The mothers, members of the largest group of foreigners at the public school, were part of what are known in South Korea as “wild geese,” families living separately, sometimes for years, to school their children in English-speaking countries like New Zealand and the United States. The mothers and children live overseas while the fathers live and work in South Korea, flying over to visit a couple of times a year.

Driven by a shared dissatisfaction with South Korea’s rigid educational system, parents in rapidly expanding numbers are seeking to give their children an edge by helping them become fluent in English while sparing them, and themselves, the stress of South Korea’s notorious educational pressure cooker.

More than 40,000 South Korean schoolchildren are believed to be living outside South Korea with their mothers in what experts say is an outgrowth of a new era of globalized education.

The phenomenon is the first time that South Korean parents’ famous focus on education has split wives from husbands and children from fathers. It has also upended traditional migration patterns by which men went overseas temporarily while their wives and children stayed home, straining marriages and the Confucian ideal of the traditional Korean family. The cost of maintaining two households has stretched family budgets since most wives cannot work outside South Korea because of visa restrictions.

In 2006, 29,511 children from elementary through high school level left South Korea, nearly double the number in 2004 and almost seven times the figure in 2000, according to the Korean Educational Development Institute, a research group that tracks the figures for the Ministry of Education. The figures, the latest available, did not include children accompanying parents who left South Korea to work or emigrate, and who could also be partly motivated by educational goals.

South Koreans now make up the largest group of foreign students in the United States (more than 103,000) and the second largest in New Zealand after Chinese students, according to American and New Zealand government statistics. Yet, unlike other foreign students, South Koreans tend to go overseas starting in elementary school ? in the belief that they will absorb English more easily at that age.

In New Zealand, there were 6,579 South Koreans in the country’s elementary and secondary schools in 2007, accounting for 38 percent of all foreign students.

“We talked about coming here for two years before we finally did it,” said Kim Soo-in, 39, who landed here 16 months ago with her two sons. “It was never a question of whether to do it, but when. We knew we had to do it at some point.”

Wild geese fathers were initially relatively wealthy and tended to send their families to the United States. But in the last few years, more middle-class families have been heading to less expensive destinations like Canada, Australia and New Zealand.

Now, there are also “eagle fathers,” who visit their families several times a year because they have the time and money. Those with neither, who are stuck in South Korea, are known as “penguin fathers.”

The national experience is considered enough of a social problem that an aide to South Korea’s president recently singled out the plight of the penguin fathers.

President Lee Myung-bak said he would start to address the problem by hiring 10,000 English teachers. “This is unprecedented,” he said. “Korea is actually the only country in the world undergoing such a phenomenon, which is very unfortunate.”

South Korean students routinely score at the top in international academic tests. But unhappiness over education’s financial and psychological costs is so widespread that it is often cited as a reason for the country’s low birthrate, which, at 1.26 in 2007, was one of the world’s lowest.

South Korean parents say that the schools are failing to teach not only English but also other skills crucial in an era of globalization, like creative thinking. That resonates among South Koreans, whose economy has slowed after decades of high growth and who believe they are increasingly being squeezed between the larger economies of Japan and China.

It could take years to see how well this wave of children will fare back in South Korea, especially since they are now going overseas at the elementary level. But earlier this decade, when the wild geese children tended to be high school students, many succeeded in plying their improved English scores to get into colleges in the United States or other English-speaking countries, education experts said. For others, their years overseas was a roundabout way to get into top South Korean colleges, like Yonsei University in Seoul, which increasingly offer courses or entire programs in English.

For New Zealand’s public schools, which charge foreign students annual tuition of $8,700, South Koreans provide an important source of revenue. The economic benefits have helped offset resentment toward an Asian influx that has remade many schools in Auckland, the country’s largest city, lending an Asian character to the business district and raising home prices in the wealthier suburbs.

At Remuera Primary, Ms. Kim said she believed that English fluency would increase her sons’ chances of gaining admission to selective secondary schools in South Korea and ultimately to a leading university in Seoul. Her husband, Park Il-ryang, 43, graduated from a little-known Korean university, and he said that the resulting lack of connections had hampered his own career.

