sábado, 6 de septiembre de 2014

So Bill Gates Has This Idea for a History Class ...

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Bill Gates, right, with David Christian, a professor from Australia with a new approach to teaching history.CreditMark Peterson/Redux, for The New York Times
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In 2008, shortly after Bill Gates stepped down from his executive role at Microsoft, he often awoke in his 66,000-square-foot home on the eastern bank of Lake Washington and walked downstairs to his private gym in a baggy T-shirt, shorts, sneakers and black socks yanked up to the midcalf. Then, during an hour on the treadmill, Gates, a self-described nerd, would pass the time by watching DVDs from the Teaching Company’s “Great Courses” series. On some mornings, he would learn about geology or meteorology; on others, it would be oceanography or U.S. history.
As Gates was working his way through the series, he stumbled upon a set of DVDs titled “Big History” — an unusual college course taught by a jovial, gesticulating professor from Australia named David Christian. Unlike the previous DVDs, “Big History” did not confine itself to any particular topic, or even to a single academic discipline. Instead, it put forward a synthesis of history, biology, chemistry, astronomy and other disparate fields, which Christian wove together into nothing less than a unifying narrative of life on earth. Standing inside a small “Mr. Rogers"-style set, flanked by an imitation ivy-covered brick wall, Christian explained to the camera that he was influenced by the Annales School, a group of early-20th-century French historians who insisted that history be explored on multiple scales of time and space. Christian had subsequently divided the history of the world into eight separate “thresholds,” beginning with the Big Bang, 13 billion years ago (Threshold 1), moving through to the origin of Homo sapiens (Threshold 6), the appearance of agriculture (Threshold 7) and, finally, the forces that gave birth to our modern world (Threshold 8).
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Threshold 1: The Big Bang Big History Project
Christian’s aim was not to offer discrete accounts of each period so much as to integrate them all into vertiginous conceptual narratives, sweeping through billions of years in the span of a single semester. A lecture on the Big Bang, for instance, offered a complete history of cosmology, starting with the ancient God-centered view of the universe and proceeding through Ptolemy’s Earth-based model, through the heliocentric versions advanced by thinkers from Copernicus to Galileo and eventually arriving at Hubble’s idea of an expanding universe. In the worldview of “Big History,” a discussion about the formation of stars cannot help including Einstein and the hydrogen bomb; a lesson on the rise of life will find its way to Jane Goodall and Dian Fossey. “I hope by the end of this course, you will also have a much better sense of the underlying unity of modern knowledge,” Christian said at the close of the first lecture. “There is a unified account.”
As Gates sweated away on his treadmill, he found himself marveling at the class’s ability to connect complex concepts. “I just loved it,” he said. “It was very clarifying for me. I thought, God, everybody should watch this thing!” At the time, the Bill & Melinda Gates Foundation had donated hundreds of millions of dollars to educational initiatives, but many of these were high-level policy projects, like the Common Core Standards Initiative, which the foundation was instrumental in pushing through. And Gates, who had recently decided to become a full-time philanthropist, seemed to pine for a project that was a little more tangible. He was frustrated with the state of interactive coursework and classroom technology since before he dropped out of Harvard in the mid-1970s; he yearned to experiment with entirely new approaches. “I wanted to explore how you did digital things,” he told me. “That was a big issue for me in terms of where education was going — taking my previous skills and applying them to education.” Soon after getting off the treadmill, he asked an assistant to set a meeting with Christian.
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‘Bill Gates’s history would be very different from somebody else’s who wasn’t worth $50-60 billion.’
A few days later, the professor, who was lecturing at San Diego State University, found himself in the lobby of a hotel, waiting to meet with the billionaire. “I was scared,” Christian recalled. “Someone took me along the corridor, knocks on a door, Bill opens it, invites me in. All I remember is that within five minutes, he had so put me at my ease. I thought, I’m a nerd, he’s a nerd and this is fun!” After a bit of small talk, Gates got down to business. He told Christian that he wanted to introduce “Big History” as a course in high schools all across America. He was prepared to fund the project personally, outside his foundation, and he wanted to be personally involved. “He actually gave me his email address and said, ‘Just think about it,’ ” Christian continued. " ‘Email me if you think this is a good idea.’ ”
Christian emailed to say that he thought it was a pretty good idea. The two men began tinkering, adapting Christian’s college course into a high-school curriculum, with modules flexible enough to teach to freshmen and seniors alike. Gates, who insisted that the course include a strong digital component, hired a team of engineers and designers to develop a website that would serve as an electronic textbook, brimming with interactive graphics and videos. Gates was particularly insistent on the idea of digital timelines, which may have been vestige of an earlier passion project, Microsoft Encarta, the electronic encyclopedia that was eventually overtaken by the growth of Wikipedia. Now he wanted to offer a multifaceted historical account of any given subject through a friendly user interface. The site, which is open to the public, would also feature a password-protected forum for teachers to trade notes and update and, in some cases, rewrite lesson plans based on their experiences in the classroom.
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CreditDan Winters for The New York Times
Gates, who had already learned about the limitations of large bureaucracies through his foundation, insisted that the course be pitched to individual schools, rather than to entire districts; that way, he reasoned, it could grow organically and improve as it did so, just like a start-up company. In 2011, the Big History Project debuted in five high schools, but in the three years since, Gates and Christian — along with a team of educational consultants, executives and teachers, mostly based in Seattle — have quietly accelerated its growth. This fall, the project will be offered free to more than 15,000 students in some 1,200 schools, from the Brooklyn School for Collaborative Studies in New York to Greenhills School in Ann Arbor, Mich., to Gates’s alma mater, Lakeside Upper School in Seattle. And if all goes well, the Big History Project will be introduced in hundreds of more classrooms by next year and hundreds, if not thousands, more the year after that, scaling along toward the vision Gates first experienced on that treadmill. Last month, the University of California system announced that a version of the Big History Project course could be counted in place of a more traditional World History class, paving the way for the state’s 1,300 high schools to offer it.
“We didn’t know when the last time was that somebody introduced a new course into high school,” Gates told me. “How does one go about it? What did the guy who liked biology — who did he call and say, ‘Hey, we should have biology in high school?’ It was pretty uncharted territory. But it was pretty cool.”
The American high school experience, at least as we now know it, is a relatively recent invention. Attendance did not start to become mandatory until the 1850s, and the notion of a nationwide standardized curriculum didn’t emerge until the turn of the century. But by the early 1900s, most children were taking the same list of classes that remains recognizable to this day: English, math, science and some form of history. For much of the 20th century, this last requirement would usually take the form of Western Civilization, a survey course that focused on European countries from around the rise of Rome through modernity.
