Allen, who is now 16, had considerably less interest in computer programming. But this spring, her chemistry teacher recommended that she apply for an eight-week computer-science program with Girls Who Code, a nonprofit that teaches middle- and high-school girls programming skills. At first, Allen told me, she was skeptical; she didn't really understand what computer science was. The experience, however, got her hooked on coding, and she has even started to teach her sister how to write software. When Allen goes to college, she expects to major in the subject.

One of the biggest challenges, according to many in the industry, may be a public-image problem. Most young people, like Allen, simply don't come into contact with computer scientists and engineers in their daily lives, and they don't really understand what they do. And to the extent that Americans do, "they think of Dilbert," explains Jeffrey Wilcox, vice president of engineering at Lockheed Martin. ("Dilbert" being shorthand, of course, for boring, antisocial, cubicle-contained drudgery, conducted mostly by awkward men in short-sleeve dress shirts — a bit like "Office Space," only worse.) "I think it's just about telling our story better," Wilcox said. "We as engineers, and I'm guilty of this, we're not great storytellers."

Public narratives about a career make a difference. The most common career aspiration named on Girls Who Code applications is forensic science. Like Allen, few if any of the girls have ever met anyone in that field, but they've all watched "CSI," "Bones" or some other show in which a cool chick with great hair in a lab coat gets to use her scientific know-how to solve a crime. This so-called "CSI" effect has been credited for helping turn forensic science from a primarily male occupation into a primarily female one.

There is, of course, no pop-culture corollary for computer science. A study financed by the Geena Davis Institute on Gender in Media found that recent family films, children's shows and prime-time programs featured extraordinarily few characters with computer science or engineering occupations, and even fewer who were female. The ratio of men to women in those jobs is 14.25 to 1 in family films and 5.4 to 1 in prime time. Whenever high-ranking people in the tech industry meet, whether at the White House or a Clinton Global Initiative conference, one executive says, "we almost always walk away from the discussion having come to the conclusion we need a television show." Nearly every tech or nonprofit executive I spoke with mentioned their hope that "The Social Network" has improved the public's perception of programmers. They also mentioned how bummed they were that the hit film didn't include more prominent female characters. Meanwhile, the National Academy of Sciences now offers a program called the Sciencesand Entertainment Exchange that gives writers and producers free consultation with all kinds of scientists. Natalie Portman's character in the superhero movie "Thor," for instance, started out as a nurse. After a consultation with scientists introduced through the exchange, she became an astrophysicist.

Casting Sofia Vergara as a hacker with a heart of gold may seem an eye-roll-worthy suggestion, but the Labor Department has estimated that there will be 1.4 million job openings for computer-related occupations this decade. The skills required to fill these jobs can be imported from places like India and China, or they can be homegrown. And right now, kids are not learning about them in school. Most elementary and public schools don't teach computer science, said Cameron Wilson, the chief operating officer at Code.org, a nonprofit that advocates for greater access to computer-science education. The few that do usually only teach how to use technology (creating a PowerPoint presentation, say) rather than how to create it. There is also the issue of recruiting teachers. The median job for people with a computer-science degree pays around $80,000 to $100,000; the typical teaching salary is closer to $45,000 or $55,000.

There are skills gaps throughout sectors of our economy, particularly in health care and advanced manufacturing. But nowhere, arguably, are workers leaving more money and benefits on the table than computer science. The young girls at home watching "CSI" represent a sizable American talent pool that has yet to be tapped.