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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.”

The logs are shipped to a mill in San Leandro, California.

The slats are waxed and kiln dried again.

The cedar logs are cut into small, pencil-length slats less than one-fourth of an inch in thickness. These are kiln dried and then tinted for the same reason women put rouge on their faces.

Don't overlook the ancestors present and distant who have a hand in transporting sixty carloads of slats across the nation.

Once in the pencil factory—$4,000,000 in machinery and building, all capital accumulated by thrifty and saving parents of mine—each slat is given eight grooves by a complex machine, after which another machine lays leads in every other slat, applies glue, and places another slat atop—a lead sandwich, so to speak. Seven brothers and I are mechanically carved from this "wood-clinched" sandwich.

The graphite is mined in Ceylon.

The graphite is mixed with clay from Mississippi in which ammonium hydroxide is used in the refining process. Then wetting agents are added such as sulfonated tallow—animal fats chemically reacted with sulfuric acid. After passing through numerous machines, the mixture finally appears as endless extrusions—as from a sausage grinder-cut to size, dried, and baked for several hours at 1,850 degrees Fahrenheit. To increase their strength and smoothness the leads are then treated with a hot mixture which includes candelilla wax from Mexico, paraffin wax, and hydrogenated natural fats.

My cedar receives six coats of lacquer. Do you know all the ingredients of lacquer? Who would think that the growers of castor beans and the refiners of castor oil are a part of it? They are.

Observe the labeling. That's a film formed by applying heat to carbon black mixed with resins. How do you make resins and what, pray, is carbon black?

My bit of metal—the ferrule—is brass. Think of all the persons who mine zinc and copper and those who have the skills to make shiny sheet brass from these products of nature. Those black rings on my ferrule are black nickel. What is black nickel and how is it applied? The complete story of why the center of my ferrule has no black nickel on it would take pages to explain. RP.18

An ingredient called "factice" is what does the erasing. It is a rubber-like product made by reacting rape-seed oil from the Dutch East Indies with sulfur chloride. Rubber, contrary to the common notion, is only for binding purposes. Then, too, there are numerous vulcanizing and accelerating agents. The pumice comes from Italy; and the pigment which gives "the plug" its color is cadmium sulfide

Actually, millions of human beings have had a hand in my creation, no one of whom even knows more than a very few of the others.

There isn't a single person in all these millions, including the president of the pencil company, who contributes more than a tiny, infinitesimal bit of know-how.

Here is an astounding fact: Neither the worker in the oil field nor the chemist nor the digger of graphite or clay nor any who mans or makes the ships or trains or trucks nor the one who runs the machine that does the knurling on my bit of metal nor the president of the company performs his singular task because he wants me.

There is a fact still more astounding: the absence of a master mind, of anyone dictating or forcibly directing these countless actions which bring me into being. No trace of such a person can be found.

For, if one is aware that these know-hows will naturally, yes, automatically, arrange themselves into creative and productive patterns in response to human necessity and demand—that is, in the absence of governmental or any other coercive masterminding—then one will possess an absolutely essential ingredient for freedom: a faith in free people. Freedom is impossible without this faith.

The Greek government chose to apply so-called collective action clauses, which it had earlier inserted into its bonds registered under Greek law. The deal maximized total debt relief for the country,

Since then, banks and regulators have taken steps to strengthen the market, mostly by making sure that investors can pay out the money they owe on swaps.

Nearly $70 billion of swaps are currently outstanding on Greek debt. But after both sides settle their accounts, the amount that will need to be paid out should be no more than $3.2 billion.

Some investors entered swaps on Greece as a way of effectively insuring themselves against losses on their Greek bonds, while others used them as a way to bet on a default happening.

The crisis is almost entirely self-inflicted. It has the quality of a nightmare.

My interpretation of the euro crisis is very different from the views prevailing in Germany. I hope that by offering you a different perspective I may get you to reconsider your position before more damage is done. That is my goal in coming here.

