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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.

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.

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.

A 2012 study comparing 16-to-65-year-olds in 20 countries found that Americans rank in the bottom five in numeracy.

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.

“I’m just not a math person,” Lampert says her education students would say with an apologetic shrug.

In the 1970s and the 1980s, cognitive scientists studied a population known as the unschooled, people with little or no formal education.

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.”

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.

The cognitive-science research suggested a startling cause of Americans’ innumeracy: school.

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.

In the process, she gave them an opportunity to realize, on their own, why their answers were wrong.

At most education schools, the professors with the research budgets and deanships have little interest in the science of teaching

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.

Some of the failure could be explained by active resistance.

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.

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.

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.

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.

“Sit on a stone for three years to accomplish anything.”

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.

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.”

“I definitely expect that things will get worse,” he said.

The European Union exported agricultural goods worth 11.8 billion euros, or $15.8 billion, to Russia last year, and sales have been rising at a rate of almost 15 percent a year.

The economic data and news that Russia was massing troops and military equipment on the Ukrainian border caused stock prices to fall across Europe on Wednesday.

Separately, the German Federal Statistical Office reported on Wednesday that new industrial orders in Germany fell 3.2 percent in June compared with May. Analysts had expected orders to increase.

For Italy, the deteriorating economy puts greater pressure on Prime Minister Matteo Renzi, who less than a week ago promised not to impose any more government budget cuts and to invest in improving the country’s roads and other infrastructure. Such promises will be difficult to keep if slower growth, which usually translates into higher unemployment and lower corporate profits, limits tax receipts.A slower economy also endangers Italy’s ability to comply with eurozone rules on budget deficits.

Italy’s 2.1 trillion euro government debt equals 136 percent of its annual gross domestic product, the second-highest debt ratio in the eurozone, after Greece.

They said Italy’s problems stemmed more from its failure make changes needed to improve the performance of its economy.

The slow pace of structural reforms is worrisome,” said Paolo Manasse, a professor of macroeconomics at Bologna University. He said there was no sign of progress on necessary steps like selling off state-owned assets or overhauling the labor market or public pension system.

Airbus has struggled to sell the planes. Orders have been slow, and not a single buyer has been found in the United States, South America, Africa or India.

While the A380 program has been a boon for the European aerospace industry, Airbus is unlikely to recover its research and development costs. The best it can now expect is to break even on production costs, according to analysts, provided that it can keep orders going.

Airbus made the wrong prediction about travel preferences. People would rather take direct flights on smaller airplanes, he said, than get on big airplanes — no matter their feats of engineering — that make connections through huge hubs.

“It’s a commercial disaster,” Mr. Aboulafia says. “Every conceivably bad idea that anyone’s ever had about the aviation industry is embodied in this airplane.”

Airline executives were wary of expanding their fleets aggressively, especially for a costly, four-engine fuel hog.

A little more than a decade ago, the two dominant airplane makers, Boeing and Airbus, looked at where their businesses were headed and saw similar facts: air traffic doubling every 15 years, estimates that the number of travelers would hit four billion by 2030 — and came to radically different conclusions about what those numbers meant for their future.

“The A380 is not made for every route, but it is ideal for high-traffic routes, high-volume routes that are congested, or where there are flying constraints,”

And there are a fair number of those routes. Around 15 of the 20 largest long-haul routes by passenger volume in the world today are slot-constrained,

Boeing, too, is facing lukewarm demand for its latest jumbo jet upgrade, known as the 747-8. The company has received just 51 orders for this big plane, which can seat about 460 passengers and lists at $357 million. By contrast, it has sold more than 1,200 twin-engine 777s, which sell for as much as $320 million.

Richard H. Anderson, Delta’s chief executive, has said the A380 is “by definition an uneconomic airplane unless you’re a state-owned enterprise with subsidies.”

Bruno Delile, Air France’s senior vice president for fleet management, says that there are a limited number of routes in its network with enough daily traffic to justify the expense of such a big plane. “The forecasts about traffic growth and market saturation haven’t exactly panned out,” he says.

Not only do airlines take a big risk on the size and cost of the A380, but they also have to gain the cooperation of airports to modify gates and widen taxiways to make room for the plane.

