That difference means that Asian children learn to count much faster than American children. Four-year-old Chinese children can count, on average, to forty. American children at that age can count only to fifteen, and most don't reach forty until they're five. By the age of five, in other words, American children are already a year behind their Asian counterparts in the most fundamental of math skills.

The regularity of their number system also means that Asian children can perform basic functions, such as addition, far more easily. Ask an English-speaking seven-year-old to add thirty-seven plus twenty-two in her head, and she has to convert the words to numbers (37 + 22). Only then can she do the math: 2 plus 7 is 9 and 30 and 20 is 50, which makes 59. Ask an Asian child to add three-tens-seven and two-tens-two, and then the necessary equation is right there, embedded in the sentence. No number translation is necessary: It's five-tens-nine.

"The Asian system is transparent," says Karen Fuson, a Northwestern University psychologist who has closely studied Asian-Western differences. "I think that it makes the whole attitude toward math different. Instead of being a rote learning thing, there's a pattern I can figure out. There is an expectation that I can do this. There is an expectation that it's sensible. For fractions, we say three-fifths. The Chinese is literally 'out of five parts, take three.' That's telling you conceptually what a fraction is. It's differentiating the denominator and the numerator."

The much-storied disenchantment with mathematics among Western children starts in the third and fourth grades, and Fuson argues that perhaps a part of that disenchantment is due to the fact that math doesn't seem to make sense; its linguistic structure is clumsy; its basic rules seem arbitrary and complicated.

Asian children, by contrast, don't feel nearly that same bafflement. They can hold more numbers in their heads and do calculations faster, and the way fractions are expressed in their languages corresponds exactly to the way a fraction actually is-and maybe that makes them a little more likely to enjoy math, and maybe because they enjoy math a little more, they try a little harder and take more math classes and are more willing to do their homework, and on and on, in a kind of virtuous circle.

When it comes to math, in other words, Asians have a built-in advantage. But it's an unusual kind of advantage. For years, students from China, South Korea, and Japan-and the children of recent immigrants who are from those countries-have substantially outperformed their Western counterparts at mathematics, and the typical assumption is that it has something to do with a kind of innate Asian proclivity for math.* The psychologist Richard Lynn has even gone so far as to propose an elaborate evolutionary theory involving the Himalayas, really cold weather, premodern hunting practices, brain size, and specialized vowel sounds to explain why Asians have higher IQs. That's how we think about math. We assume that being good at things like calculus and algebra is a simple function of how smart someone is. But the differences between the number systems in the East and the West suggest something very different-that being good at math may also be rooted in a group's culture.

In the case of the Koreans, one kind of deeply rooted legacy stood in the way of the very modern task of flying an airplane. Here we have another kind of legacy, one that turns out to be perfectly suited for twenty-first-century tasks. Cultural legacies matter, and once we've seen the surprising effects of such things as power distance and numbers that can be said in a quarter as opposed to a third of a second, it's hard not to wonder how many other cultural legacies have an impact on our twenty-first-century intellectual tasks. What if coming from a culture shaped by the demands of growing rice also makes you better at math? Could the rice paddy make a difference in the classroom?

3.

The most striking fact about a rice paddy-which can never quite be grasped until you actually stand in the middle of one-is its size. It's tiny. The typical rice paddy is about as big as a hotel room. A typical Asian rice farm might be composed of two or three paddies. A village in China of fifteen hundred people might support itself entirely with 450 acres of land, which in the American Midwest would be the size of a typical family farm. At that scale, with families of five and six people living off a farm the size of two hotel rooms, agriculture changes dramatically.

Historically, Western agriculture is "mechanically" oriented. In the West, if a farmer wanted to become more efficient or increase his yield, he introduced more and more sophisticated equipment, which allowed him to replace human labor with mechanical labor: a threshing machine, a hay baler, a combine harvester, a tractor. He cleared another field and increased his acreage, because now his machinery allowed him to work more land with the same amount of effort. But in Japan or China, farmers didn't have the money to buy equipment-and, in any case, there certainly wasn't any extra land that could easily be converted into new fields. So rice farmers improved their yields by becoming smarter, by being better managers of their own time, and by making better choices. As the anthropologist Francesca Bray puts it, rice agriculture is "skill oriented": if you're willing to weed a bit more diligently, and become more adept at fertilizing, and spend a bit more time monitoring water levels, and do a better job keeping the claypan absolutely level, and make use of every square inch of your rice paddy, you'll harvest a bigger crop. Throughout history, not surprisingly, the people who grow rice have always worked harder than almost any other kind of farmer.