For instance, the Maastricht Treaty took it for granted that only the public sector could produce chronic deficits because the private sector would always correct its own excesses. The financial crisis of 2007-8 proved that wrong.

Only at the end of 2009, when the extent of the Greek deficit was revealed, did the financial markets realize that a member country could actually default. But then the markets raised the risk premiums on the weaker countries with a vengeance.

Then the IMF and the international banking authorities saved the international banking system by lending just enough money to the heavily indebted countries to enable them to avoid default but at the cost of pushing them into a lasting depression. Latin America suffered a lost decade.

In effect, however, the euro had turned their government bonds into bonds of third world countries that carry the risk of default.

he fact that Greece blatantly broke the rules has helped to support this attitude. But other countries like Spain and Ireland had played by the rules;

As soon as the pressure from the financial markets abated, Germany started to whittle down the promises it had made at the height of the crisis.

Losing the privilege of issuing eurobonds and having to pay stiff risk premiums would be a powerful inducement to stay in compliance.

There are also widespread fears that eurobonds would ruin Germany's credit rating. eurobonds are often compared with the Marshall Plan.

They would survive on limited support from European Structural Funds and remittances

More than any other economist, Peter understood that monetary union was a legal as well as an economic construct. His careful parsing of the Maastricht Treaty explained to the economics profession exactly what the treaty did and did not allow (Kenen 1992).

Peter even anticipated the debate over TARGET2 imbalances, observing in 1999 that it was possible to “easily conceive of conditions…in which one [national central bank] would be reluctant to build up claims indefinitely on some other national central bank.” (Kenen 1999).

Finally, Peter observed that the possibility of a member state exiting from the Eurozone could not be ruled out but warned that European officials should be cautious in bandying about the idea (Kenen 1999). “The costs of defecting,” he wrote back in 1999, “could be very high.”

The new agreement suggests that in the future, banks will be bailed out by the collective effort of Eurozone countries.

First, this arrangement is to be finalised by the end of the year. This means that, in the end, the Spanish debt will rise by €100 billion (the market participants who enthusiastically celebrated the decision by raising the price of Spanish bonds will eventually understand that). Ditto in the not unlikely case that some Italian or French banks wobble before December.

Third, the arrangement is linked to the establishment of a “single supervisory mechanism involving the ECB”. This could be a single Eurozone supervisor built inside the ECB, which would go a long way to plugging one the worst mistakes in the Maastricht Treaty (lack of a joint regulation and resolution regime for banks).

This is important because a contagious banking crisis that hits several large banks would require much more money than is available in the EFSF-EMS facilities.

Light conditionality, as they requested, is bound to collapse at the foot of the Bundestag, which must approve every single loan.

There was nothing on collapsing Greece, nothing on unsustainable public debts in several countries, and no end in sight to recession in an increasing number of countries.

“He’s helping us think about what is one of the greatest challenges of our time, how to deal with what feel like friendly monopolists,” said Tim Wu, a Columbia Law School professor who studies Internet policy and antitrust. “Amazon, Google and the others give us all this stuff for free or lower prices, so we love them, but are they dangerous in ways we don’t always see?”

In the 2002 paper with Jean-Charles Rochet, Mr. Tirole defined two-sided markets, or markets that “get both sides on board” by charging more to one set of customers in order to increase demand by others.

In the tech industry, it explains why Google, Facebook and Twitter offer their services free – the more people who use them, the more advertisers they can attract. Likewise, Amazon lowered the price of its new phone to 99 cents in part because smartphones succeed when they have a lot of apps – and developers won’t want to build apps for Amazon’s phone unless a lot of people are using it.

For regulators, tech companies have been a riddle in part because they do not follow the behavior of typical monopolies: Many do not charge for their products, and companies that offer entirely different products are nonetheless competitors. For instance, Google’s chairman, Eric Schmidt, argued in a speech on Monday that Google’s biggest competitor in search is Amazon and in mobile is Facebook — even though neither one is a search engine.

