Imagine aliens have abducted you. They’re kind enough creatures, however: Theirs is the slow-motion torture of trying to make you understand them. They flash their strange alphabet at you and prompt you with esoteric questions: Are you allowed to put this symbol here? To rearrange this into that? At first you struggle. Soon enough, though, you start to see patterns; eventually you begin to answer correctly.
This, Dan Meyer says, is how too many students experience mathematics. Meyer, 33, is perhaps the most famous math educator in America today. Good-looking and wholesome, he has long charmed audiences with a lopsided smile. He’s amassed more than 40,000 Twitter followers, and his TED Talk, despite its less-than-thrilling focus on math curricula, has been viewed more than two million times. Meyer’s out to change the way students learn math—to make the subject feel like an illuminating journey through the real world, rather than an abduction into an alien culture. “I need a question to carry me through my thirties,” he wrote this summer on his blog. “I can’t think of a better one than, ‘What does the math textbook of the future look like?’”
Meyer has always been a
self-directed explorer. As a high school sophomore in Ukiah, a small California
town north of the Bay, he carted a calculus book home over winter break; by January,
he’d jumped from pre-calculus to a calculus class, immediately outscoring his
senior peers. Years later, as a twenty-two year old, Meyer set a Guinness record
for the longest paperclip chain assembled in one day. (He turned it into a math
lesson, of course.) For nearly a decade, Meyer has dissected his wide-ranging
interests—movies, graphic design, and the daily life of a teacher—on his blog,
which gradually caught the attention of non-teachers. In 2009, a post about the mathematics
of the grocery store express lane landed him on the local television news. The
next year he was named a Google fellow. Now, billing himself as a “Digital
Mathematics Curriculum Consultant,” he travels the country, sharing his gospel.
This September, after he keynotes a statewide math conference in Nebraska, he
will have worked with teachers in every state.
Meyer thinks technology can change the math classroom’s reputation as a dull, mystifying, and even traumatizing place. But he doesn’t think tech can fix everything. “There’s limitations on what kinds of work can be done on a computer without a teacher,” he said, referring to the recent interest in “adaptive learning” technology, which gives students instantaneous feedback to personalized schoolwork. “You’ll never see a free-form argument of the sort that students do in our best live classrooms—and those are the sorts of skills that we cherish and reward in modern working life,” he continued. Meyer is interested in math classrooms that involve discussion and debate, that have students building hands-on models. In his view, adaptive learning software just makes it easier to do alien-abduction mathematics—the kind where repeating right answers, rather than deep comprehension, matters most.
In 2008, a panel convened by President Bush called American math achievement “mediocre.” Bush hoped to “keep America competitive.” Given that success in mathematics is a strong predictor of college and career success, the panel was worried. The “delivery system” of the math classroom, their report declared, “is broken and must be fixed.” Alien abduction, in other words, does not work. But in the years since, scores have changed little. On national assessments this year, math scores for both fourth and eighth graders ticked down, and only 40 percent of eighth graders met the proficiency bar.
Meyer frequently cites a statistic from the 2008 panel’s report: 62 percent of algebra teachers said that their greatest challenge was unmotivated students. But through a quirk of personality, Meyer stumbled on a solution: “I saw stories—beginning, middle, end—in everything I taught,” he told me. Mathematics, he realized, was built by thinkers responding to real challenges; capture these challenges in story, and students’ curiosity can be piqued.
One popular feature of his blog is its repository of “Three-Act Math Tasks,” which take the process of mathematical modeling and turn it into narrative. First, an intriguing question is translated into mathematical symbols; then, those symbols are manipulated to produce some result; and finally the results are used to help us better understand our world. A basketball player takes a shot, and it goes up, up—will it go in? Two friends choose different paths across a beach to get to a taco stand—who will get there first? A math teacher tries to break a paperclip Guinness record—will he do it if he keeps up his current rate? Each question can launch a mathematical story. Meyer calls this “some of the most challenging, exhilarating, democratic work your students will ever do” on his blog. By asking and answering seemingly math-free questions, Meyer can engage even students who dislike the subject. Students converse about those questions—making predictions, staking claims—before the mathematical symbols ever appear.
