There is a definite and tangible link between independence and risk-taking. It depends hghly on the subject-area/domain, the nature of activity/experimentation involved, the range of possibilities in terms of consequences and the policies and infrastructure in place. In general, it helps to do a risk-assessnment analysis conducted by a subject-area expert and students should be actively involved in this process so as to make this process as democratic as possible, but also so that they can assume ownership for what they do. The spirit of innovation relies on courage and risk-taking abilities but these risks are ideally calcuted ones, and with back up alternatives that guarantee some degree of control and safety. Fundamental content knowledge is also an essential pre-requisite before application/implemetation procedures can be tried out. At the core of it all, the learning environment should instil a sense of optimism in its students where caution has its place but does not interfere with the willingness to try. The only people who never fail are the ones that never try.

I agree in all Monica’s answer and I would add some more ideas. When we are talking about risky play we should differentiate it from hazard because this second concept refers to those things that children can’t control and usually are out from those things that they can understand in their risky games. When the adult is aware of the hazards, he/she can give scaffolding to the risky play which is going to give benefits to psychological, physical, emotional and social domains. Researchers have shown that global effects. The more risk is involving the game, the more enjoy, pleasure and self-confidence is it going to give to children. It is shown that risky pay is losing importance day by day in the modern western societies as we are avoiding outdoors and free children’s play. In my opinion it is interesting to note that the possibility to offer risky play to children is related to the adult self-confidence and his/her capacity to contain his/her emotions and fears. I strongly recommend to read from risky play with the Norwegian researcher Ellen Sandseter. You can find her papers easily on internet.

Tim Gill's book, No Fear - Growing Up in a Risk Averse Society has a lot to say on this subject. PDF available via link.

http://www.gulbenkian.org.uk/pdffiles/--item-1266-223-No-fear-19-12-07.pdf