Some good research studies that support natural learning and development:

• This article indicates that there is no long term benefit to early reading interventions: Does early reading instruction help reading in the long-term? A review of empirical evidence 
• This article explains that the way schools have been teaching reading for decades is a comprehensive failure (and the implications are true across all subject areas): Why American Students Haven't Gotten Better at Reading in 20 Years
• This article shows that there is no benefit to learning to read earlier than the natural development would allow: Late Readers Close Learning Gap
• This one is heavy in the history of educational policy, but it shows that since we've been pushing reading too early in the past few decades, we've seen a tremendous decline in choice reading time in American teens and adults. Also, it shows that voluntary readers are better readers: To Read or Not to Read: A Question of National Consequence
• This article by Dr. Peter Gray is a nice summary and links to other great research about self-directed learning: A Survey of Grown Unschoolers
• This is a good research article showing just ONE positive correlation to self-directed learning: A Study on the Relationship between Self Directed Learning and Achievement in Information Technology of Students at Secondary Level