solar energy."
All of the above is an example of what is known as Place-Based Education, described by the Place-Based Education Evaluative Collaborative as an approach that "immerses students in local heritage, culture, landscapes, opportunities, and experiences as a foundation for the study of language arts, mathematics, social studies, science, and other subjects."
"It encourages teachers and students to use the schoolyard, community, public lands, and other special places as resources, turning communities into classrooms."
Weeden and many of her Hill colleagues are always looking for ways to do just that.
"I'm a firm believer in teaching what excites you," Weeden said. "I love being outside, so I started thinking about ways to take the classroom there and began to notice places on campus where that could happen."
"Before we started, I thought I would pre-plan the mathematical topics, but it didn't happen that way. On the solar project, the students asked questions and said they wanted to do a scale model and study the projected power. They set the mathematical agenda."
Weeden also credits Hill's overall educational philosophy that encourages and enables the faculty to create innovative ways to teach.
"This was so rewarding for me to do something that fell into Placed-Based Education," Weeden said. "Hill gave me the freedom to supplement the curriculum through the use of our campus. The students are still doing all the basics. But instead of learning everything out of the book, we're doing it with something that's real to them."