What and how much can children learn without subject teachers? In an attempt to find a limit to self organized learning, we explored the capacity of 10-14 year old Tamil-speaking children in a remote Indian village to learn basic molecular biology, initially on their own with a Hole-in-the-Wall public computer facility, and later with the help of a mediator without knowledge of this subject. We then compared these learning outcomes with those of similarly-aged children at a nearby average-below average performing state government school who were not fluent in English but were taught this subject and another group of children at a high-performing private school in New Delhi who were fluent in English and had been taught this subject by qualified teachers. We found that the village children who only had access to computers and Internet-based resources in the Hole-in-the-Wall learning stations achieved test scores comparable with those at the local state school and, with the support of the mediator, equal to their peers in the privileged private urban school. Further experiments were conducted with unsupervised groups of 8-12 year-olds in several English schools using the Internet to study for GCSE questions they normally would be examined on at the age of 16. We conclude that, in spite of some limitations, there are opportunities for self-organised and mediated learning by children in settings where they would otherwise be denied opportunities for good, or indeed any, schooling. We also show that this approach can be enhanced by the use of local or online mediators.