But by the early ‘70s, as the Vietnam War heightened interest in nations outside Europe, Western Civ was on the decline. In pedagogical circles, a book called “The Rise of the West: A History of the Human Community,” by William Hardy McNeill, a historian at the University of Chicago, persuasively argued that Western Civ was not merely biased against other cultures but also failed to account for the enormous influence that cultures had on one another over the millenniums. In 1976, McNeill told a roomful of teachers at an American Historical Association meeting, “I find the apathy truly amazing; suicidal; absurd.”
In the wake of McNeill’s rebuke, Western Civ was slowly replaced by World History, a more comparative class that stressed broad themes across cultures and disciplines. Over the past 30 years, World History has produced its own formidable academic institutions and journals; these days, three-quarters of all American students take World History. The course was just beginning its ascent as David Christian, then a young professor at Macquarie University in Sydney, was incubating his own form of cross-disciplinary scholarship. Christian, who was teaching a course on Russian history, liked to examine his subjects from a number of unconventional angles. In the 19th century, “on average, 40 percent of Russia’s revenues came from vodka sales, so what I realized is that if Russians stopped drinking vodka, you can’t pay for the army, and the superpower collapses,” he told me. “So I thought, Here’s a modern government building its power by selling a mind-altering substance. I was looking at it at the fiscal level, at the treasury level — but also in the village and also in the tavern.”
Christian began wondering if he could apply this everything-is-connected idea to a larger scale: “I began thinking, Could I teach a course not of Russia but of humanity?” He soon became infatuated with the concept. “I remember the chain of thought,” he said. “I had to do prehistory, so I have to do some archaeology. But to do it seriously, I’m going to talk about how humans evolved, so, yikes, I’m in biology now. I thought: To do it seriously, I have to talk about how mammals evolved, how primates evolved. I have to go back to multicelled organisms, I have to go back to primeval slime. And then I thought: I have to talk about how life was created, how life appeared on earth! I have to talk geology, the history of the planet. And so you can see, this is pushing me back and back and back, until I realized there’s a stopping point — which is the Big Bang.” He paused. “I thought, Boy, would that be exciting to teach a course like this!”
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‘When Melinda and I go on the road and talk to teachers, it’s just so clear there is a real hunger for this.’
His interest in transcending borders perhaps derived from his own peripatetic childhood. Born in Brooklyn to an American mother and a British father, Christian spent the first seven years of his life in Nigeria and then was shipped off to an English boarding school. (To this day, his accent — a bewildering mix of Colonial English, Eton and Jackie Gleason — reflects this unusual provenance.) Sitting along a wooden table in a Midtown Manhattan hotel, Christian delighted in recounting the first year he taught his history-of-everything course, in 1989, at Macquarie. Perhaps unwisely, he had committed to teaching it to incoming freshmen, some 300 students. “We didn’t know what we were doing, but the really magical thing, and I think it’s what still drives me today, was the reaction of the students,” he said. “What this course can do, however it’s taught, is validate big questions” — How did we get here? for instance, or Where are we going? — “that are impossible to even ask within a more silo-ized education.”
The Macquarie course quickly became oversubscribed, and within a few years, Christian was receiving calls from other universities, asking for advice on how they might offer something similar. In 2005, he received an invitation to speak at a conference in Boothbay Harbor, Me., where he was spotted by a scout for the Teaching Company, who asked him to tape the class in their studios just outside Washington. The 48-lecture DVD set was released in early 2008. Gates was one of his first viewers.
Christian, who is 67, now travels the world as something of an evangelist for the spread of the Big History Project. (His TED Talk, “The History of Our World in 18 Minutes,” has been viewed more than four million times online.) Since introducing the course to high-school students, he and Gates realized that they needed to make a few adjustments to help it catch on. They have monitored teacher feedback closely and decreased the course in size, from 20 units to 10. True to Christian’s original style, however, the high-school course links insights across subjects into wildly ambitious narratives. The units begin with the Big Bang and shift to lesson plans on the solar system, trade and communications, globalization and, finally, the future. A class on the emergence of life might start with photosynthesis before moving on to eukaryotes and multicellular organisms and the genius of Charles Darwin and James Watson. A lecture on the slave trade might include the history of coffee beans in Ethiopia.
“Most kids experience school as one damn course after another; there’s nothing to build connections between the courses that they take,” says Bob Bain, a professor of history and education at the University of Michigan and an adviser to the Big History Project, who has helped devise much of the curriculum. “The average kid has no way to make sense between what happens with their first-period World History class and their second-period algebra class, third-period gym class, fourth-period literature — it’s all disconnected. It’s like if I were to give you a jigsaw puzzle and throw 500 pieces on the table and say, ‘Oh, by the way, I’m not going to show you the box top as to how they fit together.’ ”
One muggy and overcast afternoon last fall, I met with Gates and Christian in a conference room at the Four Seasons Hotel in Midtown Manhattan. Gates, who operates a bit like an unofficial head of state, is managed down to the precise minute by an innumerable team of handlers and schedulers and assistants. The table before him was filled with strewn papers and gadgets, a handful of folders with old-fashioned Brother P-Touch labels and two Microsoft Surface tablet computers. A plainclothes security detail stood watch in the hallway.
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Christian and Gates at the Four Seasons in New York.CreditMark Peterson/Redux, for The New York Times
Gates, who is 58, was wearing a rumpled blue monogrammed shirt. He is slim and speaks in a sort of nasal staccato, often adding exclamation to sentences that might not seem to require them. But his curiosity about education is innate and at times obsessive. Without prompting, he recounted getting a bad grade in an eighth-grade geography course (“They paired me up with a moron, and I realized these people thought I was stupid, and it really pissed me off!”) and the only C-plus he ever received, in organic chemistry, at Harvard (“I’m pretty sure. I’d have to double-check my transcript. I think I never ever got a B ever at Harvard. I got a C-plus, and I got A’s!”).
Since starting his foundation in 2000, Gates has donated about $30 billion to organizations focusing largely on global health and development. The Gates Foundation has spent more than half a billion on educational causes, which provides some context for the comparatively modest $10 million that he has personally invested in the Big History Project. Nevertheless, Gates has insisted on tracking this venture as he would any Microsoft product or foundation project. The Big History Project produces reams of data — students and teachers are regularly surveyed, and teachers submit the results from classes, all of which allows his team to track what’s working and what isn’t as the course grows. “Our priority,” he told me from across the table, “was to get it into a form where ambitious teachers could latch onto it.”
