Fisher-Price promises its Laugh & Learn Apptivity mobile software will teach babies letters, numbers, shapes and colors.

And when a consumer group challenged those claims and complained to the federal government, the toy industry’s trade association decided it was going to fight back with science proving the benefits of the multibillion-dollar educational software market.

Except that it came to realize an awkward fact: There was no science proving the benefits of such apps.

The market for mobile technology for children has boomed, with some analysts estimating there are at least 48,000 developers churning out a wide range of apps for smartphones and tablets to help babies say words, sing nursery rhymes to them and teach children foreign languages.

But as adults shell out for the convenience and the promise of toddlers growing up tech-savvy, concern is rising over the long-term impact of parking children in front of screens. And despite advertising claims, there are no major studies that show whether the technology is helpful or harmful.

“The real point here is that we have laws in the country saying if you make claims about a product, you need to be able to substantiate them,” said Susan Linn, director of the Campaign for a Commercial-Free Childhood (CCFC). “The fact that they haven’t produced evidence is important.”

Linn’s nonprofit group brought the complaint against Fisher-Price and another app developer to the Federal Trade Commission last week. In 2007, based on a CCFC complaint, the agency forced the makers of the Baby Einstein videos to drop several educational and developmental claims. Last year, the FTC slapped a $185 million fine on the makers of the “Your Baby Can Read” set of videos, flashcards and books for false advertising.

In response to the most recent CCFC complaint, one software developer, Open Solutions, changed the way it had been marketing its Baby First Puzzle Farm and other apps aimed at children 2 and younger. On Monday, the firm removed advertising language that had claimed its games are a “new and innovative form of baby education,” according to the CCFC.

Open Solutions did not respond to requests for comment. Fisher-Price declined to be interviewed for this article. In an e-mailed statement, the company said that research goes into all of its toys.

“Grounded in 80 years of research and childhood development observations, we have appropriately extended these well researched play patterns into the digital space,” said Kathleen Alfano, the senior director of child research at ­Fisher-Price.

With the prospect of the federal government clamping down on a flourishing corner of the Internet economy, the Toy Industry Association is planning to mount a defense of the business.

But some industry officials concede that the evidence backing the claims of educational apps is thin.

“Traditionally our members have worked with physical products, so apps are really new,” said Stacy Leister, a spokesman for the Toy Industry Association.

Within hours of the CCFC’s complaint, the association’s staff decided to fight the organization’s challenge. But the group, which has focused more on safety issues, did not have its own research and did not know what studies have been done on the matter, Leister said. Several other analysts say there is no definitive study on the benefits of educational apps aimed at children.

The industry group this week hired a child psychologist based in the Netherlands to aggregate any studies on the topic and compile them into a report. Companies may have their own research, Leister said, but those studies have not been shared publicly.

On Apple’s iTunes store, ­Fisher-Price notes it sells a stuffed toy monkey to be used with its Laugh & Learn app. “Place your Apple device in the Monkey and press his paws to interact with the content on screen,” the instructions read. When a child taps on a letter, the monkey dances and sings the numbers aloud.

At the center of the FTC complaint is Fisher-Price’s claim that the app “teaches letters A-Z, numbers & counting 1-10, shapes, colors and action/re-action.”

“I’m always telling companies not to promise outcomes but rather to talk about what inputs they can provide,” said David Kleeman, a toy industry consultant and senior fellow at the Fred Rogers Center, which is focused on media and children.

“Once you say an app can make your kid smarter or read sooner, you are doing two bad things,” Kleeman said. “You are making promises you can’t keep, because you can’t control the environment of the child, and you are preying on parents’ guilt.”

Analysts are divided over the long-term impacts of the explosion in mobile technology. Some child development experts have issued warnings, recommending that parents reduce screen time, especially for toddlers. The American Academy of Pediatrics recommends against TV viewing for children under 2.

But others say mobile technology is different from TV because it is more interactive and, at times, requires thinking and problem solving.

The recommendation from the pediatrics association does not account for mobile devices, noted Dimitri Christakis, a pediatrician and professor at the University of Washington whose research was cited in the CCFC’s complaint against Baby Einstein, which is now controlled by Walt Disney Co.

Christakis said the jury is still out on mobile apps.

“Science has not kept up with the pace of technology, and the iPad may be more than just a screen like a TV or DVD screen,” he said. “It is interactive and has a lot of differences, but the truth is there is no evidence that it is beneficial. It’s just too early to say.”

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