One scheme paid parents to learn how to support their children with their schoolwork. Another even encouraged mothers who were reluctant to breastfeed by giving them shopping vouchers.
Now a new project plans to hand parents money to spend on whatever they want, to see if it makes their children cleverer.
US researchers plan to give parents of newborn babies $12,000 (pound;7,400) over three years, to test the theory that family income is a key factor in progress in the early years. When the children reach the age of 3, their development will be measured, as well as electrical activity within their brains.
In a paper outlining the project, researchers say that the figure of $4,000 a year was chosen because previous research suggested that it would produce changes in children's development.
"Our study will provide definitive evidence on the extent to which young children's cognitive development and health is affected by income reductions or enhanced by income increases - or whether income itself does not matter at all," they write.
Project leader Professor Greg Duncan, from the School of Education at the University of California, Irvine, said: "In the last 20 years we have come to understand more from neuroscience about the amazing things that take place in the early years and how vulnerable children are to environmental problems that might affect the efficiency of their brains."
The proposed research would involve 1,000 children. Half the participating parents would be given $333 a month and the other half would receive a nominal payment of just $20 a month.
At the end of three years, the researchers intend to measure electrical activity in the children's brains using an electroencephalography (EEG) test, as well as assessing their vocabulary, memory, and social and emotional development.
If the full $15 million study goes ahead, the families involved will be drawn from seven different areas in the US.
Existing research already shows that the gap between children living in poverty and their peers is apparent by the time they start school. In England, figures released by the Department for Education last week show that just 36 per cent of four- and five-year-olds who are eligible for free school meals have reached a "good level of development", compared with 55 per cent of other students.
Chris Goulden, head of the poverty team at the UK's Joseph Rowntree Foundation, which researches and campaigns on social issues, said: "There is still a lot we don't know about the relationships between incomes and improved life chances for children, but there is little doubt that when it comes to improving the outcomes of children living in poverty, money really does matter.
"More income enables parents to invest more in their children's development and, to some extent, avoid the stresses associated with living in poverty. Income also has an indirect effect on children through improvements to the home environment, maternal mental health and parenting behaviour."
Mr Goulden added that in a review of 34 studies across different nations looking at the causal relationship between money and outcomes for children, 29 found that money had a positive direct effect.
The US project has been welcomed by teachers' representatives, although there has been some scepticism about the impact of giving parents money. Russell Hobby, general secretary of the NAHT union in the UK, which represents the majority of primary school leaders, said he thought that the income effect was "probably partial".
"It's not necessarily just a lack of money but what has caused that lack of money," he added.
Professor Duncan has been awarded the Klaus J Jacobs Research Prize, worth 1 million Swiss francs (pound;680,000), to fund a 12-month pilot. Due to start in January 2014 in New York, it will recruit 25 mothers.