Reining in corruption has been the main focus of China's new president, Xi Jinping. But such campaigns are barely making a dent, critics say, in a country where children are shown as early as elementary school how to play the system.

Almost everything, from admission to grades to teacher recommendations, is negotiable in mainland schools if you know the right person or have enough cash, parents and teachers say. As a result, many believe, the education system is worsening rather than mending the vast gap between the elite and everyone else.

As middle-class parents in Haidian, one of Beijing's most competitive school districts, Yang, 42, and her husband had some money but few connections to help their daughter get into an elite school.

Then, this summer, a dance teacher pulled Yang aside. He said he knew people at the middle school her daughter had been aiming all her efforts at attending. And suddenly, Yang admits, she started looking into how much of their savings she and her husband could cobble together if the dance teacher's friends were to ask for compensation. She still hasn't decided what to do.

Their dilemma, she says, boils down to this: "If everyone else is playing the game, how can I refuse?"

In the cities, the best schools are the public ones.

Private schools are often aimed either at foreign expats or children barred from city schools, such as the offspring of low-income migrant workers.

Even by Western standards, the top public schools are often astounding. During a recent tour of Beijing's Jingshan School, administrators showed off a US$326,000, one-storey-high telescope for astronomy lessons, housed in a rotating room with a retractable ceiling; flat-screen televisions in every class; pricey computer labs; an Olympic-size pool; and a state-of-the-art hydroponics garden.

The school recently began requiring doctorate degrees for all upper-grade teachers.

Meanwhile, just a few kilometres away, at a private school for migrant families, children walked off a dirt road into a ramshackle facility with cracked walls, overcrowded classes and a single bathroom consisting of cement holes in the ground.

An intense competition has developed among parents to win admission for their offspring to the best schools.

Academic performance still matters greatly. And like many students, Yang's 12-year-old daughter, Ma Qianyi, has spent every night over the past three years, even on weekends and vacations, attending expensive cram classes.

But she is the first to admit that she does not work hard compared with her peers.

The hyper-competitiveness has driven many parents to curry favour in any way possible - delivering organic rice to a teacher worried about food safety, bringing back lavish gifts from abroad. When all else fails, store gift cards are always a safe bet.

"Sometimes, you open these cards on National Teacher's Day and find crazy amounts inside," one Beijing teacher says.

Such gifts, several parents explain, can lead to more attention for a struggling student, extra praise for gifted ones or even a seat closer to the front of the classroom.

"It's human nature," says one parent, who regularly sends her son to school with gift cards.

Like many adults interviewed for this story, she asked for anonymity to talk frankly about school corruption. "If the teacher is choosing between two kids on equal footing, the effect of a gift may be small, but it could make all the difference."

Yang used to send gift cards, too, worth US$20 or US$30 - modest in comparison to the US$200 or US$300 from other families. But she eventually stopped even that.

"It didn't seem to make a difference," she says. "I decided to save the money for things that actually contribute to my daughter's education, like cram classes."

The decision left her daughter uncomfortable and even bitter at times.

Her mother recalls the time in second grade when Qianyi lost out on a top award. "My daughter said to me: 'The teacher chose that girl because her mother was smart and gave medicine to the teacher when she was sick.' She asked me: 'Why didn't you give any medicine?'"

The question has haunted Yang, with her daughter finishing elementary school in the spring.

Getting into a good middle school means a shot at Beijing's top high schools. A top high school means proper preparation for the mainland's infamously rigorous college admissions exam, called the gaokao. A good gaokao score means a secure job, higher income, better housing, better marriage prospects.

Education in this communist country is supposedly free and funded by the government. But elite schools benefit from hefty fees and donations.

These days, admission to a decent Beijing middle school often requires payments and bribes of upwards of US$16,000, according to many parents. Six-figure sums are not unheard of.

In theory, middle school admissions are guided by where children live, but independent studies have shown that only half the students at Beijing's top public schools are chosen in that manner.

Instead, getting in often comes down to three things: talent, money and relationships, particularly ties with government or party officials.

"If you know someone, you pay a lot less," says a mother in Beijing's Chaoyang district.

Some payoffs have become semi-legal. Many government ministries and state-owned companies reserve seats for children of their employees through large donations to schools.

And most top schools charge a "school choice fee" - ranging from US$5,000 to US$40,000 - for children living outside specific school districts.

The central government has repeatedly banned such fees. But they have not only remained, they've risen in recent years. Lacking the resources of wealthier, better-connected families, Yang and her daughter decided early on to target seats reserved at most top schools for those with "speciality skills". That's why Qianyi took up dancing three years ago. "It's the only thing I'm good at," she says matter-of-factly while wolfing down noodles before a lesson.

The dance instruction has cost Yang US$5,000 in the past six months alone - a huge strain for a woman who earns US$20,000 a year and whose husband is unemployed.

But schools' evaluations of such skills have also proven susceptible to corruption.

A parent in Yang's district who was approached for bribes by a coach explains it this way: "Just because your child wins first place in a race doesn't mean he has the best chance. The school can choose the third- or even fourth-place child and simply say they have more potential."

Yang was shocked when her daughter's dancing teacher offered to help. Even now, she wonders whether his offer came from greed or genuine recognition of her daughter's talent. As she waited outside the dance studio on a recent night, she weighed their options.

Neither Yang nor her husband attended college, although she did finish vocational high school. After graduating, she managed to start her own company with a friend, selling imported sensors.

Today's China, however, is a different country from that of her youth, exponentially more competitive. Millions compete in megacities for limited jobs, housing and mates.

Yang says she has struggled to define guiding principles for herself, even as she tries to teach life lessons to her daughter.

"I want her to be able to see this society for what it is - one that is full of wolves," Yang says. "But I don't necessarily want her to be either wolf or sheep."

Yang says she is beginning to see the dancing teacher's offer less as a moral dilemma and more as a purely practical decision. "The system, the pressure, the bribes, it's all unfair," she says. "But in the end, the only thing I can do is what's best for my daughter."