In our conversation, Gates was forthright about the challenges the project has faced, particularly early on. Few schools had teachers who were willing or able to instruct a hybrid course; some schools wound up requiring that two teachers lead the class together. Gates, who had hoped to avoid bureaucracy, found himself mired in it. “You’ve got to get a teacher in the history department and the science department — they have to be very serious about it, and they have to get their administrative staff to agree. And then you have to get it on the course schedule so kids can sign up,” he said. “So they have to decide, kind of in the spring or earlier, and those teachers have to spend a lot of that summer getting themselves ready for the thing.” He sighed.
Perhaps the largest challenge facing the Big History Project, however, is Gates himself, or at least the specter of him. To his bafflement and frustration, he has become a remarkably polarizing figure in the education world. This owes largely to the fact that Gates, through his foundation, has spent more than $200 million to advocate for the Common Core, something of a third rail in education circles. He has financed an army of policy groups, think tanks and teachers’ unions to marshal support for the new rules and performance measurements that have been adopted by 44 states. Many education experts, while generally supportive of the new goals for reading and math skills, have been critical of the seemingly unilateral way in which the policy appeared to be rolled out. The standards have engendered public anger on both the right and left, and some states, including Indiana and Oklahoma, have decided to repeal the Common Core altogether.
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‘Most kids experience school as one damn course after another; there’s nothing to build connections between the courses that they take.’
In March, the American Federation of Teachers announced that it would no longer accept grants from the Gates Foundation for its innovation fund, which had already received more than $5 million from the organization. As Randi Weingarten, the A.F.T. president, told Politico, “I got convinced by the level of distrust I was seeing — not simply on Twitter, but in listening to members and local leaders — that it was important to find a way to replace Gates’s funding.” When I spoke with Weingarten last month, she elaborated on her union members’ problem with Gates. “Instead of actually working with teachers and listening to what teachers needed to make public eduction better,” she said, Gates’s team “would work around teachers, and that created tremendous distrust.”
Teachers, she continued, feared that his foundation was merely going to reduce them to test scores. While Weingarten said that she tried to work with Gates to “pierce” the animosity, she ultimately chose to part ways because “our members perceived that we were doing things in our support of Common Core because of the Gates Foundation, as opposed to because it was the right thing to do.” It was a difficult decision, Weingarten said. “Bill Gates has more money than God. People just don’t do what we did.”
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‘Frankly, in the eyes of the critics, he’s really not an expert. He just happens to be a guy that watched a DVD and thought it was a good idea and had a bunch of money to fund it.’
Beginning with the Carnegies and the Rockefellers, billionaires have long seen the nation’s education as a willing cause for their philanthropy — and, with it, their own ideas about how students should learn. The latest crop of billionaires, however, has tended to take the line that fixing our broken educational system is the key to unlocking our stagnant economy. Whether it’s hedge-fund managers like Paul Tudor Jones (who has given tens of millions to support charter schools) or industrialists like Eli Broad (who has backed “blended learning” programs that feature enhanced technology), these philanthropists have generally espoused the idea that education should operate more like a business. (The Walton Foundation, backed by the family that founded Walmart, has taken this idea to new heights: It has spent more than $1 billion supporting various charter schools and voucher programs that seek to establish alternatives to the current public-school system.) Often these patrons want to restructure the system to make it more efficient, utilizing the latest technology and management philosophies to turn out a new generation of employable students.
For many teachers, Weingarten explained, this outside influence has become off-putting, if not downright scary. “We have a really polarized environment in terms of education, which we didn’t have 10 years ago,” she said. “Public education was a bipartisan or multipartisan enterprise — it didn’t matter if you were a Republican or Democrat or elite or not elite. People viewed public education as an anchor of democracy and a propeller of the economy in the country.” Now, she said, “there are people that have been far away from classrooms who have an outsize influence on what happens inside classrooms. Beforehand, the philanthropies were viewed as one of many voices in education. Now they are viewed — and the market reformers and the tech folks — as the dominant forces, and as dissonant to those who work in schools every day. She took a deep breath and softened her tone: “In some ways, I give Bill Gates huge credit. Bill Gates took a risk to get engaged. The fact that he was willing to step up and say, ‘Public education is important,’ is very different than foundations like the Walton Foundation, who basically try to undermine public education at every opportunity.”
Gates appears to have been chastened by his experience with the A.F.T. When he speaks about his broader educational initiatives, he is careful to mention that the change he supports comes from the teachers, too. “When Melinda and I go on the road and talk to teachers, it’s just so clear there is a real hunger for this,” he said. “If you can take a teacher and give him or her the help to become a great teacher, everyone benefits: the kids, the teacher, the community, the unions. Everyone.”
Gates resists any suggestion that Big History is some sort of curio or vanity project. But some of this earlier antipathy has raised skepticism about his support of the Big History Project. “I just finished reading William Easterly’s ‘The Tyranny of Experts,’ ” says Scott L. Thomas, dean of the School of Educational Studies at Claremont Graduate University in California. “It’s about philanthropists and their effect on the poor globally. It’s this exact idea that here you have this ‘expert’ in the middle” — that is, Gates — “enabling the pursuit of this project. And frankly, in the eyes of the critics, he’s really not an expert. He just happens to be a guy that watched a DVD and thought it was a good idea and had a bunch of money to fund it.”
Diane Ravitch, an education historian at New York University who has been a vocal critic of Gates, put even it more starkly: “When I think about history, I think about different perspectives, clashing points of view. I wonder how Bill Gates would treat the robber barons. I wonder how Bill Gates would deal with issues of extremes of wealth and poverty.” (The Big History Project doesn’t mention robber barons, but it does briefly address unequal distribution of resources.) Ravitch continued: “It begins to be a question of: Is this Bill Gates’s history? And should it be labeled ‘Bill Gates’s History’? Because Bill Gates’s history would be very different from somebody else’s who wasn’t worth $50-60 billion.” (Gates’s estimated net worth is approximately $80 billion.)
