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Most delicate will be whether the Spanish banks receiving the largest cash injections, like the nationalized mortgage giant Bankia, will be forced to impose losses on holders of their subordinated bonds. Those are the investors whose bonds are not backed by collateral and are thus considered more risky.

In Spain, though, the problem is that 62 percent of the holders of Bankia’s subordinated debt are Spanish individual investors, not overseas hedge funds and investment banks. It is not likely that Madrid will be willing to hit those citizens with a 65 percent loss — the loans are currently priced at about 35 cents on the dollar — at a time of 25 percent unemployment in the country.

“There are compelling reasons for the euro zone to insist on losses for subordinated and even senior bondholders, the least of which is a reduction in moral hazard,” said Adam Lerrick, an expert on banking and sovereign debt at the American Enterprise Institute. “Losses for bondholders is now euro zone policy, so Europe’s credibility is also at stake.”

insufficient investment in research and development

5. Export surpluses create no real value if they translate into claims vis‐à‐vis countries which ultimately cannot pay their debts,

6. The ECB Council overstepped its mandate when it transferred to Eurozone national central banks, primarily the Bundesbank, the task of financing the public and private deficits of other countries.

7. Germany’s liability for the bail‐out initiatives does not total 211 billion euros, as often cited, but is actually now close to 600 billion euros if the far larger bailout initiatives of the ECB are included in this figure.

8. The Target credits and the purchase of government bonds by the ECB system transfer the investment risk of private investors and banks to the taxpayers of economically sound countries, posing a threat to the euro because they offer debtor countries incentives to advocate inflationary policies at the ECB Council which would help them defer their obligation to repay their foreign debts.

9. Eurobonds would undermine debt discipline, lead to much higher interest burdens for the German state, and anew induce capital flows in Europe that would exacerbate the external imbalances.

) Target debts are to be settled on an annual basis with interest‐bearing, marketable assets as in the US.

g) Countries that are not competitive enough to repay their foreign debts should, in their own interest, leave the Monetary Union.”

I also appreciate the fact that the declaration envisages a credit boom in Germany that would ultimately rebalance the eurozone economy. Nevertheless, this rebalancing is likely to prove painfully slow and certainly requires a prolonged period of relatively high inflation in Germany, to offset relatively low inflation in the vulnerable countries. It is far from clear that German public opinion is prepared for such an outcome.

More important, I do not believe a currency union that takes for granted the possibility of sovereign defaults and even exit would prove workable. It is a recipe for extreme financial instability, with huge runs on credit to banks, private non-banks and governments built in.

mechanisms of financing and adjustment. Permanent transfers from some countries to others, merely to offset a lack of

competitiveness (rather than accelerate income convergence), are indeed undesirable. Nevertheless, financing needs to be sufficiently large and generous to give vulnerable countries some chance of managing the adjustment to shocks, without sovereign default, mass private bankruptcies and implosion of financial systems.

Urinary infections were chosen because they are so common. American women get more than eight million of them a year. In rare cases the infections enter the bloodstream and are fatal.

A new strain of the antibiotic-resistant bug MRSA, for example, was first detected in people in Holland in 2003, and now represents 40 percent of the MRSA infections in humans in that country, according to Jan Kluytmans, a Dutch researcher. That same strain was common in pigs on farms before it was found in people, scientists say.

He thinks the Food and Drug Administration’s efforts to limit antibiotic use on farms have been weak. In 1977, the F.D.A. said it would begin to ban some agricultural uses of antibiotics. But the House and Senate appropriations committees — dominated by agricultural interests — passed resolutions against the ban, and the agency retreated. More recently, the agency has limited the use of two important classes of antibiotics in animals. But advocates say it needs to go further and ban use of all antibiotics for growth promotion. Sweden and Denmark have already done so.

Ms. Slaughter said aggressive lobbying by agribusiness interests has played a major role in blocking passage of legislation.

But the economics of food presents perhaps the biggest obstacle. On large industrial farms, animals are raised in close contact with one another and with big concentrations of bacteria-laden feces and urine. Antibiotics keep infections at bay but also create drug resistance.

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.”