For consumers, the costs include absorbing advertisers’ ad spending by paying more for their products, being tracked and shown personalized ads, and giving up privacy.

our end-users do not internalize the impact of their purchase on the other side of the market.”

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.

NATO asks member states to spend 2 percent of their gross domestic product on their armed forces, yet only a handful of them actually do. Estonia, the small Baltic state at the alliance’s far eastern edge, is one of them, and Poland, by far the largest and richest country on that flank, is at 1.95 percent.

Latvia and Lithuania are spending less than 1 percent, though both have indicated they intend to ratchet up to 2 percent by 2020

But it will be a decade before the full impact of this modernization is felt in the field, he said.

The plan NATO has agreed on — to set up forward supply bases on the alliance’s eastern front in which 4,000 or so troops could be deployed within 48 hours — might be useful in combating a small, stealth insurgency, like the masked gunmen who arrived in Ukraine to set off that crisis, but would be useless in the face of an invasion. “What is required is to be able to hold off any aggression for at least a couple of weeks, to buy some time and provide some sort of sanctuary for reinforcements”

In recent years, Russia has massed tens of thousands of troops for exercises just across their borders.

When the Baltic states entered NATO a decade ago, they were urged not to spend their limited resources on building large standing armies, but to depend on others in the alliance to come to their aid in an emergency. Instead, the Baltic countries and other former Soviet satellite states focused their military spending on building specialties that they could offer the alliance, such as Estonia’s focus on cybersecurity

One idea drawn up by ministers Antonio Catricala and Antonio Polillo, from the Finance ministry, is to move them and the military holidays to the nearest Sunday so they will in effect still be celebrated but not on the specific date itself.

'These holidays represent the best of our past, the values on which our Republic was founded on, they are in a word history and they should not be touched. You cannot tell us that there are no other ways of boosting productivity and increasing growth. ''The country should be left its history and it should be allowed to conserve its values, values that the majority of the country are fully supportive of, that is what we are asking the government to remember.''

Almost everything is being subordinated to protect retirees.

“for how long will we continue to sacrifice investments in our nation’s children and youth ... to spend more and more on the aged?”

In a Pew poll, 87 percent of respondents favored present or greater Social Security spending; only 10 percent backed cuts. Results were similar for 18 of 19 programs, foreign aid being the exception.

Eurobonds and a solidarity fund could promote growth and stabilize the interest rates faced by governments in crisis. Lower interest rates, for example, would free up money so that even countries with tight budget constraints could spend more on growth-enhancing investments.

Even well-managed banking systems would face problems in an economic downturn of Greek and Spanish magnitude; with the collapse of Spain’s real-estate bubble, its banks are even more at risk.

If these countries made a mistake, it was only that, like Germany today, they were overly credulous of markets, so they (like the United States and so many others) allowed an asset bubble to grow unchecked.

Moreover, Germany is on the hook in either case: if the euro or the economies on the periphery collapse, the costs to Germany will be high.

While structural problems have weakened competitiveness and GDP growth in particular countries, they did not bring about the crisis, and addressing them will not resolve it.CommentsView/Create comment on this paragraph

At its peak, the Zambia Consolidated Copper Mines company employed more than 65,000 Zambians and carried out services like water delivery and waste collection for five cities in the Copper Belt Province.

Mining employment has dropped to just 30,000, half of its glory-days peak, and the job of maintaining all that company housing and infrastructure has reverted back to the government.

The stats identify Switzerland as Zambia’s primary export market. This is not an indicator that Zambia hosts a thriving chocolate and suspenders sector, but rather that its copper trades are booked in the jurisdiction where they are least likely to be taxed.

Many of the mining companies pay just 0.6 percent royalties to Zambia, far below the already-meager industry standard of three percent.

This is Namwile Uzondile, the director of a rural health education project.

Last year Namwile conducted a survey of prostitutes here in Kitwe, and found that at least half of them had education certificates, but couldn’t find work. Most had been married off early, 15 or 16, and since then had either left their husbands or lost them to AIDS.

