We learn best when we’re interested in what we’re learning about. In a standards based classroom, however, it’s difficult to authorize science research about nuclear power plants when the science standards cover the parts of a plant. Rather than let students loose completely, consider giving them freedom within your grade-level curriculum. Allow students to generate questions and use those questions to drive your instruction.
Do you give your gifted students room to explore personal interests? Google does. In fact they demand it. At Google, employees are expected to spend 20% of their time at work (that’s paid time) developing a project outside of their job description. This works out to one day per week spent on an independent activity.