A group of students in a high school gym hovers over a remote controlled robot while it shoots basketballs from the free throw line with better precision than Dwight Howard. They built and programmed the robot themselves, and it won first prize in a global robotics competition.

In a classroom nearby, other students are studying leeches recently used in microsurgery to reattach a severed hand.

And down the hall, a third group of students is working on a team building exercise—competing against each other to build the tallest tower using nothing more than marshmallows and toothpicks. "We need to break these right here," says one student, as the exercise tests their communication skills and math. (Read More:Broken Education System To 'Destroy Everything' If Not Fixed: Langone)