On some level, Gates’s experience in pushing through the Common Core seems to be a large part of what so excites him about the Big History Project: This small initiative, largely unburdened by bureaucracy, relies on technology and teachers who are willingly submitting to all matter of data analytics. He is pleased, he said, that the course has more than doubled in each of its first three years, and he expects that growth to follow in the future. One day, perhaps, Big History might even become a successor to Western Civ and World History. “The current thought is that in another three years, the quality of the material, the tools that let people add in new chapters and things, the broad awareness will be such that the community takes it over, and it achieves whatever natural level it’s going to get to,” he said. But he also noted that Big History — which is already being offered in South Korea, the Netherlands and, of course, Australia — had significant global potential. “It would be nice to find both educators and philanthropists[in foreign countries] that want to carry the torch — which actually, in some countries, I can think of people who would do it.”
One morning, I entered a second-floor classroom at the Brooklyn School for Collaborative Studies, a public school in Carroll Gardens not far from the Brooklyn-Queens Expressway. Brooklyn Collaborative Studies adopted the Big History Project as a pilot two years ago after Scott Henstrand, a longtime science teacher, watched Christian’s TED Talk. He pitched the idea to the school’s principal, Alyce Barr, and won her over.
As class came to order and 30 or so teenagers scurried to drop their bags and take their seats, Henstrand introduced the day’s topic: “extinction events,” or why and how various life-forms have died out. He asked his students to contemplate their own extinction event — a somewhat heady question for the teenage mind. As they pondered their eventual nonbeing, Henstrand put on a short video lecture by Christian and took a seat among the students, whom he had clustered in groups of four. Afterward, they were handed iPads with which to generate facts to support their various arguments about human extinction, based on how other species had expired. “I felt that it was great to be able to have your own opinions and then share it with everyone and take in other people’s opinions and use everything that you compile to create new theories and new ideas, and in a way create your own sense of your own belief system,” said Benjamin Campbell, a senior. One of his classmates, a junior, overheard him and chimed in: “At first I hated it, because I was like, ‘I hate science.’ But it actually just opened my perspective that I never knew about. I wasn’t looking forward to it at all, and then I grew to love the class.”
Not all educators are so enthusiastic. Sam Wineburg, a professor of education and history at Stanford, told me that although he sees Big History as “an important intellectual movement,” he did not consider the class to be a suitable replacement for an actual history course. “At certain points, it becomes less history and more of a kind of evolutionary biology or quantum physics. It loses the compelling aspect that is at the heart of the word ‘history.’ ”
Wineburg’s deepest concern about the approach was its failure to impart a methodology to students. “What is most pressing for American high-school students right now, in the history-social-studies curriculum, is: How do we read a text? How do we connect our ability to sharpen our intellectual capabilities when we’re evaluating sources and trying to understand human motivation?” he asked. “When we think about history, what are the primary sources of Big History? The original scientific reports of the Big Bang?” Wineburg, who also has developed an electronic history curriculum, scoffed.
Barr, the principal in Brooklyn, however, came to feel that Gates’s course was better than the existing alternative. “If you were to interview many, many progressive social-studies teachers, they would tell you that World History is a completely flawed course. It’s spotty. It’s like fact soup. Kids don’t come out of it really having a sense ofglobal history,” she told me. “So I said, ‘Why are we doing this?’ ” Last year, Barr allowed the Big History Project to replace World History, which is known as Global Studies in New York, as a required course.

At the end of class, after Henstrand announced the homework assignment, he chatted for a few minutes about the future of the course. He was cautiously optimistic that it would catch on, but he also seemed to recognize how hard it is to innovate in the educational system. “I think many are driven by it, but there are also some that are like: ‘Oh, God, how do we fit this into the requirements of the day? How do we fit this and that?’ ” he said. “This course is a fundamental shift in how you deliver something. But there’s so many factors in American education that work against it.”
In many ways, education is a lousy business. Teachers are not normal economic actors; almost all of them work for less money than they might fetch in some other industry, given their skills and advanced degrees. Students are even weirder economic animals: Most of them would rather do something else with their time than sit in a room and learn algebra, even though the investment is well documented to pay off. By the same token, attempts to paint Bill Gates as a self-interested actor in his education projects don’t make much sense. Joel Klein, the former chancellor of the New York City Department of Education, who charged Microsoft with being a monopoly while a lawyer at the Justice Department, laughed off the idea that Gates had an ulterior fiscal motive. “The notion that he has an agenda other than trying to improve education is just embarrassing,” said Klein, describing how Gates continued to contribute — and even increased his contributions — to New York City public schools during Klein’s tenure. “I can’t think there is a malevolent bone in his body.”
As I walked to the subway, I thought back to my conversations with Gates. Big History may one day become an heir to Western Civ or World History, but that didn’t seem to be Gates’s goal; it was more personal. Really, Big History just seems like a class that he wished he could have taken in high school. But he wasn’t a billionaire then. Now, a flash of inspiration on the treadmill might just lead to something very big.

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miércoles, 23 de julio de 2014

Why Do Americans Stink at Math?

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CreditPhoto illustratIon by Andrew B. Myers. Prop stylIst: Randi Brookman HarrIs. Calculator icons by Tim Boelaars.
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When Akihiko Takahashi was a junior in college in 1978, he was like most of the other students at his university in suburban Tokyo. He had a vague sense of wanting to accomplish something but no clue what that something should be. But that spring he met a man who would become his mentor, and this relationship set the course of his entire career.
Takeshi Matsuyama was an elementary-school teacher, but like a small number of instructors in Japan, he taught not just young children but also college students who wanted to become teachers. At the university-affiliated elementary school where Matsuyama taught, he turned his classroom into a kind of laboratory, concocting and trying out new teaching ideas. When Takahashi met him, Matsuyama was in the middle of his boldest experiment yet — revolutionizing the way students learned math by radically changing the way teachers taught it.
Instead of having students memorize and then practice endless lists of equations — which Takahashi remembered from his own days in school — Matsuyama taught his college students to encourage passionate discussions among children so they would come to uncover math’s procedures, properties and proofs for themselves. One day, for example, the young students would derive the formula for finding the area of a rectangle; the next, they would use what they learned to do the same for parallelograms. Taught this new way, math itself seemed transformed. It was not dull misery but challenging, stimulating and even fun.
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CreditPhoto illustration by Andrew B. Myers. Prop stylist: Randi Brookman Harris.
Takahashi quickly became a convert. He discovered that these ideas came from reformers in the United States, and he dedicated himself to learning to teach like an American. Over the next 12 years, as the Japanese educational system embraced this more vibrant approach to math, Takahashi taught first through sixth grade. Teaching, and thinking about teaching, was practically all he did. A quiet man with calm, smiling eyes, his passion for a new kind of math instruction could take his colleagues by surprise. “He looks very gentle and kind,” Kazuyuki Shirai, a fellow math teacher, told me through a translator. “But when he starts talking about math, everything changes.”
