Kids in kindergarten can actually use tablets, to learn other stuff. Any stuff. They can indulge their own interests, in a way that's nearly impossible in any other medium without assistance of someone older than them.
A tablet is the first cut of the way children use the Holodeck in Star Trek. You can't (usually) just ask for what you want, and get it (kids don't have a mental model of computers that works well enough to cope with how bad computers still are at conversation)—but you sure can point at what you want, and get it.
2. Feedback. E.g., there are some good fractions apps that help students understand what it means to "divide" a set of things into a set of groups of things. you can do that on pencil/paper or with other props, but there's no tight feedback loop.
It's unclear whether (2) is strictly a good thing; learning how to validate your own results is also an important skill...
This kind of self-directed, exploratory learning can be very effective.