When Lisa Chinatti of Westford sits down to dinner with her daughters, she’s eager to hear about what happened at school that day. But her first-grader often prefers a different topic: which new apps her friends are playing with on their parents’ smartphones or iPads, and which ones she wants her own parents to buy for her.

“Mommy needs to learn about them first,’’ Chinatti responds.

But Mommy doesn’t always have time to immediately educate herself about every Hannah Montana or Star Wars app — she works, as a real estate agent, and there are dishes and laundry and snow pants to deal with — and that sometimes leaves Chinatti’s 7-year-old going to bed unhappy. “You promised we’d talk about it!’’ she wails as she’s being tucked in.

Not that they need one, but parents and children have a new battleground: the app.

With the number of children’s applications for mobile devices multiplying faster than Silly Bandz on a grade schooler’s wrist, parents are reporting bedtime app-related meltdowns, disagreements over what constitutes an appropriate game, and endless requests to borrow mom’s or dad’s phone or iPad.

And it’s only likely to get worse. There are already more than 300,000 apps, according to the International Data Corp., a Framingham-based research firm. The number of downloads is expected to hit 76.9 billion worldwide in 2014, up from 10.9 billion last year. The group predicts that worldwide revenues for mobile apps will exceed $35 billion in 2014.

Exact figures on apps for children are hard to come by, but specialists expect the children’s market to grow with the rest of the field — not only for Apple’s products but for Google’s Android devices as well.