Takahashi was especially enthralled with an American group called the National Council of Teachers of Mathematics, or N.C.T.M., which published manifestoes throughout the 1980s, prescribing radical changes in the teaching of math. Spending late nights at school, Takahashi read every one. Like many professionals in Japan, teachers often said they did their work in the name of their mentor. It was as if Takahashi bore two influences: Matsuyama and the American reformers.
Takahashi, who is 58, became one of his country’s leading math teachers, once attracting 1,000 observers to a public lesson. He participated in a classroom equivalent of “Iron Chef,” the popular Japanese television show. But in 1991, when he got the opportunity to take a new job in America, teaching at a school run by the Japanese Education Ministry for expats in Chicago, he did not hesitate. With his wife, a graphic designer, he left his friends, family, colleagues — everything he knew — and moved to the United States, eager to be at the center of the new math.
As soon as he arrived, he started spending his days off visiting American schools. One of the first math classes he observed gave him such a jolt that he assumed there must have been some kind of mistake. The class looked exactly like his own memories of school. “I thought, Well, that’s only this class,” Takahashi said. But the next class looked like the first, and so did the next and the one after that. The Americans might have invented the world’s best methods for teaching math to children, but it was difficult to find anyone actually using them.
It wasn’t the first time that Americans had dreamed up a better way to teach math and then failed to implement it. The same pattern played out in the 1960s, when schools gripped by a post-Sputnik inferiority complex unveiled an ambitious “new math,” only to find, a few years later, that nothing actually changed. In fact, efforts to introduce a better way of teaching math stretch back to the 1800s. The story is the same every time: a big, excited push, followed by mass confusion and then a return to conventional practices.
The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them. One 1965 Peanuts cartoon depicts the young blond-haired Sally struggling to understand her new-math assignment: “Sets . . . one to one matching . . . equivalent sets . . . sets of one . . . sets of two . . . renaming two. . . .” After persisting for three valiant frames, she throws back her head and bursts into tears: “All I want to know is, how much is two and two?”
Today the frustrating descent from good intentions to tears is playing out once again, as states across the country carry out the latest wave of math reforms: the Common Core. A new set of academic standards developed to replace states’ individually designed learning goals, the Common Core math standards are like earlier math reforms, only further refined and more ambitious. Whereas previous movements found teachers haphazardly, through organizations like Takahashi’s beloved N.C.T.M. math-teacher group, the Common Core has a broader reach. A group of governors and education chiefs from 48 states initiated the writing of the standards, for both math and language arts, in 2009. The same year, the Obama administration encouraged the idea, making the adoption of rigorous “common standards” a criterion for receiving a portion of the more than $4 billion in Race to the Top grants. Forty-three states have adopted the standards.
The opportunity to change the way math is taught, as N.C.T.M. declared in its endorsement of the Common Core standards, is “unprecedented.” And yet, once again, the reforms have arrived without any good system for helping teachers learn to teach them. Responding to a recent survey by Education Week, teachers said they had typically spent fewer than four days in Common Core training, and that included training for the language-arts standards as well as the math.
Carefully taught, the assignments can help make math more concrete. Students don’t just memorize their times tables and addition facts but also understand how arithmetic works and how to apply it to real-life situations. But in practice, most teachers are unprepared and children are baffled, leaving parents furious. The comedian Louis C.K. parodied his daughters’ homework in an appearance on “The Late Show With David Letterman”: “It’s like, Bill has three goldfish. He buys two more. How many dogs live in London?”
The inadequate implementation can make math reforms seem like the most absurd form of policy change — one that creates a whole new problem to solve. Why try something we’ve failed at a half-dozen times before, only to watch it backfire? Just four years after the standards were first released, this argument has gained traction on both sides of the aisle. Since March, four Republican governors have opposed the standards. In New York, a Republican candidate is trying to establish another ballot line, called Stop Common Core, for the November gubernatorial election. On the left, meanwhile, teachers’ unions in Chicago and New York have opposed the reforms.
The fact that countries like Japan have implemented a similar approach with great success offers little consolation when the results here seem so dreadful. Americans might have written the new math, but maybe we simply aren’t suited to it. “By God,” wrote Erick Erickson, editor of the website RedState, in an anti-Common Core attack, is it such “a horrific idea that we might teach math the way math has always been taught.”
The new math of the ‘60s, the new new math of the ‘80s and today’s Common Core math all stem from the idea that the traditional way of teaching math simply does not work. As a nation, we suffer from an ailment that John Allen Paulos, a Temple University math professor and an author, calls innumeracy — the mathematical equivalent of not being able to read. On national tests, nearly two-thirds of fourth graders and eighth graders are not proficient in math. More than half of fourth graders taking the 2013 National Assessment of Educational Progress could not accurately read the temperature on a neatly drawn thermometer. (They did not understand that each hash mark represented two degrees rather than one, leading many students to mistake 46 degrees for 43 degrees.) On the same multiple-choice test, three-quarters of fourth graders could not translate a simple word problem about a girl who sold 15 cups of lemonade on Saturday and twice as many on Sunday into the expression “15 + (2×15).” Even in Massachusetts, one of the country’s highest-performing states, math students are more than two years behind their counterparts in Shanghai.
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The new math of the ’60s, the new, new math of the ’80s and today’s Common Core math all stem from the idea that the traditional way of teaching math simply does not work.
Adulthood does not alleviate our quantitative deficiency. A 2012 study comparing 16-to-65-year-olds in 20 countries found that Americans rank in the bottom five in numeracy. On a scale of 1 to 5, 29 percent of them scored at Level 1 or below, meaning they could do basic arithmetic but not computations requiring two or more steps. One study that examined medical prescriptions gone awry found that 17 percent of errors were caused by math mistakes on the part of doctors or pharmacists. A survey found that three-quarters of doctors inaccurately estimated the rates of death and major complications associated with common medical procedures, even in their own specialty areas.
One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald’s Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W’s burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it.
Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray.
But our innumeracy isn’t inevitable. In the 1970s and the 1980s, cognitive scientists studied a population known as the unschooled, people with little or no formal education. Observing workers at a Baltimore dairy factory in the ‘80s, the psychologist Sylvia Scribner noted that even basic tasks required an extensive amount of math. For instance, many of the workers charged with loading quarts and gallons of milk into crates had no more than a sixth-grade education. But they were able to do math, in order to assemble their loads efficiently, that was “equivalent to shifting between different base systems of numbers.” Throughout these mental calculations, errors were “virtually nonexistent.” And yet when these workers were out sick and the dairy’s better-educated office workers filled in for them, productivity declined.
