In Dan Goldfield’s high school math class, students don’t learn about large numbers by staring at a whiteboard and copying zeros. They go to a beach and count grains of sand.
“Some of them start by counting how much sand fits in a Dixie cup, others decide to measure by weight and volume,” he said. “Either way, they learn that guess what, it’s not even close to the national debt. …. By doing math this way, students really start to understand the larger mathematical concepts — that math is a tool, not just something to get through in order to graduate.”
Goldfield is among a cadre of educators who’ve found that teaching math outside the classroom — in the park, on a city street, at a playground — is an effective way to engage math-averse students at all grade levels.
Math is everywhere, they say, so why not go out and discover it?
“It’s a big world out there,” said Goldfield, who teaches at Island High School, a continuation school in Alameda in the east Bay Area. “Learning math in a textbook isn’t really natural. But getting outside, seeing math in the everyday world, allows students to see math in large brush strokes.”
Goldfield takes his students to Muir Woods, regional parks in the Oakland hills and every year on a three-night trip to Pt. Reyes National Seashore, where they stay at a youth hostel.
But teachers don’t need to plan extensive field trips to teach math outdoors. A short walk around the block can have the same impact, said Tim Erickson, a math education consultant based in Oakland and author of “Get It Together: Math Problems for Groups, Grades 4-12.”
He’s created math lessons that have students heading outside to measure the radius of a sidewalk curb, learn ratios by measuring staircase risers and determine the distance between San Francisco and Los Angeles by measuring a car’s wheel diameter.
“In elementary school, teachers use blocks to teach math, but then in high school math becomes more abstract and teachers put away the manipulatives,” he said. “I think that’s a mistake. We can all learn by looking at concrete examples in the everyday world. It changes things up, gets students to understand math outside of a textbook.”
Showing math in different contexts is also a good way to reach students who, for whatever reason, don’t like math and don’t think they’re good at it, he said. Some students might not understand calculations in a textbook, but they can easily figure the number of blades of grass on a lawn by counting the number in a small patch and multiplying. Plus, a trip outside breaks up the monotony of the school day, he said.
“Making teenagers sit still in classrooms for six hours a day — that’s nuts,” he said. “Everyone does better with fresh air and a little exercise.”
Math excursions have been part of some schools for decades. Science museums often have math exhibits, and most amusement parks offer “math days” where visitors can learn the physics and engineering of roller coasters. In 2011, professor Daniel Clark Orey at Sacramento State University devised a “math trail” for students to learn math by walking around campus, measuring redwood trees using a ballpoint pen, or learning geometry on the baseball field. Math trails exist in other cities and countries, as well.
Joshua Gutwill, director of visitor research and evaluation at the Exploratorium science museum in San Francisco, said outside math adventures bring something crucial to the learning experience: fun.
“Our view is that joy, rather than fear, can best promote learning and self-efficacy,” he said. “It’s about quality of life. It can be really exciting to figure something out on your own, in the real world. It’s a positive experience, and that makes you want to learn more.”
Being outside a classroom and having fun helps students relax, which makes them more receptive to learning, he said. They’ll also be more focused on the process rather than the outcome of their math calculations, and are more likely to use their imaginations. Working in groups is also an important way that outside math lessons help engage students.
A 2016 study funded in part by the National Science Foundation found that students who learned math in informal settings, in addition to the classroom, were adept at problem-solving and using complex math in a variety of everyday situations.
The Exploratorium created a traveling math exhibit called Geometry Playground, which includes activities such as studying the arc of a swing in motion or a basketball free-throw, observing patterns and shapes in pavement cracks and making a four-square court using triangles.
Andee Rubin, a math and science education researcher for the Technical Education Research Center in Massachusetts, said that while learning math outside is helpful, it’s not necessary. Teachers can do plenty to make math more engaging inside the classroom — important to consider since field trips are not an option for all schools.
Maker spaces — engineering laboratories where students make their own objects — are great ways for students to learn math in an informal setting, she said. Origami is another good classroom math project.
“We need to change classroom math culture,” she said. “Kids do have a natural intellectual curiosity about math, but we just manage to kill it. … We need to make math more fun, tap into students’ natural interest. It’s not always about getting the right answer, it’s about how you think.”