Early on a drab afternoon in January, a dozen third graders from the working-class suburb of Chicago Heights, Ill., burst into the Mac Lab on the ground floor of Washington-McKinley School in a blur of blue pants, blue vests and white shirts. Minutes later, they were hunkered down in front of the Apple computers lining the room’s perimeter, hoping to do what was, until recently, considered impossible: increase their intelligence through training. “Can somebody raise their hand,” asked Kate Wulfson, the instructor, “and explain to me how you get points?” On each of the children’s monitors, there was a cartoon...