The unschooled may have been more capable of complex math than people who were specifically taught it, but in the context of school, they were stymied by math they already knew. Studies of children in Brazil, who helped support their families by roaming the streets selling roasted peanuts and coconuts, showed that the children routinely solved complex problems in their heads to calculate a bill or make change. When cognitive scientists presented the children with the very same problem, however, this time with pen and paper, they stumbled. A 12-year-old boy who accurately computed the price of four coconuts at 35 cruzeiros each was later given the problem on paper. Incorrectly using the multiplication method he was taught in school, he came up with the wrong answer. Similarly, when Scribner gave her dairy workers tests using the language of math class, their scores averaged around 64 percent. The cognitive-science research suggested a startling cause of Americans’ innumeracy: school.
Most American math classes follow the same pattern, a ritualistic series of steps so ingrained that one researcher termed it a cultural script. Some teachers call the pattern “I, We, You.” After checking homework, teachers announce the day’s topic, demonstrating a new procedure: “Today, I’m going to show you how to divide a three-digit number by a two-digit number” (I). Then they lead the class in trying out a sample problem: “Let’s try out the steps for 242 ÷ 16” (We). Finally they let students work through similar problems on their own, usually by silently making their way through a work sheet: “Keep your eyes on your own paper!” (You).
By focusing only on procedures — “Draw a division house, put ‘242’ on the inside and ‘16’ on the outside, etc.” — and not on what the procedures mean, “I, We, You” turns school math into a sort of arbitrary process wholly divorced from the real world of numbers. Students learn not math but, in the words of one math educator, answer-getting. Instead of trying to convey, say, the essence of what it means to subtract fractions, teachers tell students to draw butterflies and multiply along the diagonal wings, add the antennas and finally reduce and simplify as needed. The answer-getting strategies may serve them well for a class period of practice problems, but after a week, they forget. And students often can’t figure out how to apply the strategy for a particular problem to new problems.
How could you teach math in school that mirrors the way children learn it in the world? That was the challenge Magdalene Lampert set for herself in the 1980s, when she began teaching elementary-school math in Cambridge, Mass. She grew up in Trenton, accompanying her father on his milk deliveries around town, solving the milk-related math problems he encountered. “Like, you know: If Mrs. Jones wants three quarts of this and Mrs. Smith, who lives next door, wants eight quarts, how many cases do you have to put on the truck?” Lampert, who is 67 years old, explained to me.
She knew there must be a way to tap into what students already understood and then build on it. In her classroom, she replaced “I, We, You” with a structure you might call “You, Y’all, We.” Rather than starting each lesson by introducing the main idea to be learned that day, she assigned a single “problem of the day,” designed to let students struggle toward it — first on their own (You), then in peer groups (Y’all) and finally as a whole class (We). The result was a process that replaced answer-getting with what Lampert called sense-making. By pushing students to talk about math, she invited them to share the misunderstandings most American students keep quiet until the test. In the process, she gave them an opportunity to realize, on their own, why their answers were wrong.
Lampert, who until recently was a professor of education at the University of Michigan in Ann Arbor, now works for the Boston Teacher Residency, a program serving Boston public schools, and the New Visions for Public Schools network in New York City, instructing educators on how to train teachers. In her book, “Teaching Problems and the Problems of Teaching,” Lampert tells the story of how one of her fifth-grade classes learned fractions. One day, a student made a “conjecture” that reflected a common misconception among children. The fraction 5 / 6, the student argued, goes on the same place on the number line as 5 / 12. For the rest of the class period, the student listened as a lineup of peers detailed all the reasons the two numbers couldn’t possibly be equivalent, even though they had the same numerator. A few days later, when Lampert gave a quiz on the topic (“Prove that 3 / 12 = 1 / 4 ,” for example), the student could confidently declare why: “Three sections of the 12 go into each fourth.”
Over the years, observers who have studied Lampert’s classroom have found that students learn an unusual amount of math. Rather than forgetting algorithms, they retain and even understand them. One boy who began fifth grade declaring math to be his worst subject ended it able to solve multiplication, long division and fraction problems, not to mention simple multivariable equations. It’s hard to look at Lampert’s results without concluding that with the help of a great teacher, even Americans can become the so-called math people we don’t think we are.
Among math reformers, Lampert’s work gained attention. Her research was cited in the same N.C.T.M. standards documents that Takahashi later pored over. She was featured in Time magazine in 1989 and was retained by the producers of “Sesame Street” to help create the show “Square One Television,” aimed at making math accessible to children. Yet as her ideas took off, she began to see a problem. In Japan, she was influencing teachers she had never met, by way of the N.C.T.M. standards. But where she lived, in America, teachers had few opportunities for learning the methods she developed.
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CreditPhoto illustration by Andrew B. Myers. Prop stylist: Randi Brookman Harris. Butterfly icon by Tim Boelaars.
American institutions charged with training teachers in new approaches to math have proved largely unable to do it. At most education schools, the professors with the research budgets and deanships have little interest in the science of teaching. Indeed, when Lampert attended Harvard’s Graduate School of Education in the 1970s, she could find only one listing in the entire course catalog that used the word “teaching” in its title. (Today only 19 out of 231 courses include it.) Methods courses, meanwhile, are usually taught by the lowest ranks of professors — chronically underpaid, overworked and, ultimately, ineffective.
Without the right training, most teachers do not understand math well enough to teach it the way Lampert does. “Remember,” Lampert says, “American teachers are only a subset of Americans.” As graduates of American schools, they are no more likely to display numeracy than the rest of us. “I’m just not a math person,” Lampert says her education students would say with an apologetic shrug.
Consequently, the most powerful influence on teachers is the one most beyond our control. The sociologist Dan Lortie calls the phenomenon the apprenticeship of observation. Teachers learn to teach primarily by recalling their memories of having been taught, an average of 13,000 hours of instruction over a typical childhood. The apprenticeship of observation exacerbates what the education scholar Suzanne Wilson calls education reform’s double bind. The very people who embody the problem — teachers — are also the ones charged with solving it.
