“Baby Chacha!” she crows, swiping again to encounter another treasure. “Dada!”

On the new iPhone — the one her mother actually uses — her big sister, Izzy, 4, is utterly intent on “Dora’s Ballet Adventure,” her tiny thumb tapping away at the stars and arrows.

The iPhones, loaded with 20 children’s apps and some 1,200 photographs, are among the girls’ favorite playthings. “The little one loves to go through the pictures and name who’s in them, see her grandma and her nanny,” said their mother, Tina Deutsch, a former nursery school teacher. “The older one loves the games, and taking pictures. She loves the clicking sound, and if it’s blurry, she knows how to delete it.”

As adults turn, increasingly, to mobile devices like tablets, Kindles, and iPhones, their children — even the smallest ones — are doing so as well, according to a new study, “Zero to Eight: Children’s Media Use in America, 2013” by Common Sense Media, a San Francisco-based nonprofit organization that examines children’s use of technology, and rates children’s apps, games and Web sites.

The study is based on a nationally representative Internet survey of 1,463 parents with children under 8.

Over the last two years, the shift has been drastic. Among children under 2, the survey found, 38 percent had used mobile devices like iPhones, tablets, or Kindles — the same share as children 8 and under who had used such technology in a similar survey two years ago.

Tablets, in particular, have become far more common. Forty percent of families now own tablets, up from only 8 percent two years ago. And this year’s survey found that 7 percent of the children had tablets of their own.

“I was blown away by the rapidity of the change,” said Vicky Rideout, the author of both the new report and the 2011 version. “IPhones and tablets are game changers, because they’re so easy to use. While there was some floor on how young you could go with computers and video games, a young child who can touch a picture can open an app, or swipe the screen.”

Though many parents express pride and amazement that their young children are so tech-savvy, she said, what has really happened is that technology has gotten much easier to use.

Certainly, mobile devices are more convenient than traditional technology, whether for a parent’s own use or for distracting a fussy child in a restaurant.

“I know if I need Zoe to be quiet for an hour, I can hand her the iPad and I won’t hear from her,” said Dr. Laurel Glaser, a Philadelphia physician with two daughters, Zoe, 5, and Maya, 1,

Dr. Glaser was one of the few parents interviewed who said she tried to follow the American Academy of Pediatrics’ recommendation that children under 2 should have no screen time.

“I’m not superstrict and sometimes we have the television on and both girls see it,” she said. “But we don’t have any baby apps for Maya.”

Mostly, the group’s recommendation is ignored. The survey found that children under 2, on average, spend an hour a day in front of screens — engaging in activities like watching television, using computers, viewing DVDs, playing with mobile apps. Children ages 2 to 4 averaged two hours a day, and those 5 to 8, two hours and 20 minutes.

There are vast numbers of apps for babies and children, available free or at low cost: educational apps to teach letters, numbers, shapes, sign language; apps featuring television characters like Dora the Explorer; game apps (Angry Birds is a favorite with all ages); and art and music apps.

Many families, like the Deutsches, have smartphones with collections of family photos and videos of their children’s recent outings, haircuts or play dates.

“It used to be that a screen was a screen was a screen, and children just sat and watched,” said Ms. Rideout. “But now it can be lots of different things.”

The time younger children spent on mobile devices was still relatively short, the study found. On average, children under 8 spent 15 minutes a day on mobile devices, up from 5 minutes a day in 2011. Among those who used a mobile device during a typical day, the average was an hour and seven minutes, up from 43 minutes in 2011.

But as mobile devices have become more popular, the amount of time children spend with the screens of more traditional technology — television, DVDs, video games and computers — has declined by half an hour a day over the last two years.

Television still dominates, though, taking up about half of all children’s screen media time.

Almost all parents of children under 8 have televisions, the survey found, and most have cable as well. Three in 10 now have Internet connectivity with their televisions, so they can stream shows to their set from Netflix or other services. And increasingly, television is time-shifted — streamed, on demand, or recorded for later use — to suit the viewers’ convenience.

The study was conducted with a probability-based online panel by GfK, a research company. The data was collected May 20 to June 12 and has a sampling error of plus or minus four percentage points.