With versions that seat 210 to 330 passengers, and with a range of about 9,000 miles, the 787 allows airlines to fly pretty much anywhere in the world and connect smaller airports without going through a hub.

And passengers are willing to pay more to avoid a connection

f most airlines appear skeptical of the A380, Emirates is a true believer. It stunned the industry in December when it ordered 50 more of the planes, beyond the 90 it already had on order, throwing Airbus a much needed lifeline

The airport handled 66 million passengers last year, rivaling Heathrow as the busiest international hub.

for Emirates, the biggest selling point of the A380 is its ability to pack in more business-class seats and create an environment that appeals to big-spending passengers.

The team eliminated 1 out of every 5 parts. It cut the cost of the materials by 25 percent.

the team cut the work hours necessary to assemble the water heater from 10 hours in China to two hours in Louisville.

Time-to-market has also improved, greatly.

four weeks on the boat from China and one week dockside to clear customs.

Total time from factory to warehouse: 30 minutes.

there is an inherent understanding that moves out when you move the manufacturing out. And you never get it back.”

At the end of the day, they say, ‘If we were doing this for the U.S. market, we should never have gone to China in the first place.’ ”

But the logic of onshoring today goes even further—and is driven, in part, by the newfound impatience of the product cycle itself.

Just a few years ago, the design of a new range or refrigerator was assumed to last seven years. Now, says Lou Lenzi, GE’s managers figure no model will be good for more than two or three years.

The country accounts for over a quarter of global greenhouse gas emissions.

Even assuming that China’s population does not grow at all over the next 30 years, that the energy efficiency of its economy increases at a faster pace than most developed and developing countries and that it manages to decarbonize its energy sources faster than pretty much anybody else, China would still be emitting a lot more carbon in 2040 than it does today, according to E.I.A. calculations.

Can the United States or anybody else do anything to speed China down a low-carbon path?

The latest report from the United Nations Intergovernmental Panel on Climate Change, issued in April, suggested several ways to allot responsibilities. If one starts counting in the 18th century and counts only emissions from industry and energy generation, the United States is responsible for more than a quarter of all greenhouse gases that humanity has put into the air. China, by contrast, is responsible for 10 percent.But if one starts counting in 1990, when the world first became aware that CO2 was a problem, and includes greenhouse gases emitted from changes in land use, the United States is responsible for only 18 percent, and China’s share rises to 15 percent. Rich and poor countries, unsurprisingly, disagree on the proper measure. Photo

Not everybody will meet their Copenhagen pledges. Japan, which unplugged its nuclear energy after the disaster at the Fukushima nuclear power plant, will fall behind. So will Canada and Australia, whose new conservative governments have lost interest in the pledges of their predecessors.

The methane is like a hangover that you can get over if you stop drinking,” said Raymond T. Pierrehumbert, a climate scientist at the University of Chicago and the author of a textbook on planetary atmospheres. “CO2 is more like lead poisoning — it sticks around, you don’t get rid of it, and it causes irreversible harm.”

Aggressively controlling methane, they say, would help slow the warming sharply over the coming decades.

By contrast, “our success in controlling CO2 emissions is likely to make very little difference on temperature over the next 40 years,” said Drew Shindell, a longtime NASA climate scientist who is leaving for Duke University.

Experts say that, looking at the more distant future, it is hugely important to keep carbon dioxide out of the atmosphere now, even if that requires burning more gas. Dr. Pierrehumbert and Dr. Shindell largely agree on this point, with Dr. Pierrehumbert discounting the gas-is-worse-than-coal argument as “bunkum.”

American, European and Chinese regulators have put in effect energy-efficiency rules that phase out the use of incandescent bulbs. Big multinationals that make light bulbs like Philips, Osram and General Electric have responded by embracing light-emitting diodes, which use one-fifth of the electricity of incandescent bulbs and half the electricity of fluorescent bulbs.

Many Chinese producers also have a poor and worsening reputation for quality, which may hurt them in the long term.

The industry, for instance, is highly segmented.

Lighting accounts for about 6 percent of the world’s emissions of greenhouse gases, and LEDs have the potential to steeply reduce them.

