Godslove Ampah (right), with math teacher Tonya Howard: “Whenever I look at an equation, I just want to use my brain to figure it out.” Credit: Maya McFadden photos Time to math! The standard ...

This summer, battle lines were drawn over a simple math problem: 8 ÷ 2(2 + 2) = ? If you divide 8 by 2 first, you get 16, but if you multiply 2 by (2 + 2) first, you get 1. So, which answer is right?

Children as young as 4 years old are capable of finding efficient solutions to complex problems, such as independently inventing sorting algorithms developed by computer scientists. The scientists ...