Until recently, each journey meant either a two-hour round trip to the river valley, or a hike to a dribbling spring at the top of a nearby hill where she would have to queue for her turn, often late into the night. Fatima, like most of the girls in the area, has never been spared from these labours to go to school.
The difficulty of obtaining water has blighted the lives of the girls and women in the mountain villages in this area for decades. "In the past, girls from other villages did not want to marry into our village because there was no water," said Ma Quanshan, a 32-year-old teacher. Even when the water was finally carried to the village, it was muddy and contaminated with animal excrement.
Two months ago all this changed for Dabang, the result of local people who decided something had to be done, and the donation of pounds 117 from the little-known British Partnership Scheme. Not a penny was allowed near the local government officials down in the valley; nor did any expensive foreign consultants appear on the books.
The money paid for the materials and the skilled labour to construct a "water-box", a utilitarian concrete container, over a previously buried natural spring. Every family sent someone to help, and this small amount of carefully-targeted money has transformed the life of the village. Inside the water-box is a permanent supply of hundreds of gallons of clean drinking water, just a 20-minute round-trip from Dabang. Teacher Ma's wife grinned: "It saves me an hour and a half for each trip. At the top of the mountain we used to have to wait for a long time, but now the water is ready waiting for us."
It was the simplest of ideas, and it worked. In all, by the end of this autumn, pounds 1,800 of British aid money will have built 15 such water-boxes in these hills, bringing convenient water to 1,100 villagers. The question is why it took until 1997 and needed British money to happen.
Dabang village, in the eastern part of Qinghai province, is one of the poorest in China. The region has a high proportion of minority nationalities, mainly Muslim Hui and Buddhist Monguor people. The mountain villagers exist at subsistence level; Dabang's adobe mud houses are heated by burning straw in the winter, when temperatures can fall to -20C, the harvests are regularly hit by lack of rain, and electricity did not arrive until 1990. The village has yet to acquire a television.
The status of women is particularly diminished by a reluctance to "waste" money educating girls who will "marry out". In Dabang village primary school, for instance, only two of 20 pupils are girls; by law, all girls should be in school.
But the reason that little has changed in these villages after two decades of Chinese economic reform has just as much to do with the culture of Chinese government and the helplessness which these illiterate villagers feel in the face of corrupt cadres. Qinghai is poor, but not poor enough to stop 15 provincial officials going on a two-week "inspection tour" of Israel and Egypt this summer. (There is, incidentally, no foreign investment or trade link with Egypt, and no likelihood of any.) The next scheduled provincial inspection tour will be to Japan.
Dabang is remote, but not that remote. It is a one-hour hike from the main road in the valley, up a hilly path. Yet not one senior official from the Zhongchuan township government in the valley, let alone anyone from the Minhe county government, has come to see what living conditions are like in the villages over which they have jurisdiction.
One old villager, whom it would be unwise to name, said: "The township governor and the party secretary have not visited here for three years. In the past, the old governor came here regularly." Another added: "This is the poorest sort of place. Transportation is poor, so they cannot come by car. So they don't come." They don't care, he could have added.
This newspaper's experience says it all. Arrival in Minhe county capital immediately prompted the appearance of three cadres who ordered huge amounts of food which this paper refused to pay for. One was despatched to accompany me, and on arrival at Zhongchuan township, a veteran local figure, who has held one or other senior township position for the past three decades, ordered and started munching his way through large plates of mutton - safe in the knowledge that the foreign journalist would pick up the bill.
The next day, as we set off up the mountain, there were no township officials in sight, and the Minhe minder decided that he could not, after all, face the walk up to the villages.
On arrival in Dabang, the warmest of welcomes and two-hours of non-stop cooking was laid on in thanks for the British money and the water-box, regardless of who the British visitor was. "It's really a good thing! Before, the water was dirty water. Now it is clean water," said Ma Sane, 30, whose 11-year-old daughter has been fetching the water for two years.
No township official has yet bothered to turn up for an official "opening" of a water-box. When we returned to the valley at the end of the day, the main comment from the Minhe cadre was that it would be a far, far better thing if the British money could in future be channelled instead through Minhe county government - a change that the British will not be making.