WASHINGTON — President Obama’s top technology adviser cringes when she hears highly educated adults say how bad they are at science and math, particularly when they do so in front of children.

“That has to change,” the adviser, Megan J. Smith, firmly told a group of teachers at the White House not long ago. “We would never say that about reading.”

Ms. Smith, 50, an M.I.T.-trained mechanical engineer and former Google executive, is working hard to bring her Silicon Valley sensibility to the Obama administration. But four months into her job as the chief technology officer of the United States, the woman whose division at Google dreamed up Google Glass and the driverless car is facing culture shock in a federal bureaucracy ruled by creaky technology and run in part on the floppy disk.

Not only does she now carry a BlackBerry, she uses a 2013 Dell laptop: new by government standards, but clunky enough compared with the cutting-edge devices of her former life that her young son asked what it was.