continuous partial attention
n. A state in which most of one's attention is on a primary task, but where one is also monitoring several background tasks just in case something more important or interesting comes up.
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One of the most interesting talks came from a former Apple and Microsoft executive named Linda Stone. Her emphasis was less economic than social. It was a plea to consider an epidemic she identified as continuous partial attention (CPA).

She couldn't have picked a more perfect audience. During the presentations, the faces of at least half the crowd were lit with the spooky reflection of the laptops open before them. Those without computers would periodically bow their heads to the palmtop shrine of the BlackBerry. Every speaker was competing with the distractions of e-mail, instant messaging, Web surfing, online bill paying, blogging and an Internet chat "back channel" where conferencees supplied snarky commentary on the speakers. Stone nailed the behaviour so precisely that some audience members actually raised their faces and started listening intently.
—Steven Levy, “(Some) Attention Must Be Paid!,” Newsweek, March 27, 2006
Continuous partial attention is that state most of us enter when we're in front of a computer screen, or trying to check out at the grocery store with a cellphone pressed to an ear — or blogging the proceedings of a conference while it's underway. We're aware of several things at once, shifting our attention to whatever's most urgent — perhaps the chime of incoming e-mail, or the beep that indicates the cellphone is low on juice. It's not a reflective state.
—Scott Kirsner, “Are your feeds turning into too many long tails? Filter!,” The Boston Globe, June 27, 2005
2001 (earliest)
The Davos World Economic Forum is always useful for gauging global trends. … My favorite, though, was that we now live in an age of what a Microsoft researcher, Linda Stone, called continuous partial attention. I love that phrase. It means that while you are answering your e-mail and talking to your kid, your cell phone rings and you have a conversation. You are now involved in a continuous flow of interactions in which you can only partially concentrate on each.
—Thomas L. Friedman, “Cyber-Serfdom,” The New York Times, January 30, 2001
Linda Stone, a Microsoft researcher, coined the phrase continuous partial attention in 1998.