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Some folks in Silicon Valley and elsewhere say a conventional education can't possibly give kids with outsize talents what they need. Others, like Vivek Wadhwa, a fellow at Stanford Law School who teaches and advises startup companies, say dropping out to pursue a dream is like "buying a lottery ticket — that's how good your odds are here. More likely than not, you will become unemployed. For every success, there are 100,000 failures."

Instead of teaching specific skills that may only be useful in specific areas, Lumosity targets core cognitive processes that underlie performance in many different areas. These processes include memory, attention and other abilities that are critical in the real world.

By the time the 15 minutes were up, they had spent only about 65 percent of the observation period actually doing their schoolwork.

Attending to multiple streams of information and entertainment while studying, doing homework, or even sitting in class has become common behavior among young people—so common that many of them rarely write a paper or complete a problem set any other way.

o detrimental is this practice that some researchers are proposing that a new prerequisite for academic and even professional success—the new marshmallow test of self-discipline—is the ability to resist a blinking inbox or a buzzing phone.