That last statement may seem a little odd, because most of us have a sense that everyone in the premodern world worked really hard. But that simply isn't true. All of us, for example, are descended at some point from hunter-gatherers, and many hunter-gatherers, by all accounts, had a pretty leisurely life. The !Kung bushmen of the Kalahari Desert, in Botswana, who are one of the last remaining practitioners of that way of life, subsist on a rich assortment of fruits, berries, roots, and nuts-in particular the mongongo nut, an incredibly plentiful and protein-rich source of food that lies thick on the ground. They don't grow anything, and it is growing things-preparing, planting, weeding, harvesting, storing-that takes time. Nor do they raise any animals. Occasionally, the male !Kung hunt, but chiefly for sport. All told, !Kung men and women work no more than about twelve to nineteen hours a week, with the balance of the time spent dancing, entertaining, and visiting family and friends. That's, at most, one thousand hours of work a year. (When a bushman was asked once why his people hadn't taken to agriculture, he looked puzzled and said, "Why should we plant, when there are so many mongongo nuts in the world?")

Or consider the life of a peasant in eighteenth-century Europe. Men and women in those days probably worked from dawn to noon two hundred days a year, which works out to about twelve hundred hours of work annually. During harvest or spring planting, the day might be longer. In the winter, much less. In The Discovery of France, the historian Graham Robb argues that peasant life in a country like France, even well into the nineteenth century, was essentially brief episodes of work followed by long periods of idleness.

"Ninety-nine percent of all human activity described in this and other accounts [of French country life]," he writes, "took place between late spring and early autumn." In the Pyrenees and the Alps, entire villages would essentially hibernate from the time of the first snow in November until March or April. In more temperate regions of France, where temperatures in the winter rarely fell below freezing, the same pattern held. Robb continues:

The fields of Flanders were deserted for much of the year. An official report on the Nievre in 1844 described the strange mutation of the Burgundian day-laborer once the harvest was in and the vine stocks had been burned: "After making the necessary repairs to their tools, these vigorous men will now spend their days in bed, packing their bodies tightly together in order to stay warm and eat less food. They weaken themselves deliberately."

Human hibernation was a physical and economic necessity. Lowering the metabolic rate prevented hunger from exhausting supplies.... People trudged and dawdled, even in summer.... After the revolution, in Alsace and the Pas-de-Calais, officials complained that wine growers and independent farmers, instead of undertaking "some peaceful and sedentary industry" in the quieter season, "abandon themselves to dumb idleness."

If you were a peasant farmer in Southern China, by contrast, you didn't sleep through the winter. In the short break marked by the dry season, from November through February, you busied yourself with side tasks. You made bamboo baskets or hats and sold them in the market. You repaired the dikes in your rice paddy, and rebuilt your mud hut. You sent one of your sons to work in a nearby village for a relative. You made tofu and dried bean curd and caught snakes (they were a delicacy) and trapped insects. By the time lahp cheun (the "turning of the spring") came, you were back in the fields at dawn. Working in a rice field is ten to twenty times more labor-intensive than working on an equivalent-size corn or wheat field. Some estimates put the annual workload of a wet-rice farmer in Asia at three thousand hours a year.

4.

Think, for a moment, about what the life of a rice farmer in the Pearl River Delta must have been like. Three thousand hours a year is a staggering amount of time to spend working, particularly if many of those hours involve being bent over in the hot sun, planting and weeding in a rice paddy.

What redeemed the life of a rice farmer, however, was the nature of that work. It was a lot like the garment work done by the Jewish immigrants to New York. It was meaningful. First of all, there is a clear relationship in rice farming between effort and reward. The harder you work a rice field, the more it yields. Second, it's complex work. The rice farmer isn't simply planting in the spring and harvesting in the fall. He or she effectively runs a small business, juggling a family workforce, hedging uncertainty through seed selection, building and managing a sophisticated irrigation system, and coordinating the complicated process of harvesting the first crop while simultaneously preparing the second crop.

And, most of all, it's autonomous. The peasants of Europe worked essentially as low-paid slaves of an aristocratic landlord, with little control over their own destinies. But China and Japan never developed that kind of oppressive feudal system, because feudalism simply can't work in a rice economy. Growing rice is too complicated and intricate for a system that requires farmers to be coerced and bullied into going out into the fields each morning. By the fourteenth and fifteenth centuries, landlords in central and Southern China had an almost completely hands-off relationship with their tenants: they would collect a fixed rent and let farmers go about their business.