Lampert witnessed the effects of the double bind in 1986, a year after California announced its intention to adopt “teaching for understanding,” a style of math instruction similar to Lampert’s. A team of researchers that included Lampert’s husband, David Cohen, traveled to California to see how the teachers were doing as they began to put the reforms into practice. But after studying three dozen classrooms over four years, they found the new teaching simply wasn’t happening. Some of the failure could be explained by active resistance. One teacher deliberately replaced a new textbook’s problem-solving pages with the old worksheets he was accustomed to using.
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Teachers primarily learn to teach by recalling their memories of having been taught, about 13,000 hours of instruction during a typical childhood — a problem since their instruction wasn’t very good.
Much more common, though, were teachers who wanted to change, and were willing to work hard to do it, but didn’t know how. Cohen observed one teacher, for example, who claimed to have incited a “revolution” in her classroom. But on closer inspection, her classroom had changed but not in the way California reformers intended it to. Instead of focusing on mathematical ideas, she inserted new activities into the traditional “I, We You” framework. The supposedly cooperative learning groups she used to replace her rows of desks, for example, seemed in practice less a tool to encourage discussion than a means to dismiss the class for lunch (this group can line up first, now that group, etc.).
And how could she have known to do anything different? Her principal praised her efforts, holding them up as an example for others. Official math-reform training did not help, either. Sometimes trainers offered patently bad information — failing to clarify, for example, that even though teachers were to elicit wrong answers from students, they still needed, eventually, to get to correct ones. Textbooks, too, barely changed, despite publishers’ claims to the contrary.
With the Common Core, teachers are once more being asked to unlearn an old approach and learn an entirely new one, essentially on their own. Training is still weak and infrequent, and principals — who are no more skilled at math than their teachers — remain unprepared to offer support. Textbooks, once again, have received only surface adjustments, despite the shiny Common Core labels that decorate their covers. “To have a vendor say their product is Common Core is close to meaningless,” says Phil Daro, an author of the math standards.
Left to their own devices, teachers are once again trying to incorporate new ideas into old scripts, often botching them in the process. One especially nonsensical result stems from the Common Core’s suggestion that students not just find answers but also “illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.” The idea of utilizing arrays of dots makes sense in the hands of a skilled teacher, who can use them to help a student understand how multiplication actually works. For example, a teacher trying to explain multiplication might ask a student to first draw three rows of dots with two dots in each row and then imagine what the picture would look like with three or four or five dots in each row. Guiding the student through the exercise, the teacher could help her see that each march up the times table (3x2, 3x3, 3x4) just means adding another dot per row. But if a teacher doesn’t use the dots to illustrate bigger ideas, they become just another meaningless exercise. Instead of memorizing familiar steps, students now practice even stranger rituals, like drawing dots only to count them or breaking simple addition problems into complicated forms (62+26, for example, must become 60+2+20+6) without understanding why. This can make for even poorer math students. “In the hands of unprepared teachers,” Lampert says, “alternative algorithms are worse than just teaching them standard algorithms.”
No wonder parents and some mathematicians denigrate the reforms as “fuzzy math.” In the warped way untrained teachers interpret them, they are fuzzy.
When Akihiko Takahashi arrived in America, he was surprised to find how rarely teachers discussed their teaching methods. A year after he got to Chicago, he went to a one-day conference of teachers and mathematicians and was perplexed by the fact that the gathering occurred only twice a year. In Japan, meetings between math-education professors and teachers happened as a matter of course, even before the new American ideas arrived. More distressing to Takahashi was that American teachers had almost no opportunities to watch one another teach.
In Japan, teachers had always depended on jugyokenkyu, which translates literally as “lesson study,” a set of practices that Japanese teachers use to hone their craft. A teacher first plans lessons, then teaches in front of an audience of students and other teachers along with at least one university observer. Then the observers talk with the teacher about what has just taken place. Each public lesson poses a hypothesis, a new idea about how to help children learn. And each discussion offers a chance to determine whether it worked. Withoutjugyokenkyu, it was no wonder the American teachers’ work fell short of the model set by their best thinkers. Without jugyokenyku, Takahashi never would have learned to teach at all. Neither, certainly, would the rest of Japan’s teachers.
The best discussions were the most microscopic, minute-by-minute recollections of what had occurred, with commentary. If the students were struggling to represent their subtractions visually, why not help them by, say, arranging tile blocks in groups of 10, a teacher would suggest. Or after a geometry lesson, someone might note the inherent challenge for children in seeing angles as not just corners of a triangle but as quantities — a more difficult stretch than making the same mental step for area. By the end, the teachers had learned not just how to teach the material from that day but also about math and the shape of students’ thoughts and how to mold them.
If teachers weren’t able to observe the methods firsthand, they could find textbooks, written by the leading instructors and focusing on the idea of allowing students to work on a single problem each day. Lesson study helped the textbook writers home in on the most productive problems. For example, if you are trying to decide on the best problem to teach children to subtract a one-digit number from a two-digit number using borrowing, or regrouping, you have many choices: 11 minus 2, 18 minus 9, etc. Yet from all these options, five of the six textbook companies in Japan converged on the same exact problem, Toshiakira Fujii, a professor of math education at Tokyo Gakugei University, told me. They determined that 13 minus 9 was the best. Other problems, it turned out, were likely to lead students to discover only one solution method. With 12 minus 3, for instance, the natural approach for most students was to take away 2 and then 1 (the subtraction-subtraction method). Very few would take 3 from 10 and then add back 2 (the subtraction-addition method).
But Japanese teachers knew that students were best served by understanding both methods. They used 13 minus 9 because, faced with that particular problem, students were equally likely to employ subtraction-subtraction (take away 3 to get 10, and then subtract the remaining 6 to get 4) as they were to use subtraction-addition (break 13 into 10 and 3, and then take 9 from 10 and add the remaining 1 and 3 to get 4). A teacher leading the “We” part of the lesson, when students shared their strategies, could do so with full confidence that both methods would emerge.
By 1995, when American researchers videotaped eighth-grade classrooms in the United States and Japan, Japanese schools had overwhelmingly traded the old “I, We, You” script for “You, Y’all, We.” (American schools, meanwhile didn’t look much different than they did before the reforms.) Japanese students had changed too. Participating in class, they spoke more often than Americans and had more to say. In fact, when Takahashi came to Chicago initially, the first thing he noticed was how uncomfortably silent all the classrooms were. One teacher must have said, “Shh!” a hundred times, he said. Later, when he took American visitors on tours of Japanese schools, he had to warn them about the noise from children talking, arguing, shrieking about the best way to solve problems. The research showed that Japanese students initiated the method for solving a problem in 40 percent of the lessons; Americans initiated 9 percent of the time. Similarly, 96 percent of American students’ work fell into the category of “practice,” while Japanese students spent only 41 percent of their time practicing. Almost half of Japanese students’ time was spent doing work that the researchers termed “invent/think.” (American students spent less than 1 percent of their time on it.) Even the equipment in classrooms reflected the focus on getting students to think. Whereas American teachers all used overhead projectors, allowing them to focus students’ attention on the teacher’s rules and equations, rather than their own, in Japan, the preferred device was a blackboard, allowing students to track the evolution of everyone’s ideas.
