But high education costs coincide with slower growth of the Chinese economy and surging unemployment among recent college graduates. Whether young people like Ms. Wu find jobs on graduation that allow them to earn a living, much less support their parents, could test China’s ability to maintain rapid economic growth and preserve political and social stability in the years ahead。

　　Leaving the Village

　　The ancient village of Mu Zhu Ba is perched on a tree-covered crag overlooking a steep-sided mountain gorge in southwestern Shaanxi province, deep in China’s interior, 900 miles southwest of Beijing. The few scarce acres of flat land next to a stream on the valley floor were reserved until recently for garden-size plots of rice, corn and vegetables。

　　Villagers were subsistence farmers. Every adult and all but the youngest children worked from dawn to dusk, planting, weeding, hand-watering and harvesting rice, corn and vegetables to feed themselves. They also built and maintained three-foot-wide terraces where the sides of the valley began to curve upward before turning into vertiginous, forested slopes that soared into the clouds。

　　The relentless work left little opportunity for education. Mrs. Cao, now 39, learned to read some Chinese characters at first- and second-grade classes conducted in her village. But later grades were taught at a school in a larger village at the other end of the valley, a seven-mile walk away, and Mrs. Cao dropped out in third grade。

　　Her husband, now 43, grew up in a similarly poor village on the other side of the mountain and did not attend school at all。

　　They married early, and Mrs. Cao had just turned 20 when she gave birth to Ms. Wu. The couple earned just $25 a month. As their baby grew into a toddler, they began worrying that she would inevitably drop out of school early if she had to walk so far to classes every day. So like hundreds of millions of other Chinese over the last two decades, they decided to leave their ancestral village and their families。

　　“All the parents in the village want their children to go to college, because only knowledge changes your fate,” Mrs. Cao said。

　　By the time Ms. Wu reached middle school, the crystalline mountain air of Mu Zhu Ba was a dim memory. The family had moved to Hanjing, a coal mining community on the plains of northern Shaanxi province, nearly 300 miles northeast of their ancestral village。

　　A Coal Miner’s Daughter

　　Mr. Wu built the family’s two-room brick house himself. They bought their first small refrigerator, a coal stove and a used stereo, and a bare light bulb for the living room and another for the bedroom。

　　The house, on the town’s rural outskirts, was across a two-lane paved road from a small coal mine where Mr. Wu learned to maneuver a shoulder-carried, 45-pound electric drill in narrow spaces far under the earth, working long shifts and coming home covered with coal dust. He earned nearly $200 a month then, providing more money to educate their daughter. In the family bedroom, where calendar posters of the actress Zhang Ziyi had been plastered on the wall for extra insulation, Mrs. Cao carefully kept all of her daughter’s school papers. Wu Caoying was in seventh grade, but her village school was already teaching her geometry and algebra at a level beyond most American seventh graders. She was also studying geography, history and science, filling homework notebooks with elegant penmanship。

　　The problem was English, an increasingly important subject for students who wanted to qualify for anything but the worst universities。

　　The village had an English teacher, and Ms. Wu started learning the language in fourth grade. But then the teacher left, so she was not able to study English during fifth and sixth grade。

　　Ms. Wu resumed English classes in the seventh grade, but her mother was concerned and began hiring substitute teachers as English tutors for her daughter。

　　Mrs. Cao said that she was convinced that this would help her daughter become the first in the family to attend college. “If we had not come here, she would have needed to stay home, to help cook and cut wood,” Mrs. Cao said。

　　But their financial sacrifices were only beginning。

　　For high school, Wu Caoying began attending a government-run boarding school two miles from the family’s house. Many high schools in China are boarding schools, an arrangement that allows local governments to impose hefty fees on parents. Tuition was $165 a semester. Food was $8 a week. Books, tutorials and exam fees were all extra。

　　Boarding School

　　Ms. Wu and seven other teenage girls had bunk beds in a cramped dormitory room. She dressed better than the other girls, in a tight blue coat her mother had just given her for Chinese New Year。

　　She woke at 5:30 every morning to study, had breakfast at 7:30, then attended classes from 8:30 a.m. to 12:30, 1:30 to 5:30 in the afternoon and 7:30 to 10:30 in the evening. For entertainment, there were occasional showings of patriotic movies. She studied part of the day on Saturdays and Sundays. But she also joined a volunteer group that visited the elderly — social work that might help on a college application in the United States but not in China, where the national entrance exam for universities is all-important。

　　Mr. Wu no longer worked at the coal mine across the street, which had been closed because of a combination of safety regulators’ concerns and depletion of the coal seam. He had become a migrant once more, taking a job 13 hours away by train at a coal mine in a northern desert. Mr. Wu worked 10-hour shifts up to 30 consecutive days. Safety standards were lower at the new mine, in an industry that kills thousands of Chinese miners in industrial accidents each year and maims many more。

　　The new job, however, allowed Mr. Wu to double his income, and he brought back his pay every two months to his wife to pay for their daughter’s education。

　　Their main worry was their daughter’s academic performance; they thought she did not study hard enough. “She likes to talk to boys, although she doesn’t have a boyfriend,” Mrs. Cao said。

　　Their daughter ranked 16th in her class of 40, respectable but not good enough in their eyes. But they despaired of being able to help Ms. Wu when she came home on weekends. “We just have an elementary school education. We don’t really know what she’s studying,” Mrs. Cao acknowledged。

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