Before coming here, the parents had sent one son, Jun-sung, now 10, to evening cram schools and their other son, Jun-woo, now 8, to an English preschool. Parents in their apartment building talked incessantly about their children’s education.

Even so, the sons were not making sufficient progress in English, the parents said. They hired a private English tutor to supplement the supplementary cram schools. “We didn’t think the cram schools were doing any good, but we were too insecure to stop sending them, because the other parents were sending their children,” Ms. Kim said.

At their house recently, the sons peeked through the living-room blinds to see whether their neighbor, Charles Price, was free to play. In no time, the boys were coming and going, barefoot, between the houses, carrying “Bionicle” action figures.

The parents were pleased that their sons had integrated well into the neighborhood and school, and were now even speaking English to each other. But Ms. Kim was worried that her younger son was making shockingly simple mistakes in his spoken Korean and might not form a solid “Korean identity.”

Striking the right balance would be critical to the brothers’ re-entry into South Korea, with its fierce competition to get into the best schools.

South Korean women’s rising social status and growing economic power have fueled the wild geese migration, according to education experts like Oh Ook-whan, a professor at Ehwa Womans University who has studied the separated families. Conservatives have criticized the wild geese mothers for being obsessed about their children’s education at the risk of destroying their marriages. The women’s real intention, they say, is to get as far away as possible from their mothers-in-law.

The mothers say they are the modern-day successors to one of the most famous mothers in East Asia: the mother of Mencius, the fourth-century Chinese Confucian philosopher. In a story known in South Korea, as well as China and Japan, Mencius’s mother moved to three neighborhoods before finding the environment most favorable to her son’s education.

“I don’t know why Mencius’s mother is so revered and why we wild geese mothers are so criticized,” said Chang Soo-jin, 37, who moved here with her two children nearly two years ago. “Our coming out here is exactly the same as what she did.”

Here, the English skills of her 6-year-old daughter, Amy, have improved so much that she now has the reading abilities of an 8-year-old, said her teacher at Sunderland, a small private school where all 16 foreign students come from South Korea.

Yet Amy’s father, Kevin Park, 41, was not totally convinced that the benefits had been worth splitting up the family. He had reluctantly agreed with his wife’s decision to come here with the children and then extend their stay, twice.

After his family left Seoul, Mr. Park, an engineer, moved into what South Koreans call an “officetel,” a building with small units that can be used as apartments or offices. Hearing about wild geese fathers becoming dissolute living by themselves, he stopped drinking at home.

“I’m alone, I miss my family,” Mr. Park said grimly in an interview in Seoul. “Families should live together.”

Living apart for years strains marriages and undermines the role of a father, traditionally the center of the family in South Korea’s Confucian culture, education experts and psychologists said. Some spouses have affairs; some marriages end in divorce.

“Even if there are problems, some couples choose to ignore them for the sake of their children’s education,” said Choi Yang-suk, a psychologist at Yonsei who has studied wild geese families in the United States and Canada.

Here, Park Jeong-won, 40, and her husband, Kim Yoon-seok, 45, an ophthalmologist who was here on a visit, said their marriage had grown stronger despite living apart for four and a half years. Every reunion, they said, was like a honeymoon.

But while Ms. Park said she talked to her husband a couple of hours daily by phone, she said her son and daughter never asked to talk to their father. He, in turn, never asked to talk to his children, the couple said.

“We may be a strange family,” Ms. Park said.

Dr. Kim said his own father had always been too busy with work to spend much time with the family, and on weekends woke up at 4 a.m. to play golf.

“Maybe that’s why, now that I’m a father, I have a similar relationship with my son,” he said.

Asked whether she missed her father, Ellin, 11, said: “I don’t miss him that much. I see him every year.”

“Do you think that’s enough?” her mother asked, a little surprised.

Ellin corrected herself and said she saw him twice a year.