KQED News Mind/Shift – Claudia Wallis 
A teacher stands at a white board in front of her fourth-grade class and begins teaching one of math’s most fundamental concepts: the meaning of an equal sign in the middle of an equation. This is not easy. Young students tend to think of the equal sign as the endpoint of a problem. Now, instead of the usual 8 + 4 = ?, they are asked to ponder 8 + 4 = ? + 6. Mastering this concept will open the door to algebra and higher math. Almost any teacher giving this lesson will instinctively move her hands in predictable ways, pointing to the equal sign, sweeping her hand toward the left side of the equation and then sweeping it toward the right. She might hold both hands palms-up in a balancing gesture to suggest equivalency. (more)