"The thing about wet-rice farming is, not only do you need phenomenal amounts of labor, but it's very exacting," says the historian Kenneth Pomerantz. "You have to care. It really matters that the field is perfectly leveled before you flood it. Getting it close to level but not quite right makes a big difference in terms of your yield. It really matters that the water is in the fields for just the right amount of time. There's a big difference between lining up the seedlings at exactly the right distance and doing it sloppily. It's not like you put the corn in the ground in mid-March and as long as rain comes by the end of the month, you're okay. You're controlling all the inputs in a very direct way. And when you have something that requires that much care, the overlord has to have a system that gives the actual laborer some set of incentives, where if the harvest comes out well, the farmer gets a bigger share. That's why you get fixed rents, where the landlord says, I get twenty bushels, regardless of the harvest, and if it's really good, you get the extra. It's a crop that doesn't do very well with something like slavery or wage labor. It would just be too easy to leave the gate that controls the irrigation water open a few seconds too long and there goes your field."

The historian David Arkush once compared Russian and Chinese peasant proverbs, and the differences are striking. "If God does not bring it, the earth will not give it" is a typical Russian proverb. That's the kind of fatalism and pessimism typical of a repressive feudal system, where peasants have no reason to believe in the efficacy of their own work. On the other hand, Arkush writes, Chinese proverbs are striking in their belief that "hard work, shrewd planning and self-reliance or cooperation with a small group will in time bring recompense."

Here are some of the things that penniless peasants would say to one another as they worked three thousand hours a year in the baking heat and humidity of Chinese rice paddies (which, by the way, are filled with leeches):

"No food without blood and sweat."

"Farmers are busy; farmers are busy; if farmers weren't busy, where would grain to get through the winter come from?"

"In winter, the lazy man freezes to death."

"Don't depend on heaven for food, but on your own two hands carrying the load."

"Useless to ask about the crops, it all depends on hard work and fertilizer."

"If a man works hard, the land will not be lazy."

And, most telling of all: "No one who can rise before dawn three hundred sixty days a year fails to make his family rich." Rise before dawn? 360 days a year? For the !Kung leisurely gathering mongongo nuts, or the French peasant sleeping away the winter, or anyone else living in something other than the world of rice cultivation, that proverb would be unthinkable.

This is not, of course, an unfamiliar observation about Asian culture. Go to any Western college campus and you'll find that Asian students have a reputation for being in the library long after everyone else has left. Sometimes people of Asian background get offended when their culture is described this way, because they think that the stereotype is being used as a form of disparagement. But a belief in work ought to be a thing of beauty. Virtually every success story we've seen in this book so far involves someone or some group working harder than their peers. Bill Gates was addicted to his computer as a child. So was Bill Joy. The Beatles put in thousands of hours of practice in Hamburg. Joe Flom ground away for years, perfecting the art of takeovers, before he got his chance. Working really hard is what successful people do, and the genius of the culture formed in the rice paddies is that hard work gave those in the fields a way to find meaning in the midst of great uncertainty and poverty. That lesson has served Asians well in many endeavors but rarely so perfectly as in the case of mathematics.

5.

A few years ago, Alan Schoenfeld, a math professor at Berkeley, made a videotape of a woman named Renee as she was trying to solve a math problem. Renee was in her mid-twenties, with long black hair and round silver glasses. In the tape, she's playing with a software program designed to teach algebra. On the screen are a y and an x axis. The program asks the user to punch in a set of coordinates and then draws the line from those coordinates on the screen. For example, when she typed in 5 on the y axis and 5 on the x axis, the computer did this:

At this point, I'm sure, some vague memory of your middle-school algebra is coming back to you. But rest assured, you don't need to remember any of it to understand the significance of Renee's example. In fact, as you listen to Renee talking in the next few paragraphs, focus not on what she's saying but rather on how she's talking and why she's talking the way she is.

The point of the computer program, which Schoenfeld created, was to teach students about how to calculate the slope of a line. Slope, as I'm sure you remember (or, more accurately, as I'll bet you don't remember; I certainly didn't), is rise over run. The slope of the line in our example is 1, since the rise is 5 and the run is 5.

So there is Renee. She's sitting at the keyboard, and she's trying to figure out what numbers to enter in order to get the computer to draw a line that is absolutely vertical, that is directly superimposed over the y axis. Now, those of you who remember your high school math will know that this is, in fact, impossible. A vertical line has an undefined slope. Its rise is infinite: any number on the y axis starting at zero and going on forever. It's run on the x axis, meanwhile, is zero. Infinity divided by zero is not a number.

But Renee doesn't realize that what she's trying to do can't be done. She is, rather, in the grip of what Schoenfeld calls a "glorious misconception," and the reason Schoenfeld likes to show this particular tape is that it is a perfect demonstration of how this misconception came to be resolved.

Renee was a nurse. She wasn't someone who had been particularly interested in mathematics in the past. But she had somehow gotten hold of the software and was hooked.

"Now, what I want to do is make a straight line with this formula, parallel to the y axis," she begins. Schoenfeld is sitting next to her. She looks over at him anxiously. "It's been five years since I did any of this."