Hi. I know you're referring to Duke's Talent Identification Program for gifted kids, www.tip.duke.edu/
My son was invited to participate in a similar program at another nationally recognized university, but he wasn't keen on a live-away camp at the time. Instead, he did participate in some Mon-Fri. enrichment programs at a local college, and I think he enjoyed both the variety of "non-traditional classes" as well as meeting other bright kids who shared similar interests. Those were definite plusses.
As far as long-term benefits, they're harder to quantify. Truthfully, my son is in college now, and we didn't even think to include those elementary school G/T program experiences on his college applications, because there were more recent high school academic and extracurricular activities. Perhaps Duke's program is different, and there might be more long-term benefits. With girls, more lasting friendships might be made by meeting and interacting with other bright females. I'm surprised they (Duke) can't give you names of past participants from your area, so you can talk directly to those families.
No matter what, you might like to join Greatschools Gifted Group at community.greatschools.net/groups/11537
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