Prices have fallen by nearly half in the last year for low-end, low-wattage LEDs made in China, and by 15 to 20 percent for the higher-wattage versions made elsewhere, buyers and manufacturing executives said.

“We do not buy Chinese LEDs,” said Mike Pugh, the procurement director at Xicato in San Jose, Calif., a large provider of indoor lighting systems for retailers and hotels. “We just can’t take that chance.”

Xicato instead buys LEDs from multinationals like Cree of Durham, N.C.; Philips Lumileds, based in San Jose, Calif.; and Osram Opto Semiconductors of Regensburg, Germany.

Three-quarters of China’s electricity still comes from burning coal, which contributes to severe air pollution as well as global warming.

She earns $500 a month plus medical benefits and free food and lodging in an air-conditioned dormitory where employees sleep four to six i

the solar and LED industries in China received huge loans at low interest rates from state-owned banks following directives from Beijing

Russia accounts for 13 percent of Ukraine's iron and steel exports, and the political crisis has already hit shipments from Ukrainian steelmakers this year.

Sales of rebar - a steel bar or mesh of steel wires used in reinforced concrete - to the Commonwealth of Independent States (CIS), a bloc of former Soviet states, fell 70 percent to 45,000 tonnes in January compared with the average monthly export figure in the first half of 2013.Russian steelmakers have aggressively lobbied their government to implement measures to defend domestic producers from Ukrainian imports.

Tough competition on the international steel market makes the chance of (steelmakers) expanding their export market presence very low," Eavex Capital metals analyst Ivan Dzvinka said in Kiev

Manufacturers of train carts and turbo engines, which together account for 2.5 percent of Ukraine's total exports, will be hit particularly hard.

"Re-orienting these industries to Europe would be nearly impossible without very heavy investment,

"The point of the FTA is not to make it possible for Ukraine to export Soviet-era tractors to Europe. That's not going to happen. But it could eventually lead to Ukraine becoming a producer of Peugeots, Volkswagens, fridges or Nokia telephones," the EUISS's Popescu said.

But the rosy outlook changed in late March, when Brink’s started calculating its sales using the recently created exchange rate of about 50 bolívares to the dollar

Companies have ways of chipping away at the locked-up profits, including charging higher fees to Venezuelan subsidiaries for goods and services provided by the parent corporation. But many foreign companies are stuck holding vast troves of bolívares that shrink in value each time there is a devaluation.

Procter & Gamble said in April that it had the equivalent of about $900 million in cash in this country and that it was taking a $275 million write-down as a result of applying the government’s intermediate exchange rate to its Venezuelan balance sheet. Colgate-Palmolive wrote down $174 million, while Ford wrote down about $316 million.

“All the companies knew there would be a loss because everyone knew there wouldn’t be dollars” available at the fixed exchange rate, said an executive with an American company in Venezuela who spoke on the condition of anonymity. “We were trapped because the law here did not give you a way out.”

Stores are often out of basic products such as dish soap or corn flour. DirecTV has stopped taking on new customers because it cannot get the dollars to import more dish antennas.

Without dollars, car companies cannot import the parts needed to assemble vehicles; Ford and Toyota were forced to temporarily close their factories.

In yet another reflection of the currency restrictions, the government has refused to let airlines operating in Venezuela trade the bolívares they receive for ticket sales and other services here for dollars. The International Air Transport Association says that the airlines have more than $4 billion in revenues held up in the country, based on the government’s base exchange rate at the time the tickets were sold.

American Airlines says that it is owed $750 million by the country’s government.

To do so, CO2 emissions from industry and energy use would have to fall to at most 1.6 tons a year for every person on the planet by midcentury.

That is less than a tenth of annual American emissions per person today and less than a third of the world average

Lacking any understanding of the feasibility of the exercise, governments postured and jockeyed over which country should be responsible for what

This is not achievable by going after low-hanging fruit, such as replacing coal with natural gas in power plants.

The decarbonization paths rely on aggressive assumptions about our ability to deploy new technologies on a commercial scale economically.

Russia, for instance, hit the target. But Oleg Lugovoy of the Environmental Defense Fund, who worked on the Russian plan, observed that “if we don’t have carbon capture and storage we would have to reconsider.”