First, you go to the tribal chief. Ninety-four percent of the land in Zambia is customary or traditional, no one has a title to it. It’s not just sitting there, people are living on it, farming, grazing animals, it’s just technically under the control of a chief.

In Zambia most of the chiefs require a gift just to get a meeting. This might mean taking them lunch at a restaurant in Lusaka, or it could mean buying their daughter a car—it’s up to them.

Another reason Zambia lacks skills is that some parts of the workforce operate as cartels. Take lawyers. Zambia only has 1,000 of them, and they’re concentrated where the money is: Lusaka (government), Copper Belt (mining) and Livingstone (safari tourists).

Last year, only six lawyers were admitted to the bar out of 164 who took the exam. The year before that, it was 16 out of 145. Keep in mind, these aren’t people coming in off the streets. These are people who have a law degree.

More than 60 percent of Zambia’s government revenue comes from the copper mines.

Taxing all this informal activity would be costly in both resources and voter goodwill. In 2012, Zambia collected just $2.3 million in income taxes from its citizens.

It goes as high up as you want to follow it. Michael Sata, the president of Zambia, appointed his uncle the finance minister, his nephew the deputy finance minister, his niece the local government minister, and cousins as ambassador to Japan and chief justice.

Zambia’s cabinet has ballooned to 20 ministers and 47 deputy ministers, the largest in Africa. With salaries three to four times higher than opposition MPs and each ministerial post bundled with perks like a company car, free fuel, house servants, and mobile phone talk-time, you get the feeling politicians aren’t jumping from opposition into government on moral sentiment alone.

In 2011, Zambia spent a total of $4.3 billion running itself. Stretch that to cover every man, woman, and child, and it amounts to just $325 per person per year. That amount—less than a dollar per person per day—has to cover education, health care, infrastructure, law enforcement, foreign debt … everything.

Now she goes all NGO. “Little government capacity,” she says, is the nicest way to put it. “There are simply no systems for routine government services,” she says. Getting a license, a permit, certificates, approvals to start work, visas for expats to fly down here—nothing is in one place, nothing is fast or easy.

“Sometimes we have to pay for the inspectors to come to our mines,” Jane says.

The conversation goes like this: Jane tells the local certification body that she needs an inspector to sign off for a permit. The local certification body tells her that they would be happy to come out to the site, but they don’t have fuel for their cars, or enough petty cash to pay per diems. Jane offers to pay their costs, but only their costs, and the payments aren’t related to clearing the inspection.

The company has even paid the police to follow up on complaints or to investigate thefts. “They say, ‘We don’t have this in our budget’ or ‘We’ll need you to pay for it,’” Jane says. So the company fixes the police cars, covers their travel expenses, treats them to lunch.

“We tell them, ‘The company I work for, we’re not going to pay up.’ But at the end of the day, they know you’re on a short timeline, and they aren’t.”

Thomas’ family told him his nephews didn’t need to be in school. From their perspective, that’s not totally irrational. In a country with so few formal jobs and so much competition for getting them, I can see how spending hundreds of hours, thousands of kwachas, on education would seem superfluous. Thomas’ daughter wants to become a lawyer. You could almost forgive Thomas if he told her that the bar exam failure rate is more than 90 percent, so what’s the use?

International investors pledged $750 million last year to build infrastructure.

If one is only interested in estimating the domestic value-added embedded in a country’s or sector’s gross exports, applying Leontief’s insight is sufficient. However, for many economic and policy applications, one also needs to quantify other components in gross exports and their structures. In such circumstances Leontief’s original insight is not sufficient, as it does not provide a way to decompose intermediate trade flows across countries into various value-added terms according to their final absorption,

Our gross trade accounting framework in fact allows one to further decompose each of the four major parts of gross exports above into finer components with economic interpretations

By the gross statistics, presented in column 1 of Table 1, the trade is highly imbalanced – Chinese exports to the US ($176.9 billion in 2011) are five times that of US exports to China ($35.1 billion in 2011). If we separate exports of final goods and of intermediate goods (reported in columns 2a and 2b of Table 1), we see that most of the Chinese exports consist of final goods, whereas most of the US exports consist of intermediate goods.

