THE propaganda message, scrawled in white paint on the side of a wood-frame house, could hardly be more blunt: “Cure stupidity, cure poverty”. The cure for both, in one of China’s poorest counties, seems to be a daily nutritional supplement for children. At a pre-school centre in Songjia, as in more than 600 other poor villages across China, children aged three to six gather to get the stuff with their lunch. If China is to narrow its urban-rural divide, thousands more villages will need to do this much, or more. Widespread malnutrition still threatens to hold back a generation of rural Chinese.

China used to have more undernourished people than anywhere in the world except India: about 300m, or 30% of the population in 1980. Economic growth has pulled half of them out of poverty and hunger. But that still leaves about 150m, mainly in the countryside. Out of 88m children aged six to 15 in the poorest rural areas, around a third suffer from anaemia because of a lack of iron, according to survey data. Iron deficiency can stunt brain development, meaning many of these children will grow up ill-equipped to better their lot. “They are far behind compared with urban kids,” says Lu Mai, secretary-general of China Development Research Foundation (CDRF), a government-run charity. Mr Lu and other experts have been prodding the government to do more. The state subsidises school lunches for 23m children in the 680 poorest counties, as well as nutritional supplements for hundreds of thousands of babies. It is not enough.

Even where children get the calories they need—as most do in rural China—they are not being fed the right things. In one study of 1,800 infants in rural Shaanxi province in China’s north-west, 49% were anaemic and 40% were significantly hampered in developing either cognitive or motor skills. Fewer than one in ten were stunted or wasting, meaning that in most cases the problem was not lack of calories, but lack of nutrients.

China shares this affliction with much of the developing world. But it has the resources to respond. Parents have the means to feed their babies properly. And with a relatively modest investment, the government could do a better job of improving childhood nutrition. The difficulties lie in educating parents—and officials.

“Babies are probably 50% malnourished” in poor rural areas, says Scott Rozelle, co-director of the Rural Education Action Programme (REAP), a research outfit at Stanford University which has done extensive tests on anaemia in rural China. “But almost no mums are malnourished.” Mr Rozelle says that in one of his surveys rural mothers showed a better understanding of how to feed pigs than babies: 71% said pigs need micronutrients, whereas only 20% said babies need them.

Mr Lu’s charity and REAP argue that a nutritional supplement called ying yang bao should be available to rural mothers. A powdery concoction of soyabeans, iron, zinc, calcium and vitamins, it is supposed to be sprinkled on food once a day. Each packet costs less than one yuan (16 cents) to produce and one yuan to distribute, paid by the government.

Trials conducted since 2006 have consistently shown that ying yang bao reduces anaemia and improves growth and development in infants and toddlers. But persuading parents of this (or grandparents, if the parents are off working in cities) has not been easy. About half give up feeding it to their children. “Poor people feel very suspicious”, Mr Lu says. They wonder if free supplements are unsafe, or fake. “Then they worry will we charge later?”

This may be the legacy in rural China of years of seeing government invest little—and often charge a lot—for basic services. Moreover, at the local level the workers who are meant to help mothers may well be family-planning officials responsible for controlling population, a role that hardly inspires trust.

At higher levels of government, too, officials need a lot of persuading that nutrition programmes are not a waste of public money. In 2011 China began instituting a programme similar to America’s federal school-lunch programme for the poor, at a cost of 16 billion yuan ($2.6 billion) a year. But one assessment suggests that perhaps half the schools are providing substandard, uncooked meals, partly because some local governments refuse to foot the bill for kitchens and cooks.

In 2012 the health ministry made a modest investment of 100m yuan to provide supplements to 270,000 babies in 100 counties. This year 400,000 babies in 300 counties are meant to get them. Later this year Mr Lu’s charity will begin a tiny pilot of an early-parenting programme, akin to America’s Head Start, in 50 villages, with 50 more villages being used for controlled comparison. James Heckman, an economist and Nobel laureate who has researched early-childhood development, is helping design the study. Such programmes look promising. But they are tiny.

Part of the problem in getting local or provincial governments to spend money on childhood nutrition is that the payoffs are years in the making. And the returns might not go to the village or province, but to cities miles away, in the form of more skilled workers who move there. Central ministries are keen to invest, Mr Lu says, but they want to spend their cash on things that officials crave more than children do—like buildings in villages for each ministry.

For Mr Lu one kind of building does promise a big payoff—village early-education centres, or preschools. His charity has set them up in 677 villages, often using redundant elementary schools. In Songjia village Tian Lin, 22, and her older sister, Tian Hongjiao, teach 26 children aged three to six, including the younger sister’s own three-year-old son. They cook lunch with whatever the children bring from home. Those with migrant-worker parents, who are a bit better off, may have a chunk of pork; others bring a meagre potato or vegetable. Either way all the children get a ying yang bao with their lunch.

In 2012 a study found the anaemia rate among the three- to five-year-olds in this county was close to 18%, more than twice the average for poor rural areas nationwide, according to Mr Lu’s CDRF. He reckons that, on coming to the centres, the children show only 20% of the memory retention of their urban counterparts and 40-60% of their language abilities and cognition. But nutritional supplements help. A study of nine- and ten-year olds, co-written by Mr Rozelle, found that taking a daily chewable vitamin with iron for six months not only cut anaemia levels. It also improved their maths.