That’s hard to do on paper. Traditional textbooks “perform the first and last acts for students,” Meyer has written, “leaving only the most mathematical, most abstract act behind.” Instead of beginning with a player taking a shot, the textbook provides an equation: x for time, y for height. Students just plug in an x value and compute. The swift jump to symbols turns away students who find them intimidating—or simply boring.
“The quadratic formula wasn’t invented just to torment kids with a rhyme thousands of years later,” Meyer told me. “We invented these skills for a reason. Part of a teacher’s job is to help students see why.” Too often, he says, teachers provide the aspirin of a math lesson before kids even know they have a headache.
In 2010, Meyer left his classroom to pursue a doctorate in education at Stanford. He traveled to so many speaking gigs that, at his first annual review, his advisors there recommended he come back when he could focus. But he stayed and buckled down, finding research—like Guershon Harel’s ideas of “intellectual need”—that deepened his earlier thinking. This spring Meyer completed a dissertation that shows how peer-to-peer conversation can improve student comprehension, even in online environments. (The dissertation will be published next year, though in typical fashion, Meyer has made it available on his blog).
Today, Meyer is the Chief Academic Officer at Desmos, a San Francisco startup that offers an online graphing calculator. The company is now building on that tool by offering complete, interactive lesson plans. Like the calculator, the lessons are free to the masses; Desmos plans to profit by selling the product to corporate entities.
The lessons use interactive technology to help students begin with the concrete: One lesson starts with a slab of pavement that must be divided into equally sized parking spaces; another asks students to recreate an animation in graph form. The emphasis is slightly different than Meyer’s old “Three-Act Tasks”: exploration and communication are now privileged over stories. In the parking lot lesson, students draw and redraw their dividers, getting immediate feedback as cars try to pull into their spaces; only gradually do they begin to work with numbers and variables. Other modules ask students to share their models with the class, which allows them to revise their thinking based on the ideas of their peers. Desmos’s lessons are based on the idea of constructivism, a theory that views knowledge as something that must be built by learners themselves.
This is a progressive and rather controversial notion. Developed from the ideas of Swiss psychologist Jean Piaget and American philosopher John Dewey in the twentieth century, it was popularized by reform-minded educators starting in the 1960s. In mathematics, constructivism and other “student-centered” forms of teaching have come under particular fire in mathematics: Are kids really supposed to discover 10,000 years of math all on their own? Meyer’s advisor at Stanford, Jo Boaler, well known for her efforts to make math more widely accessible, has described a concerted effort to discredit her work.
Meyer dismisses his own critics
as ideologues. If they see anything that deviates from clear, straightforward
explanation, he says, “they have a fuse that is tripped, a certain surge goes
through their brain,” he said. “The question is not should we explain, but when should we explain.” Meyer believes
we need to provide certain experiences to students before we lecture: showing
why a tool is needed, for example, or provoking cognitive conflict, or
providing an opportunity to create informal algorithms before the standard
algorithms are taught.
I’m a former high school math teacher, and I worked for five years coaching teachers in Mississippi. The students in the schools where I worked were nearly all African American, and many faced the steep challenges of rural poverty. When I first encountered Meyer’s TED Talk in 2010, I was skeptical. But over time I saw too many students who were doing math just because they were told they had to; I began incorporating the ideas of constructivism into the lessons I developed for teachers. The few I could compel to try these lessons found their students’ perceptions of the subject transformed.
But my initial skepticism—and the skepticism of the teachers I coached—is telling. Constructivism is now an old theory, but it’s still uncommon, often associated with privileged private schools. (Meyer says he and his team test all their lessons in classrooms around the Bay Area, and aim to include a range of economic backgrounds and previous experiences with mathematics.) It’s is an ambitious form of teaching, putting high demands on a teachers—who must respond in the moment to each student’s developing ideas. That goes against the cut-the-workload-with-technology mentality pursued by Meyer’s competitors, and it’s a hard sell to administrators at struggling schools, who are often asked to make quick changes in test scores.
Which means Meyer’s quest can’t end with the creation of a few lesson plans, or even an entire textbook. He sees this as a generational project. “You really need the students in these classrooms to grow up and become teachers,” he says. “At that point a cycle begins.” The alien abductions will be over; math will be something that students do, rather than something that’s done to them.