Japanese schools are far from perfect. Though lesson study is pervasive in elementary and middle school, it is less so in high school, where the emphasis is on cramming for college entrance exams. As is true in the United States, lower-income students in Japan have recently been falling behind their peers, and people there worry about staying competitive on international tests. Yet while the United States regularly hovers in the middle of the pack or below on these tests, Japan scores at the top. And other countries now inching ahead of Japan imitate the jugyokenkyu approach. Some, like China, do this by drawing on their own native jugyokenkyu-style traditions(zuanyan jiaocai, or “studying teaching materials intensively,” Chinese teachers call it). Others, including Singapore, adopt lesson study as a deliberate matter of government policy. Finland, meanwhile, made the shift by carving out time for teachers to spend learning. There, as in Japan, teachers teach for 600 or fewer hours each school year, leaving them ample time to prepare, revise and learn. By contrast, American teachers spend nearly 1,100 hours with little feedback.
It could be tempting to dismiss Japan’s success as a cultural novelty, an unreproducible result of an affluent, homogeneous, and math-positive society. Perhaps the Japanese are simply the “math people” Americans aren’t. Yet when I visited Japan, every teacher I spoke to told me a story that sounded distinctly American. “I used to hate math,” an elementary-school teacher named Shinichiro Kurita said through a translator. “I couldn’t calculate. I was slow. I was always at the bottom of the ladder, wondering why I had to memorize these equations.” Like Takahashi, when he went to college and saw his instructors teaching differently, “it was an enlightenment.”
Learning to teach the new way himself was not easy. “I had so much trouble,” Kurita said. “I had absolutely no idea how to do it.” He listened carefully for what Japanese teachers call children’s twitters — mumbled nuggets of inchoate thoughts that teachers can mold into the fully formed concept they are trying to teach. And he worked hard on bansho, the term Japanese teachers use to describe the art of blackboard writing that helps students visualize the flow of ideas from problem to solution to broader mathematical principles. But for all his efforts, he said, “the children didn’t twitter, and I couldn’t write on the blackboard.” Yet Kurita didn’t give up — and he had resources to help him persevere. He went to study sessions with other teachers, watched as many public lessons as he could and spent time with his old professors. Eventually, as he learned more, his students started to do the same. Today Kurita is the head of the math department at Setagaya Elementary School in Tokyo, the position once held by Takahashi’s mentor, Matsuyama.
Of all the lessons Japan has to offer the United States, the most important might be the belief in patience and the possibility of change. Japan, after all, was able to shift a country full of teachers to a new approach. Telling me his story, Kurita quoted what he described as an old Japanese saying about perseverance: “Sit on a stone for three years to accomplish anything.” Admittedly, a tenacious commitment to improvement seems to be part of the Japanese national heritage, showing up among teachers, autoworkers, sushi chefs and tea-ceremony masters. Yet for his part, Akihiko Takahashi extends his optimism even to a cause that can sometimes seem hopeless — the United States. After the great disappointment of moving here in 1991, he made a decision his colleagues back in Japan thought was strange. He decided to stay and try to help American teachers embrace the innovative ideas that reformers like Magdalene Lampert pioneered.
Today Takahashi lives in Chicago and holds a full-time job in the education department at DePaul University. (He also has a special appointment at his alma mater in Japan, where he and his wife frequently visit.) When it comes to transforming teaching in America, Takahashi sees promise in individual American schools that have decided to embrace lesson study. Some do this deliberately, working with Takahashi to transform the way they teach math. Others have built versions of lesson study without using that name. Sometimes these efforts turn out to be duds. When carefully implemented, though, they show promise. In one experiment in which more than 200 American teachers took part in lesson study, student achievement rose, as did teachers’ math knowledge — two rare accomplishments.
Training teachers in a new way of thinking will take time, and American parents will need to be patient. In Japan, the transition did not happen overnight. When Takahashi began teaching in the new style, parents initially complained about the young instructor experimenting on their children. But his early explorations were confined to just a few lessons, giving him a chance to learn what he was doing and to bring the parents along too. He began sending home a monthly newsletter summarizing what the students had done in class and why. By his third year, he was sending out the newsletter every day. If they were going to support their children, and support Takahashi, the parents needed to know the new math as well. And over time, they learned.
To cure our innumeracy, we will have to accept that the traditional approach we take to teaching math — the one that can be mind-numbing, but also comfortingly familiar — does not work. We will have to come to see math not as a list of rules to be memorized but as a way of looking at the world that really makes sense.
The other shift Americans will have to make extends beyond just math. Across all school subjects, teachers receive a pale imitation of the preparation, support and tools they need. And across all subjects, the neglect shows in students’ work. In addition to misunderstanding math, American students also, on average, write weakly, read poorly, think unscientifically and grasp history only superficially. Examining nearly 3,000 teachers in six school districts, the Bill & Melinda Gates Foundation recently found that nearly two-thirds scored less than “proficient” in the areas of “intellectual challenge” and “classroom discourse.” Odds-defying individual teachers can be found in every state, but the overall picture is of a profession struggling to make the best of an impossible hand.
Most policies aimed at improving teaching conceive of the job not as a craft that needs to be taught but as a natural-born talent that teachers either decide to muster or don’t possess. Instead of acknowledging that changes like the new math are something teachers must learn over time, we mandate them as “standards” that teachers are expected to simply “adopt.” We shouldn’t be surprised, then, that their students don’t improve.
Here, too, the Japanese experience is telling. The teachers I met in Tokyo had changed not just their ideas about math; they also changed their whole conception of what it means to be a teacher. “The term ‘teaching’ came to mean something totally different to me,” a teacher named Hideto Hirayama told me through a translator. It was more sophisticated, more challenging — and more rewarding. “The moment that a child changes, the moment that he understands something, is amazing, and this transition happens right before your eyes,” he said. “It seems like my heart stops every day.”

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