Henderson distributed paper copies of the empty cube logo, urging the audience of kids from San Francisco, Minneapolis, Philadelphia, and other cities to fill the blank space with words that describe their own Third Space.
Their thoughts were captured in a word cloud, laden with upbeat nouns such as peace, laughter, and friends. The presentation earned the East Camden duo, both 14, a standing ovation.
Two weeks after their return from Colorado, I meet Miller and Henderson in the cafeteria at East Camden Middle, where both participate in the EducationWorks after-school and summer enrichment program.
EducationWorks is funded through a federal grant and serves about 400 students at East Camden Middle, Woodrow Wilson High School, and the McGraw and Cramer Elementary Schools. It aims to broaden horizons, develop character, and help students build leadership, collaboration, and other skills.
A letter Williams wrote last fall to Chase V. Miller, the EducationWorks middle school coordinator, provided the inspiration for The Third Space.
"Vaughn had some behavioral and academic issues," Miller says.
"I was pretty hyper," Williams says, laughing.
"Vaughn talked in the letter about sometimes he breaks, but how we all put him back together again because there are so many positive individuals in this space," Miller continues. "The letter was a window into how our program works for kids."
Miller thought of the letter again this year when he got an invitation from the Youth Development Institute, seeking students to speak at the national conference using the popular "TED Talk" format.
"He told me about the third space, and I did some research," Williams says. He became familiar with sociologist Ray Oldenburg's book The Great Good Place, which talks about the importance of informal social gathering places outside of home and work.
The more Williams thought about it, he realized that a person's third space can be a mental, as well as a physical, locale.
"My third space is EducationWorks," he says. "No one gives up on you in EW."
Miller and Williams put together a video in collaboration with Philadelphia filmmaker Mike Dennis. It won Vaughn a slot at the conference.
"We've used this video to show what productive youth-adult partnerships look like," says Sarah Zeller-Berkman, director of community youth development.
Williams began collaborating with Henderson, and soon his friend was officially on board to help develop the presentation, Miller says.
"They put a lot of hard work into this," he adds. "They gave up lunch period! They did this for a city that doesn't get as much recognition as it should, for a school that doesn't get as much attention as it should."
He had Williams memorize "great pieces of oratory"; Henderson studied TED Talks on YouTube to pick up pointers on how to engage audiences.
"They were representing Camden, and they were very aware of the bad rap Camden gets and the bad rap the school district has been dealing with," says EducationWorks director Bianca M. White.
I've seen a rough video cut of the presentation; Williams and Henderson do themselves, their city, and their "third space" proud.