In other words, the US exports rely overwhelmingly on its own value-added (only 2.1% from China and 5.8% from other countries in 2011), whereas the Chinese exports use more foreign value-added, especially value-added from third countries (with 3.2% from the US and 23.1% from Japan, Korea, and all other countries).

As a consequence of these differences in the structure of value-added composition, the China–US trade balance in this sector looks much smaller when computed in terms of domestic value-added than in terms of gross exports.

By identifying which parts of the official data are double counted and the sources of the double counting, our gross trade accounting method provides a transparent way to bridge official trade statistics (in gross terms) and national accounts (in value-added terms) consistent with the System of National Accounts standard.

Central banks that buy sovereign debt issued by fiscal authorities offset market-imposed discipline on borrowing costs, effectively subsidizing public-sector profligacy.

Zombie-like companies were kept on artificial life-support in the false hope that time alone would revive them. It was not until late in the decade, when the banking sector was reorganized and corporate restructuring was encouraged,

Like Japan, America’s post-bubble healing has been limited – even in the face of the Fed’s outsize liquidity injections. Household debt stood at 112% of income in the third quarter of 2012 – down from record highs in 2006, but still nearly 40 percentage points above the 75% norm of the last three decades of the twentieth century. Similarly, the personal-saving rate, at just 3.5% in the four months ending in November 2012, was less than half the 7.9% average of 1970-99.

Crisis-torn peripheral European economies still suffer from unsustainable debt loads and serious productivity and competitiveness problems. And a fragmented European banking system remains one of the weakest links in the regional daisy chain.

That leaves a huge sum of excess liquidity sloshing around in global asset markets. Where it goes, the next crisis is inevitably doomed to follow.

Willem Buiter, Chief Economist at Citigroup, has been most vocal in predicting that these facilities will be inadequate when Spain and Italy hit the wall and that more extreme measures will have to be taken.

The basic dilemma here is that almost all of the eurozone governments including Germany carry high debt burdens in excess of the Maastricht Treaty. For example, Germany has been in breach of Maastricht Treaty in 8 of 10 years since 2002, has been over the Maastricht 60% hurdle in each of those ten years, and now carries a debt to GDP burden above 80%.

Where prices were rigid, as in goods and labour markets, fewer euros meant slow disinflation but rapid contraction in output and a big rise in unemployment.

If there had been no single currency, the northward capital flight would have depreciated peripheral currencies. Had the periphery borrowed in its own currency, that would have imposed losses on its foreign creditors while also boosting its export industry. Had peripheral economies instead borrowed in dollars or deutschmarks their debt burdens would have ballooned with depreciation, potentially pushing banks and sovereigns into default—but the depreciation boost to competitiveness would have remained. Either way, the depreciation of the currency would effectively shrink the value of wealth in the periphery.

Between 2000 and 2011, on average, 17 manufacturers closed up shop every day across the country, according to research from the Information Technology and Innovation Foundation.

yes, it means jobs, but on nowhere near the scale there was before, because machines have replaced humans at almost every point in the production process. Take Parkdale: The mill here produces 2.5 million pounds of yarn a week with about 140 workers. In 1980, that production level would have required more than 2,000 people.

But he was frustrated with the quality, and the lengthy process.

“We just avoid so many big and small stumbles that invariably happen when you try to do things from far away,” he said. “We would never be where we are today if we were overseas. Nowhere close.”

Time was foremost among them. The Indian mill needed too much time — three to five months — to perfect its designs, send samples, schedule production, ship the fabric to the United States and get it through customs. Mr. Winthrop was hesitant to predict demand that far in advance.

There were also communication issues.

like moving half-finished yarn between machines on forklifts.

The North American Free Trade Agreement in 1994 was the first blow, erasing import duties on much of the apparel produced in Mexico.