Maybe we should read the primary source--Abhijit Banerjee and Esther Duflo's paper--instead of relying on an OP-ED:
This low level of expenditure on education is not because the children are out of school. In 12 of the 13 countries in our sample, with the exception of Cote d’Ivoire, at least 50 percent of both boys and girls aged 7 to 12 in extremely poor households are in school. In about half the countries, the proportion enrolled is greater than 75 per cent among girls, and more than 80 percent among boys.
The reason spending is low is that children in poor households typically attend public schools or other schools that do not charge a fee. In countries where poor households spend more on education, it is typically because government schools have fees (as in Indonesia and Cote d’Ivoire). What they are doing might therefore be perfectly sensible, given that this is the reason why public education exists. The one concern comes from the mounting evidence, reported below, that public schools are often dysfunctional: This could be the reason why even very poor parents in Pakistan are pulling their children out of public schools and spending money to send them to private schools.
One reason is that poor parents, who may often be illiterate themselves, may have a hard time recognizing that their children are not learning much. One survey shows that poor parents in Eastern Uttar Pradesh in India have limited success in predicting whether their school-age children can read (Banerjee et al., 2005). Moreover, how can parents be confident that a private school would offer a better education, given that the teacher there is usually less qualified than the public school teachers? After all, researchers have only discovered this pattern in the last few years. As for putting pressure on the government, it is not clear that the average villager would know how to organize and do so.
So the question becomes: given that a significant percentage of these children are attending school (many for free), the poor quality of (and, presumably, often lack of access to) private for-fee schools, the poor ability of uneducated poor parents to assess the quality of education their children receive or organize to pressure the government to improve education, would a poor family saving less than an extra nickle a day (to potentially spend on education instead of alcohol and tobacco) make any meaningful difference in educating their six children?
It may also be of interest to note that, according to January 2012's CPI report
the average American household only spend 3.2% on education/child care