With millions of parents happily handing their smartphones nd tablets over to their children to play with, there are dozens of startups focusing on making apps for kids. UK-headquartered Mindshapes is one of them, having released two iOS apps based on its own JellyToons characters and two on more traditional children's fare: fairy tale Jack And The Beanstalk and nursery rhyme Hickory Dickory Dock.

The latter is the company's newest app, teaching children the time with the help of the well-known song and a cute cartoon mouse. It's great fun, and wears its educational aspects lightly. That, says the company's director of mobile product development Jinhee Ahn Kim, is the point.

"The whole idea behind Mindshapes is to take educational principles and mix them with creative passion," she says. "It's the marriage of both. We'll choose an age group and subject, think about the educational principles and how they fit into the school curriculum, and then layer creative talent – game designers, artists and creatives – so we don't just end up with a flash-card app. How can we include gameplay in this so children almost don't notice they're learning?"

Kim quickly adds that she thinks there's a place for pure flash-card learning apps – there are certainly plenty on the app stores – but says Mindshapes wants to sit at the intersection between those and pure games.

Mindshapes' best app so far is Jack And The Beanstalk, which like other fairy-tale book-apps from companies like Nosy Crow and Ideal Binary, has imagination and production values that make it stand out from the hundreds of cheap, unappealing rivals. It has some canny modern elements, too, such as Jack's console gaming habit.

"We wanted to create an interactive e-book designed for young boys, who can be reluctant emerging readers," says Kim. "That's why we chose a classic story that appealed to boys, versus one of those princess or fairy type things. And we wanted to give it that modern twist."

Another noticeable thing about Jack And The Beanstalk is that the interaction – and there's a lot of it – is closely tied into the story, rather than simply flinging objects around the screen to show off a physics engine. According to Kim, that's important.

"We're putting all the interactivity into the reading of the story," she says. "The gameplay on each of the pages reinforces the content and the reading comprehension. It's immersive and draws the children in, with the character and gameplay keeping them in the story. With interaction, it's always about how does it drive the story?"

One trend that's coming through with the best book-apps for children is that they're not just aimed at the kids: there are often little nods to parents too, with references to popular culture or sly humour. This isn't a new idea of course – watch a Pixar movie for plenty of examples – but in apps it reinforces the idea that these are made to be used by children with their parents, not just on their own.

"A lot of us are parents, and have gone through that whole process where the joy of reading a book – especially for a young child – is to be sharing it with their parents," says Kim. "It's that break during the day when they're sat on your lap having a chuckle over something, or the parent is teaching something. It's that quiet, quality time we're hoping is there for the parent and child using our apps."

Kim says that doesn't mean Mindshapes apps can't be used by a child on their own – "there are times when you're driving or need to be cooking dinner…" – so there are read-to-me modes in the company's book-apps, and lots of focus-group testing before release to see how children get on with the apps.

Mindshapes has several more apps coming out this year, including book-apps, games and playful digital toys. Kim says the company is deliberately not tying itself to one particular kind of app, like books.

"Some app companies have a very specific look and gameplay, or just do interactive e-books, but we are spanning from very gamey, to very educational, to very interactive books," she says.

Thus far, Mindshapes has chosen to focus on its own intellectual property, the JellyToons, or traditional (out-of-copyright) children's content, using its character design skills in the latter case, as shown by the mouse in Hickory Dickory Dock.

Kim says that on a creative level, coming up with new characters is a fun way to work, albeit one that is also rigorously tested out in local nurseries to see which characters children are drawn to. Mindshapes is up against some big brands on the App Store, from Sesame Street to Dora the Explorer and Peppa Pig, so there's little room for error in its character design if it is to compete.

"It's about tapping into what resonates with different age groups, and providing engaging characters," she says. "If children learn something with, for example, Elmo, they retain it and learn it a lot better. If there are recognisable characters, the child has empathy for them, and that helps them remember and process better."

There's another challenge here: discovery on the App Store (for now, Mindshapes is iOS-only). Apps based on popular children's brands will be recognised by the parents who are buying, but new characters and even nursery rhymes and fairy tales face a hurdle of trust.

Kim says word of mouth continues to be the way most parents find out about good apps, although Mindshapes is also focusing part of its PR strategy on parenting blogs to help build buzz around its apps. "It's not easy to get discovered on the App Store, so you have to go in non-traditional ways," she says.

Meanwhile, Kim says she is excited about the potential for apps on smartphones and tablets, particularly as schools start to embrace the latter.

"Entire kindergartens are getting outfitted with iPads: the class computer is being replaced," she says.

"It's a really exciting area, I think: bringing learning to the kids on a personal level. And these days, teachers have to make learning appealing to the kids who have lots of screen-time at home, whether that's TV, video games or using mobile devices. There's a lot of innovation going on, and it's raising the bar. Kids are very sophisticated in what they're exposed to and what they feel is good. You certainly can't talk down to them with poor quality apps."