"Of course when CCTs [conditional cash transfers] force children back into school the children might not learn to read and might not learn to divide, but they will learn an important, if tragic, life lesson: when you are poor the state has power and you do not." from Lant Pritchett posting at the World Bank's Development Blog
The post is a good read. In short he talks about some survey data that early 1900s kids working in factories preferred the factory over the school by a 4 to 1 margin. In short school was not a desirable place to be. Pritchett goes on to talk about how in modern India many schools lack the ability to actually improve math or reading outcome. Despite this the poorest countries adopt a solution conditional cash transfers that pay money to families but only if their children to go to school.
As I have blogged previously I'm not sure CCTs can work in all countries. In short countries where CCTs have increased schooling substantially (Mexico and Brazil) are relatively well off, while Pritchett contrasts this with the poorest regions in India, which lack the schooling infrastructure or political capacity to run such programs. Most of the research I'm aware of though suggests that unconditional cash transfer can also lead to increases in schooling, when programs are stated to be intended for children's development and money is given to the mother. For example in Malawi one of the poorest countries in the world conditional and unconditional cash transfer payment to girls have been about as equally effective.
I wonder returning to the child in early 20th century factor, if they prefer the factory because they have some autonomy over their wages. That is when they collect their payment from the factory they get to spend some portion of it. One difference between the Malawi programs and most of the others I have seen is the payment were made directly to the girls as opposed to their mothers.